9410 lines
174 KiB
Plaintext
9410 lines
174 KiB
Plaintext
#LyX 2.3 created this file. For more info see http://www.lyx.org/
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\end_header
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\begin_body
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\begin_layout Title
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Visual Search Coursework
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\end_layout
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\begin_layout Author
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Andy Pack (6420013)
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\end_layout
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\begin_layout LyX-Code
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\begin_inset Newpage pagebreak
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\end_inset
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\end_layout
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\begin_layout Section*
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Abstract
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\end_layout
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\begin_layout Standard
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The efficacy of various descriptors for visual search was investigated by
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applying them to the MSRCv2 dataset.
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Descriptors of varying complexity were considered from the less discriminative
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global colour histogram to spatial techniques that consider both colour
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and shape information.
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\end_layout
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\begin_layout Standard
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Following these results the use of principal component analysis was used
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to lower the dimensionality of descriptors and aid in extraction and processing.
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The associated Mahalanobis distance tended to provide an improvement to
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a standard Euclidean distance measure but the L1 generally outperformed
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the both.
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\end_layout
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\begin_layout Standard
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Spatial texture techniques, specifically a combination of colour and texture,
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were found to be the best performing with PCA providing extra performance
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when applied to the correct degree.
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Internal parameters were generally found not to increase performance linearly
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but achieve a peak before degrading.
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\end_layout
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\begin_layout LyX-Code
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\begin_inset CommandInset toc
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LatexCommand tableofcontents
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\end_inset
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\end_layout
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\begin_layout Quotation
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\begin_inset Newpage pagebreak
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\end_inset
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\end_layout
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\begin_layout Section
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Introduction
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\end_layout
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\begin_layout Standard
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An application of computer vision and visual media processing is that of
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visual search, the ability to quantitatively identify features of an image
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such that other images can be compared and ranked based on similarity.
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\end_layout
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\begin_layout Standard
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These measured features can be arranged as a data structure or descriptor
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and a visual search system can be created through the extraction and comparison
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of these descriptors.
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This is an example of content based image retrieval or CBIR.
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\end_layout
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\begin_layout Standard
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Visual search is used in consumer products to generate powerful results
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such as Google Lens and Google reverse image search.
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It also has applicability as smaller features of products such as 'related
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products' results.
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\end_layout
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\begin_layout Subsection
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Extraction
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\end_layout
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\begin_layout Standard
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When arranged as three 2D arrays of intensity for each colour channel, an
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image can be manipulated and measured to identify features using colour
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and shape information.
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The methods for doing so have varying applicability and efficacy to a visual
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search system, many also have variables which can be tuned to improve performan
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ce.
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\end_layout
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\begin_layout Subsection
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Comparison
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\end_layout
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\begin_layout Standard
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Typically a descriptor is a single column vector of numbers calculated about
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an image.
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This vector allows an image descriptor to plotted as a point in a feature
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space of the same dimensionality as the vector.
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Images that are close together in this feature space will indicate that
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they have similar descriptors.
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Methods for calculating the distance will determine how images are ranked.
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\end_layout
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\begin_layout Section
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Descriptors
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\end_layout
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\begin_layout Subsection
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Average Colour
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\end_layout
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\begin_layout Standard
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Average colour represents one of the most basic descriptors capable of being
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calculated about an image, an array of three numbers for the average red,
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green and blue intensity values found in the image.
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\end_layout
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\begin_layout Standard
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These three numbers represent nothing about the distribution of colour throughou
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t the image and nothing regarding edge and shape information.
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The lack of either hinders it's practicality for real world applications
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and as a result it is not used as a descriptor on it's own in this paper.
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Instead average colour will be used as a sub-descriptor during spatial
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colour investigations aided by its low dimensionality.
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\end_layout
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\begin_layout Subsection
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Global Colour Histogram
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\end_layout
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\begin_layout Standard
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A global colour histogram extracts colour distribution information from
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an image which can be used as a descriptor.
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\end_layout
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\begin_layout Standard
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Each pixel in an image can be plotted as a point in it's 3D colour space
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with the axes being red, green and blue intensity values.
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Visually inspecting this colour space will provide information about colour
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scattering found throughout the image.
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As different resolutions of images will produce datasets of different sizes
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in the feature space, a descriptor must be devised that transforms this
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data into a resolution agnostic form which can be compared.
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\end_layout
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\begin_layout Standard
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Each axes is partitioned into
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\begin_inset Formula $q$
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\end_inset
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divisions so that a histogram can be calculated for each colour channel.
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Each channel's intensity value,
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\begin_inset Formula $val$
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\end_inset
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, can be converted into an integer bin value using equation
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\begin_inset CommandInset ref
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LatexCommand ref
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reference "eq:integer-bin-calc"
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plural "false"
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caps "false"
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noprefix "false"
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\end_inset
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, where floor strips a float value into an integer by truncating all values
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past the decimal point.
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\end_layout
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\begin_layout Standard
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\begin_inset Formula
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\begin{equation}
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bin\:val=floor\left(q\cdotp\frac{val}{256}\right)\label{eq:integer-bin-calc}
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\end{equation}
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\end_inset
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\end_layout
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\begin_layout Standard
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This allows each pixel to now be represented as three 'binned' values, a
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full RGB colour space has been reduced to three colour histograms, one
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for each channel.
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In order to arrange this as a descriptor each point should be further reduced
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to a single number so that a global histogram can be formed of these values.
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This is done by taking decimal bin integers and concatenating them into
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a single number in base
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\begin_inset Formula $q$
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\end_inset
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.
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For an RGB colour space, each pixel can be augmented as shown in equation
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\begin_inset CommandInset ref
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LatexCommand ref
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reference "eq:base-conversion"
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plural "false"
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caps "false"
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noprefix "false"
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\end_inset
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.
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\begin_inset Formula
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\begin{equation}
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pixel\:bin=red\:bin\cdotp q^{2}+green\:bin\cdotp q^{1}+blue\:bin\cdotp q^{0}\label{eq:base-conversion}
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\end{equation}
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\end_inset
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\end_layout
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\begin_layout Standard
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Calculating a histogram of each pixel's bin value will function as a descriptor
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for the image once normalised.
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This normalisation will remove the effect of changing resolutions of image.
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\end_layout
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\begin_layout Standard
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Each descriptor plots an image as a point in a
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\begin_inset Formula $q^{3}$
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\end_inset
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-dimensional feature space where similarity can be computed using a suitable
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distance measure (L2 norm for example).
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\end_layout
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\begin_layout Subsubsection
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Efficacy
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\end_layout
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\begin_layout Standard
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The advantage of global colour histogram over the average RGB descriptor
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is that amounts of colours are now represented in the descriptor.
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Clusters of similar colours representing objects or backgrounds will be
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captured and can be compared.
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\end_layout
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\begin_layout Standard
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A global histogram, however, holds no spatial colour information, this is
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lost by plotting the pixels in their colour space.
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\end_layout
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\begin_layout Standard
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This suggests that performing a pixel shuffling operation on the image will
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not affect the extracted descriptor which has implications on the adequacy
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of the methodology for a visual search system.
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\end_layout
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\begin_layout Subsection
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Spatial Colour
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\end_layout
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\begin_layout Standard
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Spatial techniques involve descriptors that represent information from different
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areas of the image.
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This is done by dividing the image into a grid of cells and then calculating
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individual 'sub-descriptors' which are concatenated into a global image
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descriptor.
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\end_layout
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\begin_layout Standard
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These sub-descriptors can be calculated using any appropriate method however
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a main consideration should be the dimensionality of the final descriptor.
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This can be calculated using the following equation,
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\end_layout
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\begin_layout Standard
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\begin_inset Formula
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\[
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D_{total}=W\cdotp H\cdotp D_{sub-descriptor}
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\]
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\end_inset
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\end_layout
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\begin_layout Standard
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Where
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\begin_inset Formula $W$
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\end_inset
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and
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\begin_inset Formula $H$
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\end_inset
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refer to the number of columns and rows of the determined grid respectively.
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\end_layout
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\begin_layout Standard
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It would be feasible to calculate a colour histogram however this already
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generates a descriptor of
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\begin_inset Formula $q^{3}$
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\end_inset
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dimensionality, where
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\begin_inset Formula $q$
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\end_inset
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is the number of bins.
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\end_layout
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\begin_layout Standard
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For example using a
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\begin_inset Formula $q$
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\end_inset
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value of 4 and a spatial grid of 6 x 4 would produce a descriptor in 1536
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dimensions, while a
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\begin_inset Formula $q$
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\end_inset
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of 6 with a a grid of 10 x 6 is 12,960 dimensional.
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\end_layout
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\begin_layout Standard
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This is an extremely high value and will increase the time taken to calculate
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and compare descriptors.
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\end_layout
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\begin_layout Standard
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For a spatial colour descriptor the average RGB values for each cell can
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be used as these sub descriptors will be three dimensional reducing the
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total size.
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\end_layout
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\begin_layout Subsubsection
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Efficacy
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\end_layout
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\begin_layout Standard
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Computing a spatial colour descriptor can increase performance when highlighting
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the difference to a colour histogram.
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While a colour histogram will describe how many of each colour is present
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in an image, spatial colour techniques of the type described above will
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indicate the colours found in each area of the image.
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Considering an image of a cow in a field, the colour histogram will identify
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and count the brown pixels of the cow and the green pixels of the field,
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spatial colour techniques will identify an area of brown surrounded by
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an area of green.
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\end_layout
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\begin_layout Subsection
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Spatial Texture
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\end_layout
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\begin_layout Standard
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Spatial texture replaces the colour sub-descriptor from before with a descriptor
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that reflects the texture found in the image as described by the edges
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that can be detected.
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\end_layout
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\begin_layout Subsubsection
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Edge Detection
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\end_layout
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\begin_layout Standard
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Edges can be detected in an image by finding areas where neighbouring pixels
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have significantly different intensities.
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\end_layout
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\begin_layout Standard
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Mathematically this can be seen as taking the first derivative of the image
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by convolving it with a Sobel filter.
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The Sobel filters are a pair of 3x3 kernels, one for each axes (see figure
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\begin_inset CommandInset ref
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LatexCommand ref
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reference "fig:3x3-Sobel-filter"
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plural "false"
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caps "false"
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noprefix "false"
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\end_inset
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), which approximates the gradient of the grey-scale intensity of an image.
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\begin_inset Float figure
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wide false
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sideways false
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status open
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\begin_layout Plain Layout
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\align center
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\begin_inset Formula $S_{x}=\begin{bmatrix}-1 & 0 & +1\\
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-2 & 0 & +2\\
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-1 & 0 & +1
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\end{bmatrix}$
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\end_inset
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\begin_inset space \qquad{}
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\end_inset
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\begin_inset Formula $S_{y}=\begin{bmatrix}+1 & +2 & +1\\
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0 & 0 & 0\\
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-1 & -2 & -1
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\end{bmatrix}$
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\end_inset
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\end_layout
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\begin_layout Plain Layout
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\begin_inset Caption Standard
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\begin_layout Plain Layout
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3x3 Sobel filter kernels for
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\begin_inset Formula $x$
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\end_inset
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and
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\begin_inset Formula $y$
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\end_inset
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axes
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\begin_inset CommandInset label
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LatexCommand label
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name "fig:3x3-Sobel-filter"
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\end_inset
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Plain Layout
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Standard
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The results of convolving each filter with the image are two images that
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express the intensity of edges in that axes.
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\end_layout
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\begin_layout Standard
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From here a composite edge magnitude image of the two can be calculated
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as shown,
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\end_layout
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\begin_layout Standard
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\begin_inset Formula
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\[
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G_{composite}=\sqrt{G_{x}^{2}+G_{y}^{2}}
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\]
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\end_inset
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\end_layout
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\begin_layout Standard
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With the angles of the edges calculated as follows,
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\end_layout
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\begin_layout Standard
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\begin_inset Formula
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\[
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\Theta=\arctan\left(\frac{G_{y}}{G_{x}}\right)
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\]
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\end_inset
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\end_layout
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\begin_layout Subsubsection
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Application
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\end_layout
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\begin_layout Standard
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To create a descriptor, both the angle and magnitude information will be
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used, the descriptor itself will reflect information about the angles of
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the edges found.
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\end_layout
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\begin_layout Standard
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First the image grid cells will be thresholded using the magnitude values.
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Magnitude values can be seen to represent the confidence with which edges
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can be found and so here a decision is effectively being made as to what
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are and are not edges, this value can be tuned to best match the application.
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\end_layout
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\begin_layout Standard
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Once a thresholded edge magnitude image has been found, a normalised histogram
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will be calculated for the angles of these edges.
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This histogram for each grid cell will act as the descriptor when concatenated
|
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into a vector of dimensionality,
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\begin_inset Formula $D$
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\end_inset
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|
,
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\end_layout
|
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\begin_layout Standard
|
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\begin_inset Formula
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|
\[
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D_{total}=W\cdotp H\cdotp q
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\]
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|
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|
\end_inset
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|
|
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\end_layout
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|
\begin_layout Standard
|
|
Where
|
|
\begin_inset Formula $q$
|
|
\end_inset
|
|
|
|
refers to the number of edge histogram bins.
|
|
\end_layout
|
|
|
|
\begin_layout Section
|
|
Principal Component Analysis
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
When extracting a descriptor from an image an important design factor is
|
|
keeping the dimensionality as low as appropriate.
|
|
This is so as to reduce the effect of the 'curse of dimensionality', a
|
|
set of adverse phenomena which arise when analysing high dimensional data.
|
|
Each additional dimension exponentially increases the volume of the feature
|
|
space, a higher dimensional descriptor requires a longer time to extract,
|
|
process and store.
|
|
Many of these dimensions will have little to no variation and so their
|
|
addition adds complexity without adding significant extra value.
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
Principal component analysis is the process of identifying the orthogonal
|
|
directions and magnitudes of variation in a dataset.
|
|
For a multidimensional descriptor this is called the covariance.
|
|
The covariance can be decomposed, or 'factorised', into matrices of eigenvector
|
|
s and values defining the directions and magnitudes of the model's variations.
|
|
This allows low variation dimensions to be remove by identifying vectors
|
|
with low eigenvalues.
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
This reduced model can be used to project the dataset into the same lower
|
|
dimensionality, reducing complexity but retaining the majority of variation
|
|
in the remaining dimensions.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Float figure
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\align center
|
|
\begin_inset Graphics
|
|
filename pca-example.png
|
|
lyxscale 30
|
|
width 70col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
Visual depiction of principal 2D component analysis resulting in a new reference
|
|
frame
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:pca-visual-depiction"
|
|
|
|
\end_inset
|
|
|
|
|
|
\begin_inset CommandInset citation
|
|
LatexCommand cite
|
|
key "setosa_pca"
|
|
literal "false"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The process can be seen in figure
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:pca-visual-depiction"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
.
|
|
The left hand side shows the data presented in the root reference frame.
|
|
The right hand side shows the same data plotted in the reference frame
|
|
defined by it's own variation, in essence 'recentering' the axes around
|
|
the data.
|
|
\end_layout
|
|
|
|
\begin_layout Section
|
|
Distance Measures
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
Once image descriptors are plotted in a feature space, a visual search system
|
|
makes comparisons by measuring the distance between them.
|
|
This is calculated by finding the vector between the two points in space.
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
In mathematics the length of a vector is evaluated using a function referred
|
|
to as a norm.
|
|
Different types of norm can affect the performance of the system and therefore
|
|
different norms should be used and compared.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Float figure
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\align center
|
|
\begin_inset Graphics
|
|
filename l2norm.jpg
|
|
lyxscale 30
|
|
width 30col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
A single 2D Cartesian co-ordinate with it's component lengths in blue and
|
|
its Euclidean magnitude in red
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:norm"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Subsection
|
|
L1 Norm
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The L1 norm, or Manhattan distance, is the sum of the absolute values of
|
|
the vector.
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
For a 2D vector,
|
|
\begin_inset Formula $x=\left(i,j\right)$
|
|
\end_inset
|
|
|
|
, the L1 norm can be calculated by,
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Formula
|
|
\[
|
|
\left\Vert x\right\Vert _{1}=\left|i\right|+\left|j\right|
|
|
\]
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The L1 norm of the point defined in figure
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:norm"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
can be found by summing the lengths of the blue lines.
|
|
\end_layout
|
|
|
|
\begin_layout Subsection
|
|
L2 Norm
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The L2 norm, or Euclidean distance, is the shortest distance between two
|
|
points in space, it is also referred to as the magnitude of a vector.
|
|
In a three dimensional Euclidean space the magnitude of a vector,
|
|
\begin_inset Formula $x=\left(i,j,k\right)$
|
|
\end_inset
|
|
|
|
, is given by,
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Formula
|
|
\[
|
|
\left\Vert x\right\Vert _{2}=\sqrt{i^{2}+j^{2}+k^{2}}
|
|
\]
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
It's intuitive
|
|
\begin_inset Quotes eld
|
|
\end_inset
|
|
|
|
as the crow flies
|
|
\begin_inset Quotes erd
|
|
\end_inset
|
|
|
|
distance measurement makes it the most commonly used norm in Euclidean
|
|
space.
|
|
In figure
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:norm"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
the length of the red line defines this point's Euclidean distance.
|
|
\end_layout
|
|
|
|
\begin_layout Subsection
|
|
Mahalanobis Distance
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The Mahalanobis distance extends the L2 norm to better account for the nature
|
|
of a data model defined through principal component analysis.
|
|
Instead of calculating the distance between two points in a feature space,
|
|
a model represents a region in space and here a more useful distance would
|
|
that between a point and the closest part of that region in space.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The Mahalanobis distance allows this to be calculated by measuring the standard
|
|
deviations away from the model's mean a point is, in doing so normalising
|
|
for the model's shape in space.
|
|
When moving from the root frame of reference to the frame defined by a
|
|
model defined through PCA, the Mahalanobis distance becomes Euclidean distance.
|
|
In essence we are finding the distance a point is from a model from the
|
|
model's frame of reference.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The Mahalanobis distance,
|
|
\begin_inset Formula $d$
|
|
\end_inset
|
|
|
|
, can be calculated with
|
|
\begin_inset Formula
|
|
\[
|
|
d^{2}=\left(x-\mu\right)^{T}C^{-1}\left(x-\mu\right)
|
|
\]
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
When the covariance,
|
|
\begin_inset Formula $C$
|
|
\end_inset
|
|
|
|
, undergoes eigendecomposition the eigenvectors,
|
|
\begin_inset Formula $U$
|
|
\end_inset
|
|
|
|
, and eigenvalues,
|
|
\begin_inset Formula $V$
|
|
\end_inset
|
|
|
|
, can be used to calculate the Mahalanobis distance with
|
|
\begin_inset Formula
|
|
\[
|
|
d^{2}=\left|V^{-1}U^{-1}\left(x-\mu\right)\right|
|
|
\]
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Section
|
|
Test Methods
|
|
\end_layout
|
|
|
|
\begin_layout Subsection
|
|
Dataset
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "subsec:Dataset"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
For the purposes of these experiments the Microsoft MSRC
|
|
\begin_inset CommandInset citation
|
|
LatexCommand cite
|
|
key "microsoft_msrc"
|
|
literal "false"
|
|
|
|
\end_inset
|
|
|
|
version 2 dataset was used.
|
|
The set is made up of 591 images across 20 categories, the classifications
|
|
for which can be seen in appendix
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "sec:MSRC-Dataset-Classifications"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
Worth noting about the dataset is that there are some similarities and overlap
|
|
between categories which has implications on the results which can be calculate
|
|
d when using it.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
For example category 1 is a collection of images of cows, sheep and horses
|
|
on grass however cows and sheep each have their own distinct categories.
|
|
Category 18 also has many similarities to category 20 with both being mainly
|
|
shots of bodies of water and boats in water of varying sizes.
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
During the evaluation of implemented visual search techniques the classification
|
|
of each image is done by referencing the group index they are named with.
|
|
As such, occurrences of false negatives may increase as images that do
|
|
in fact look similar as they are both, say, images of cows will be marked
|
|
as not the right category and measure negatively for the performance of
|
|
the method.
|
|
\end_layout
|
|
|
|
\begin_layout Subsection
|
|
Precision and Recall
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
When comparing the effectiveness of different descriptors the main measurements
|
|
are those of precision and recall.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
Once the visual search system has ranked a dataset on similarity to a query
|
|
image, the precision and recall can be calculated up to
|
|
\begin_inset Formula $n$
|
|
\end_inset
|
|
|
|
images through the ranked list.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
At each
|
|
\begin_inset Formula $n$
|
|
\end_inset
|
|
|
|
the precision is defined as the number of images up to
|
|
\begin_inset Formula $n$
|
|
\end_inset
|
|
|
|
that are classed as relevant.
|
|
Higher precision values indicate better system performance and an ideal
|
|
system response as
|
|
\begin_inset Formula $n$
|
|
\end_inset
|
|
|
|
increases would be a precision of 1 until all relevant documents have been
|
|
returned at which point it would gradually reduce to a minimum value of
|
|
the fraction of relevant documents in the dataset.
|
|
This would indicate that the system is able to select a relevant image
|
|
every time one is available.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The recall is defined at
|
|
\begin_inset Formula $n$
|
|
\end_inset
|
|
|
|
as how many of the available relevant results have been returned up to
|
|
|
|
\begin_inset Formula $n$
|
|
\end_inset
|
|
|
|
.
|
|
Higher recall values at
|
|
\begin_inset Formula $n$
|
|
\end_inset
|
|
|
|
indicate that the system can recall relevant documents faster with less
|
|
false positives and begins at 0 before increasing to a maximum of 1 as
|
|
|
|
\begin_inset Formula $n$
|
|
\end_inset
|
|
|
|
increases when all have been returned.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
While both measurements appear to reflect similar concepts there is a difference.
|
|
Precision is a measure of how accurately a system can decide whether a
|
|
document is relevant while recall can be thought of as a measure of a systems
|
|
repeated accuracy and measures how long it takes to retrieve all relevant
|
|
documents.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
A system with high recall but low precision at
|
|
\begin_inset Formula $n$
|
|
\end_inset
|
|
|
|
will indicate that the system is effectively able to retrieve all relevant
|
|
documents eventually however there will be false positives within the results.
|
|
Results of this quality would be advantageous when it is important to obtain
|
|
all relevant results however not when the relevance of each and every one
|
|
is valued.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
A system with high precision but low recall at
|
|
\begin_inset Formula $n$
|
|
\end_inset
|
|
|
|
would indicate that the system is very confident in its selection of relevant
|
|
documents but may indicate an increase in false negatives where the system
|
|
cannot correctly recognise a target image.
|
|
\end_layout
|
|
|
|
\begin_layout Subsection
|
|
Precision Recall Curve
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
A way to visualise the response of a visual search system is to calculate
|
|
both precision and recall for all values of
|
|
\begin_inset Formula $n$
|
|
\end_inset
|
|
|
|
and plot each pair in a precision-recall or PR curve.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
When plotted in this fashion with recall along the
|
|
\begin_inset Formula $x$
|
|
\end_inset
|
|
|
|
axis and and precision along
|
|
\begin_inset Formula $y$
|
|
\end_inset
|
|
|
|
the curve can be thought to plot the system performance over normalised
|
|
time to retrieve the query's category set.
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
Perfect system performance is given by,
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Formula
|
|
\[
|
|
y=\begin{cases}
|
|
1 & 0<x\leq1\\
|
|
0 & x>1
|
|
\end{cases}
|
|
\]
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Subsection
|
|
Methods
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
Results were calculated for the global colour histogram, spatial colour,
|
|
spatial texture and a combined descriptor of spatial colour and texture.
|
|
Principal component analysis was also conducted on the spatial colour and
|
|
texture descriptor in order to identify the optimum levels of dimensionality
|
|
reduction.
|
|
Each descriptor has parameters that can be varied to alter it's performance.
|
|
For each varying parameter a category response test was conducted.
|
|
\end_layout
|
|
|
|
\begin_layout Subsubsection
|
|
Category Response
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The category response test performs a number of queries on different images
|
|
in order to calculate average performance values.
|
|
These values are used to describe the performance of the applied descriptor,
|
|
in order to make comparisons between descriptors valid the same query images
|
|
are used for all investigations.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The category response aims to control for a descriptor's varying performance
|
|
at each of the dataset's classifications by selecting 1 query image from
|
|
each that was visually deemed to well represent the rest.
|
|
The query set filenames used in these tests can be seen in appendix
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "sec:Query-Set"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
.
|
|
Each query iteration has precision and recall calculated for all
|
|
\begin_inset Formula $n$
|
|
\end_inset
|
|
|
|
to allow the mean average precision to be calculated.
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
An average precision-recall curve was calculated by plotting the average
|
|
precision and recall values for the 20 category iteration results.
|
|
An example of the 20 precision-recall curves reduced to an average line
|
|
is seen in appendix
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "subsec:Global-Colour-Histogram-pr-n-4"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
Completing an iteration for each category also allows a confusion matrix
|
|
to be constructed.
|
|
For each iteration the top 25 results were evaluated, this number was chosen
|
|
as it is similar to the average category size.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The completed confusion matrix allows the main category confusions to be
|
|
identified and discussions to be made, each column represents an iteration
|
|
of the category response test and the matrix has been normalised by column.
|
|
\end_layout
|
|
|
|
\begin_layout Subsubsection
|
|
Global Colour Histogram
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
For the global colour histogram the number of bins was varied to view the
|
|
effect of this on the MAP.
|
|
Values between 1 and 20 were investigated.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The effect was measured using L1, Euclidean and Mahalanobis distance measures
|
|
although not all bin values could be evaluated for Mahalanobis distance
|
|
due to prohibitively high processing time.
|
|
\end_layout
|
|
|
|
\begin_layout Subsubsection
|
|
Spatial Colour
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
For spatial colour, category response tests were completed as the grid dimension
|
|
s were varied from 1x1 to 20x20.
|
|
The resulting matrix of results were plotted as a surface to see how variations
|
|
in grid size affected mean average precision.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The average precision recall curve was plotted for the best performing parameter
|
|
s found in these investigations.
|
|
These experiments were doing using L2 (Euclidean) Distance.
|
|
\end_layout
|
|
|
|
\begin_layout Subsubsection
|
|
Spatial Texture
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
For spatial texture the grid dimensions were brought forward from a high
|
|
achieving spatial colour investigation in order to evaluate the effect
|
|
of varying both bin count and threshold value.
|
|
While investigating each, the other was kept the same.
|
|
Following calculations for both, the best value for each was used to test
|
|
the effect of varying grid dimensions.
|
|
Grid dimensions were not varied as widely as for spatial colour due to
|
|
the prohibitively long processing time.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The initial threshold value to be held stable during bin count investigations
|
|
was picked by visualising different threshold values, examples can be seen
|
|
in figures
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:Angle-magnitude-0.01"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
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\end_inset
|
|
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|
through
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:Angle-magnitude-0.2"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
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\end_inset
|
|
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|
.
|
|
A value of 0.08 was selected, the visualisation can be seen in figure
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:Angle-magnitude-0.08"
|
|
plural "false"
|
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caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
.
|
|
These experiments were doing using Euclidean Distance.
|
|
\begin_inset Float figure
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\align center
|
|
\begin_inset Graphics
|
|
filename ../data/edgeThresholds/10_14_s.png
|
|
lyxscale 30
|
|
width 20col%
|
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|
|
\end_inset
|
|
|
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|
\begin_inset space \quad{}
|
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\end_inset
|
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|
|
|
|
\begin_inset Graphics
|
|
filename ../data/edgeThresholds/10_14_flower_edge.png
|
|
lyxscale 30
|
|
width 20col%
|
|
|
|
\end_inset
|
|
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\begin_inset Caption Standard
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|
|
\begin_layout Plain Layout
|
|
Image 10_14_s from the flower category followed by visualisation of detected
|
|
edges
|
|
\end_layout
|
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|
\end_inset
|
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\end_layout
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\end_inset
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\begin_inset Float figure
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wide false
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sideways false
|
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status open
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|
\begin_layout Plain Layout
|
|
\align center
|
|
\begin_inset Graphics
|
|
filename ../data/edgeThresholds/5_15_s.png
|
|
lyxscale 30
|
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width 20col%
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\end_inset
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\begin_inset space \quad{}
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\end_inset
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\begin_inset Graphics
|
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filename ../data/edgeThresholds/5_15_cow_edge.png
|
|
lyxscale 30
|
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width 20col%
|
|
|
|
\end_inset
|
|
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|
\begin_inset Caption Standard
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|
|
\begin_layout Plain Layout
|
|
Image 5_15_s from the cow category followed by visualisation of detected
|
|
edges
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:cow-pic"
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|
|
|
\end_inset
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\end_layout
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\end_inset
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\end_layout
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\end_inset
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\begin_inset Float figure
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wide false
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sideways false
|
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status open
|
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|
|
\begin_layout Plain Layout
|
|
\align center
|
|
\begin_inset Graphics
|
|
filename ../data/edgeThresholds/flower-t-0.01.png
|
|
lyxscale 30
|
|
width 20col%
|
|
|
|
\end_inset
|
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|
|
\begin_inset space \quad{}
|
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\end_inset
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|
|
\begin_inset Graphics
|
|
filename ../data/edgeThresholds/cow-t-0.01.png
|
|
lyxscale 30
|
|
width 20col%
|
|
|
|
\end_inset
|
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\end_layout
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\begin_layout Plain Layout
|
|
\begin_inset Caption Standard
|
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\begin_layout Plain Layout
|
|
Angle magnitude images with threshold 0.01
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:Angle-magnitude-0.01"
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\end_inset
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\end_layout
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\end_inset
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\begin_inset Float figure
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wide false
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sideways false
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status open
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\begin_layout Plain Layout
|
|
\align center
|
|
\begin_inset Graphics
|
|
filename ../data/edgeThresholds/flower-t-0.08.png
|
|
lyxscale 30
|
|
width 20col%
|
|
|
|
\end_inset
|
|
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|
|
\begin_inset space \quad{}
|
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\end_inset
|
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|
|
\begin_inset Graphics
|
|
filename ../data/edgeThresholds/cow-t-0.08.png
|
|
lyxscale 30
|
|
width 20col%
|
|
|
|
\end_inset
|
|
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|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
Angle magnitude images with threshold 0.08
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:Angle-magnitude-0.08"
|
|
|
|
\end_inset
|
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\end_layout
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\end_inset
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\end_layout
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\end_inset
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\begin_inset Float figure
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wide false
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sideways false
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status open
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|
\begin_layout Plain Layout
|
|
\align center
|
|
\begin_inset Graphics
|
|
filename ../data/edgeThresholds/flower-t-0.2.png
|
|
lyxscale 30
|
|
width 20col%
|
|
|
|
\end_inset
|
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|
\begin_inset space \quad{}
|
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\end_inset
|
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|
\begin_inset Graphics
|
|
filename ../data/edgeThresholds/cow-t-0.2.png
|
|
lyxscale 30
|
|
width 20col%
|
|
|
|
\end_inset
|
|
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|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
Angle magnitude images with threshold 0.2
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:Angle-magnitude-0.2"
|
|
|
|
\end_inset
|
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\end_layout
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\end_inset
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\end_layout
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|
\end_inset
|
|
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|
|
\end_layout
|
|
|
|
\begin_layout Subsubsection
|
|
Spatial Colour and Texture
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The same spatial texture and grid dimension parameters were used when the
|
|
colour and texture descriptors were combined in order to allow comparison
|
|
between the results.
|
|
The grid dimensions were also varied between the same ranges.
|
|
These experiments were doing using Euclidean Distance.
|
|
\end_layout
|
|
|
|
\begin_layout Subsubsection
|
|
Principal Component Analysis
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The covariance of all descriptors is calculated in order to define a model
|
|
for the dataset.
|
|
In doing so dimensions with low variation can be identified and dropped
|
|
by sorting the eigenvectors by magnitude of eigenvalue.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The Mahalanobis distance was found between each pair of images.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The proportion of eigenvalues that are dropped is referred to as the percentage
|
|
energy reduction and this energy reduction can be varied.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
To visualise the effect of varying dimensionality reduction, descriptors
|
|
with previously used parameter sets were tested with varying levels of
|
|
energy reduction to view it's effect on achievable mean average precision.
|
|
\end_layout
|
|
|
|
\begin_layout Subsubsection
|
|
Descriptor Distance Measure
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
With well performing spatial parameters ascertained, mean average precision
|
|
results were taken for L1, L2 (Euclidean) and Mahalanobis distance measures.
|
|
These results were used to compare the performance of each distance measure
|
|
with each descriptor and also as final results to summarise the relative
|
|
performance of each descriptor.
|
|
\end_layout
|
|
|
|
\begin_layout Section
|
|
Results
|
|
\end_layout
|
|
|
|
\begin_layout Subsection
|
|
Global Colour Histogram
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The effect of varying numbers of histogram bins can be seen in figure
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:colour-histogram-bin-vary"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
.
|
|
L1 performed slightly better than L2 at lower bins but continues to increase
|
|
in performance as Euclidean and Mahalanobis distances peak and begin to
|
|
decline.
|
|
Euclidean and Mahalanobis distance both peak at 5 bins (0.145 and 0.152 respectiv
|
|
ely) while the L1 norm peaks at 15 with a value of 0.167.
|
|
3 bins has a noticeably lower MAP result for all distance measures, 4 bins
|
|
also seems to be slightly below the trend of increase.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Float figure
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\align center
|
|
\begin_inset Graphics
|
|
filename ../data/colourHistogram/map-line.png
|
|
lyxscale 30
|
|
width 80col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
Global colour histogram mean average precision values for varying numbers
|
|
of bins
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:colour-histogram-bin-vary"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
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|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The average PR curve for the best L2 mean average precision, a bin count
|
|
of 5, can be seen in figure
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:colour-histogram-avg-pr-n=5"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
.
|
|
\begin_inset Float figure
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\align center
|
|
\begin_inset Graphics
|
|
filename ../data/colourHistogram/pr-curves-n-5-avg.png
|
|
lyxscale 30
|
|
width 40col%
|
|
|
|
\end_inset
|
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|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
Global colour histogram mean precision recall curve for
|
|
\begin_inset Formula $n=5$
|
|
\end_inset
|
|
|
|
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:colour-histogram-avg-pr-n=5"
|
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|
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\end_inset
|
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\end_layout
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\end_inset
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\end_layout
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\begin_layout Plain Layout
|
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|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The confusion matrix for 5 bins can be seen in figure
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:colour-histogram-confusion"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
.
|
|
The most confused category combinations were confusing cars for bikes and
|
|
bikes for faces.
|
|
The best classified category was book shelves.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Float figure
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\align center
|
|
\begin_inset Graphics
|
|
filename /home/andy/dev/matlab/cv-coursework/data/colourHistogram/cm-5.jpg
|
|
lyxscale 30
|
|
width 100col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
Global colour histogram confusion matrix for 5 bins
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:colour-histogram-confusion"
|
|
|
|
\end_inset
|
|
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|
|
|
\end_layout
|
|
|
|
\end_inset
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|
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\end_layout
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|
|
|
\begin_layout Plain Layout
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Subsection
|
|
Spatial Colour
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The surface plotted by each dimension combination's MAP can be seen in figure
|
|
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:spatial-colour-map-surfaces"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
, the results up to 15x10 can be seen in appendix
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "sec:spatial-colour-grid-maps"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
.
|
|
The MAP starts at a low value with either dimension being 1, the lowest
|
|
value being for a 1x2 grid (0.1079).
|
|
As rows increase from 1 to 2 a performance increase can be seen.
|
|
This then decreases for 3 rows before increasing to a maxima at 4.
|
|
The increase from 1 to 2 columns sees a decrease in MAP before increasing
|
|
up to 4 columns.
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
Past 4 in either dimension the performance tends to decrease.
|
|
The highest achieved MAP was for 14 rows and 4 columns with a value of
|
|
0.156.
|
|
The average PR curve for this result can be seen in figure
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:spatial-colour-avg-pr"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
.
|
|
\begin_inset Float figure
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\align center
|
|
\begin_inset Graphics
|
|
filename ../data/spatialColour/mapSurface2.png
|
|
lyxscale 20
|
|
width 50col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\begin_inset Graphics
|
|
filename ../data/spatialColour/mapSurfaceWithMax.png
|
|
lyxscale 20
|
|
width 50col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
Mean average precision values for varying dimensions of spatial colour grid,
|
|
maximum value labelled
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:spatial-colour-map-surfaces"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\begin_inset Float figure
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\align center
|
|
\begin_inset Graphics
|
|
filename ../data/spatialColour/avg-pr-4-14.png
|
|
lyxscale 30
|
|
width 40col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
Mean precision recall curve for spatial colour grid 14 rows, 4 columns
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:spatial-colour-avg-pr"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
parameter
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Subsection
|
|
Spatial Texture
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
A grid of 4x4 was used initially due to it's favourable results for spatial
|
|
colour.
|
|
The MAP values achieved for different numbers of histogram bins can be
|
|
seen in figure
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:Spatial-texture-bin-vary"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
.
|
|
The MAP generally increases up to 7 bins with a value of 0.210, before decreasin
|
|
g.
|
|
Odd numbers of bins tended to achieve higher MAPs than even bins up to
|
|
this maxima before linearly decreasing.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Float figure
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\align center
|
|
\begin_inset Graphics
|
|
filename ../data/spatialTexture/map-bin-vary.png
|
|
lyxscale 30
|
|
width 70col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
Spatial texture mean average precision values for varying numbers of bins,
|
|
grid size 4x4, threshold 0.08
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:Spatial-texture-bin-vary"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The MAP values for varying edge magnitude thresholds can be seen in figure
|
|
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:Spatial-texture-thresh-vary"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
.
|
|
The MAP increases as threshold increases until a threshold of 0.09 (0.214).
|
|
From here it decreases.
|
|
\begin_inset Float figure
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\align center
|
|
\begin_inset Graphics
|
|
filename ../data/spatialTexture/map-thresh-vary.png
|
|
lyxscale 30
|
|
width 70col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
Spatial texture mean average precision values for varying threshold, grid
|
|
size 4x4, 7 bins
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:Spatial-texture-thresh-vary"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
A threshold of 0.09 and bin count of 7 was used to measure the effect of
|
|
grid dimensions on mean average precision, the results for which can be
|
|
seen in figure
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:spatial-texture-map-surface"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
.
|
|
The highest MAP was achieved for 4 rows and 3 columns with a value of 0.231.
|
|
The lowest recorded value was 0.157 for 1 row and 6 columns.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Float figure
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\align center
|
|
\begin_inset Graphics
|
|
filename ../data/spatialTexture/mapSurface.png
|
|
lyxscale 20
|
|
width 50col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\begin_inset Graphics
|
|
filename ../data/spatialTexture/mapSurfaceWithMax.png
|
|
lyxscale 20
|
|
width 50col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
Mean average precision values for varying dimensions of spatial texture
|
|
grid, 7 bins, threshold 0.09
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:spatial-texture-map-surface"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The average PR curve using the best performing of each parameter and a grid
|
|
of 4x3 can be seen in figure
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:spatial-texture-avg-pr"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
.
|
|
|
|
\begin_inset Float figure
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\align center
|
|
\begin_inset Graphics
|
|
filename ../data/spatialTexture/avg-pr-4-3-7-0.09.png
|
|
lyxscale 30
|
|
width 40col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
Mean precision recall curve for spatial texture 4x3 grid, 7 bins, threshold
|
|
0.09
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:spatial-texture-avg-pr"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The confusion matrix for spatial texture can be seen in figure
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:Spatial-texture-confusion-matrix"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
.
|
|
The largest confusion was the system selecting planes and classifying them
|
|
as water features, 60% of the top 25 were misclassified in this fashion.
|
|
The best classified categories were planes and trees.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\align center
|
|
\begin_inset Float figure
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\align center
|
|
\begin_inset Graphics
|
|
filename ../data/spatialTexture/cm-4x3-7-0.09.jpg
|
|
lyxscale 30
|
|
width 100col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
Spatial texture confusion matrix 4x3 grid, 7 bins, threshold 0.09
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:Spatial-texture-confusion-matrix"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Subsection
|
|
Spatial Colour and Texture
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The same parameters from spatial texture (7 bins, edge magnitude threshold
|
|
0.09) were used to investigate how grid dimensions affect mean average precision
|
|
, the results for which can be seen in figure
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:spatial-colour-texture-map-surface"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Float figure
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\align center
|
|
\begin_inset Graphics
|
|
filename ../data/spatialColourTexture/mapSurface.png
|
|
lyxscale 20
|
|
width 50col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\begin_inset Graphics
|
|
filename ../data/spatialColourTexture/mapSurfaceWithMax.png
|
|
lyxscale 20
|
|
width 50col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
Mean average precision values for varying dimensions of spatial colour and
|
|
texture grid, 7 bins, threshold 0.09
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:spatial-colour-texture-map-surface"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
As rows increase the MAP increases up to 4 rows before tending to decrease
|
|
past here.
|
|
As columns increase from 1 to 2 the mean average precision decreases before
|
|
increasing for 3 columns and then decreasing.
|
|
The highest MAP was found at 4 rows and 3 columns with a value of 0.217.
|
|
The lowest value was found at 2 columns and 1 row with a value of 0.1489.
|
|
The average PR curve for the best performing grid dimensions can be seen
|
|
in figure
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:spatial-colour-texture-avg-pr"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Float figure
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\align center
|
|
\begin_inset Graphics
|
|
filename ../data/spatialColourTexture/avg-pr-4-3-7-0.09.png
|
|
lyxscale 30
|
|
width 40col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
Mean precision recall curve for spatial colour and texture, 4 rows, 3 columns,
|
|
7 bins, threshold 0.09
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:spatial-colour-texture-avg-pr"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The confusion matrix for combined spatial colour and texture can be seen
|
|
in figure
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:spatial-colour-texture-confusion-matrix"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
.
|
|
Here the largest errors are classifying sheep as birds, farm animals as
|
|
cows and signs as book shelves.
|
|
The most correctly classified images were trees and sheep.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
Comparing with the spatial texture matrix, the high proportion of plane's
|
|
being classed as water features decreased from 60% to 12%.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Float figure
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\align center
|
|
\begin_inset Graphics
|
|
filename ../data/spatialColourTexture/cm-4x3-7-0.09.jpg
|
|
lyxscale 30
|
|
width 100col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
Confusion matrix for spatial colour and texture, 4 rows, 3 columns, 7 bins,
|
|
threshold 0.09
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:spatial-colour-texture-confusion-matrix"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Subsection
|
|
Principal Component Analysis
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The spatial colour and texture parameters from before (4x3 grid, 7 bins,
|
|
0.09 threshold) were used to ascertain how varying model energy reduction
|
|
affects mean average precision, the results for which can be seen in figure
|
|
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:pca-colour-texture-map"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
.
|
|
As energy is reduced the MAP increases to a maximum between 0.5% and 4%.
|
|
Beyond this reduction the mean average precision decreases to a constant
|
|
value.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The red line indicates the mean average precision achieved with the same
|
|
descriptor parameters without PCA.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Float figure
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\align center
|
|
\begin_inset Graphics
|
|
filename ../data/PCA/colour-texture-4x3-7-0.09-deflation-100.png
|
|
lyxscale 30
|
|
width 60col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
\align center
|
|
\begin_inset Graphics
|
|
filename ../data/PCA/colour-texture-4x3-7-0.09-deflation-20.png
|
|
lyxscale 30
|
|
width 60col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
\align center
|
|
Red line indicates MAP without PCA
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
MAP for spatial colour and texture (4x3, 7 bins, thres.
|
|
0.09) as percentage energy is reduced
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:pca-colour-texture-map"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The summary data table of these results can be seen in table
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "tab:pca-colour-texture-map"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
, varying resolution's of the independent variable are in order to highlight
|
|
the important values of energy reduction, namely the points at which it
|
|
exceeds the non-PCA value and the highest achieved value.
|
|
A higher resolution table of values can be seen in appendix
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "sec:pca-map"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
.
|
|
Red values again indicate improvements over queries without PCA.
|
|
The highest achieved MAP was 0.251 at 1.4% reduction.
|
|
This represents a 16% increase over the 0.217 value for queries without
|
|
PCA.
|
|
\begin_inset Float table
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\align center
|
|
\begin_inset Tabular
|
|
<lyxtabular version="3" rows="12" columns="2">
|
|
<features tabularvalignment="middle">
|
|
<column alignment="center" valignment="top" width="0pt">
|
|
<column alignment="center" valignment="top" width="0pt">
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Percentage Energy Reduction
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Mean Average Precision
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.1208
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.5
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2067
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
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\color red
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\end_inset
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\begin_inset Text
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\color red
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\color red
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\color red
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3
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4
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\color red
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\color red
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4.2
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\begin_layout Plain Layout
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5
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\end_layout
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<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
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\begin_layout Plain Layout
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0.2023
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</cell>
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</row>
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</lyxtabular>
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\end_inset
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\end_layout
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\begin_layout Plain Layout
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\align center
|
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Red values indicate improvements over query without PCA (0.217)
|
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\end_layout
|
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\begin_layout Plain Layout
|
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\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
Mean average precision values for spatial colour and texture (4x3, 7 bins,
|
|
thres.
|
|
0.09) as dimensionality is reduced through PCA
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "tab:pca-colour-texture-map"
|
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\end_inset
|
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\end_layout
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\end_inset
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\end_layout
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\end_inset
|
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\end_layout
|
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\begin_layout Standard
|
|
The confusion matrix for spatial colour and texture with PCA can be seen
|
|
in figure
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:pca-colour-texture-confusion-matrix"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
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.
|
|
The largest confusions were classifying signs as bookshelves, cat's as
|
|
the coast and sheep as birds.
|
|
The most correctly classified categories were planes, book shelves and
|
|
trees.
|
|
\end_layout
|
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|
|
\begin_layout Standard
|
|
Looking to the confusion matrix without PCA, the already high confusion
|
|
of sign's as bookshelves has increased from 32% to 40% despite the correct
|
|
classifications also increasing from 44% to 48%.
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The high confusion of sheep as bird's has decreased from 44% to 32%.
|
|
However the percentage of farm animals being classed as bird's has increased
|
|
from 12% to 28%.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Float figure
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\align center
|
|
\begin_inset Graphics
|
|
filename /home/andy/dev/matlab/cv-coursework/data/PCA/colour-texture-cm-4x3-7-0.09-1.4.jpg
|
|
lyxscale 30
|
|
width 100col%
|
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|
|
\end_inset
|
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|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
Spatial colour and texture confusion matrix with PCA, 4 rows, 3 columns,
|
|
7 bins, threshold 0.09
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:pca-colour-texture-confusion-matrix"
|
|
|
|
\end_inset
|
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|
|
\end_layout
|
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\end_inset
|
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\end_layout
|
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|
\begin_layout Plain Layout
|
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|
\end_layout
|
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|
\end_inset
|
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|
\end_layout
|
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|
|
\begin_layout Subsection
|
|
Descriptor Distance Measurements
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
Figure
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:descriptor-map-comparison"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
shows a comparison of mean average precision values for different descriptors
|
|
using their best achieved results.
|
|
For spatial descriptors all have a grid of 4 by 4 in order to allow a direct
|
|
comparison, spatial texture descriptors also use a bin count of 7 and edge
|
|
magnitude threshold of 0.09 in order to do the same.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Float figure
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\align center
|
|
\begin_inset Graphics
|
|
filename /home/andy/dev/matlab/cv-coursework/data/MAPComparison.png
|
|
lyxscale 30
|
|
width 70col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
Mean average precision for different descriptors at same parameters
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:descriptor-map-comparison"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
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|
\begin_layout Plain Layout
|
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|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The inclusion of spatial texture over solely colour derived descriptors
|
|
saw a general increase in mean average precision the outlier being Mahalanobis
|
|
distance for spatial texture which the lowest recorded value.
|
|
L1 was the best performing distance measure overall being the best for
|
|
all descriptors except spatial colour.
|
|
The use of PCA and Mahalanobis distance was the second best performing
|
|
distance in all cases except spatial texture.
|
|
This leaves Euclidean distance performing the worst of all categories except
|
|
spatial texture.
|
|
The use of L1 with a spatial colour and texture descriptor had a 53% higher
|
|
mean average precision than a global colour histogram with an L1 measure.
|
|
\end_layout
|
|
|
|
\begin_layout Section
|
|
Discussion
|
|
\end_layout
|
|
|
|
\begin_layout Subsection
|
|
Global Colour Histogram
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
All three of the distance measures increased in performance up to a peak
|
|
value.
|
|
This can be attributed to the descriptor becoming more discriminative.
|
|
Low bin counts will mean that many more pixels are placed in each bin to
|
|
the point that comparisons are less meaningful.
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
Equally, performance decreases past a certain point as the descriptor starts
|
|
to over-fit to the data.
|
|
Over-fitting describes a descriptor that is too sensitive to differences
|
|
in images such that it is no longer comparing meaningful variables.
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
For the global colour histogram if the bin size continued to increase, each
|
|
bin would eventually be comprised of only one or a handful of pixels which
|
|
cannot be compared effectively.
|
|
This explains why for bin count and many other descriptor parameters there
|
|
is an optimum value and performance doesn't just increase linearly with
|
|
that parameter.
|
|
\end_layout
|
|
|
|
\begin_layout Subsection
|
|
Spatial Colour
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The lower dimension configurations of the spatial colour descriptor performing
|
|
worse can be explained the same way as low bin numbers for the global colour
|
|
histogram.
|
|
A 1x1 grid indicates that the average colour values are taken for the image
|
|
in it's entirety, this 3D descriptor would not be particularly discriminative.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The significance of the best performing configuration having 14 rows is
|
|
not particularly high.
|
|
Looking to figure
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:spatial-colour-map-surfaces"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
either dimension being 4 gives similarly good results with little variation,
|
|
the best being 14 by a slim margin.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
An interesting result was that increasing the row count from 1 to 2 increased
|
|
MAP while increasing the columns in the same fashion decreased performance.
|
|
\end_layout
|
|
|
|
\begin_layout Subsection
|
|
Spatial Texture
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The trend of increase in performance for increasing bin counts can be attributed
|
|
to creating a more discriminative descriptor.
|
|
For example, a bin count of 1 will mean that each cell's sub-descriptor
|
|
is made up of only the count of pixels deemed to be edges without any further
|
|
information as to which direction they are facing.
|
|
As the count increases from here a maximum performance can be attained
|
|
before the descriptor starts over-fitting to the data.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The interesting results of odd numbers of bins giving better than even bins
|
|
could suggest that the edges of this combination of query and dataset are
|
|
naturally more discriminative when quantised into odd numbers of bins as
|
|
opposed to even although this would require investigation to comment further.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
Worth noting is that during the spacial texture experiments optimal parameters
|
|
were used as fixed variables for further testing, namely the bin count
|
|
and threshold values.
|
|
In doing so good results for the descriptor could be evaluated for this
|
|
query however the results are query and data dependent as are the rest
|
|
of the results in this coursework.
|
|
Cascading optimal parameters in further experiments like this does not
|
|
necessarily represent the best set of parameters for this descriptor as
|
|
each optimum value was found with the others fixed.
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
This query and dataset's set of optimum parameters for a descriptor could
|
|
be experimentally found with more complex testing methods however this
|
|
is not within the scope of this work.
|
|
\end_layout
|
|
|
|
\begin_layout Subsection
|
|
Spatial Colour and Texture
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
Looking to figure
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:spatial-colour-texture-map-surface"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
this surface can be seen to be a combination of the two traced by spatial
|
|
colour and texture individually.
|
|
The spatial colour characteristic of decreasing performance from 1 to 2
|
|
columns but increasing from 1 to 2 rows is visible, but the maximum value
|
|
at 4x3 from spatial texture is also apparent.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
Looking to the confusion matrices of spatial texture and spatial colour
|
|
and texture, the combinatory descriptor does not perform better in every
|
|
category.
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
While spatial colour and texture does, for example, reduce the mis-classificatio
|
|
n of planes as water features the percentage of correct water feature classifica
|
|
tions only increases by 4%.
|
|
Spatial colour and texture performed worse at correctly classifying
|
|
\end_layout
|
|
|
|
\begin_layout Itemize
|
|
Birds
|
|
\end_layout
|
|
|
|
\begin_layout Itemize
|
|
Buildings
|
|
\end_layout
|
|
|
|
\begin_layout Itemize
|
|
Cars
|
|
\end_layout
|
|
|
|
\begin_layout Itemize
|
|
Coast
|
|
\end_layout
|
|
|
|
\begin_layout Itemize
|
|
Cows
|
|
\end_layout
|
|
|
|
\begin_layout Itemize
|
|
Human Figures
|
|
\end_layout
|
|
|
|
\begin_layout Itemize
|
|
Planes
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
Worth noting is the cow query classification column which shows that only
|
|
8% of the top 25 results were of the cow category.
|
|
44% were farm animals, with reference to section
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "subsec:Dataset"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
this can be explained by the visual overlap between the two categories.
|
|
Inspecting the dataset, half of the farm animals category are photos of
|
|
groups of cows which can lead to false negatives.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
Also interesting, looking to figure
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:descriptor-map-comparison"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
, was the slight increase in mean average precision between spatial texture
|
|
and the inclusion of colour information.
|
|
It could be expected that including both would provide greater improvements
|
|
over applying either separately than were observed.
|
|
\end_layout
|
|
|
|
\begin_layout Subsection
|
|
Principal Component Analysis
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The reduction of eigenvalue energy for a model was seen to increase achievable
|
|
MAP for the spatial colour and texture descriptor when done within a specific
|
|
range.
|
|
The initial increase in performance can be attributed to removing dimensions
|
|
of low variance and importance.
|
|
In doing so the remaining descriptor can be more discriminative.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
However past this point relevant information starts being removed resulting
|
|
in degradation of performance.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
In summary the use of PCA and Mahalanobis distance does not inherently increase
|
|
performance but using a reasonable level of energy reduction such as 2%
|
|
can increase performance.
|
|
\end_layout
|
|
|
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\begin_layout Subsection
|
|
Comparisons
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
Looking to figure
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:descriptor-map-comparison"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
it can be seen that spatial texture descriptors can achieve better mean
|
|
average precision values than solely colour information based descriptors.
|
|
This indicates that using spatial information can form a more discriminative
|
|
descriptor than without.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The slight performance gain from the colour histogram to spatial colour
|
|
suggests that when looking solely at colour, spatial information does not
|
|
necessarily well surpass a colour histogram.
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
When thinking about a picture of a cow like in figure
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:cow-pic"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
, the spatial colour descriptor will identify an average of green surrounding
|
|
an average of brown.
|
|
The colour histogram however still identifies both the brown and green
|
|
pixels and encodes them.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
While it may have been thought that spatial techniques were better as a
|
|
whole than the global colour histogram, they in fact perform comparably
|
|
indicating that they may have different applications.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
Spatial texture descriptors represent the largest increase in performance.
|
|
This can be attributed to spatial texture techniques attempting to identify
|
|
and describe the shapes of objects within the image as opposed to just
|
|
the colours present.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
Colour exclusive methods can be less discriminative as different objects
|
|
can generate similar descriptors by being similar colours.
|
|
This could explain the global colour histogram frequently confusing cars
|
|
and bikes as both have similar metallic colours.
|
|
Using shape information allows for discrimination between images such as
|
|
those seen in figure
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:sheep-flower"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
where both are white objects on a green background.
|
|
Here using shape information provides an opportunity to distinguish between
|
|
the two.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Float figure
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
\align center
|
|
\begin_inset Graphics
|
|
filename /home/andy/dev/matlab/cv-coursework/data/9_21_s.png
|
|
lyxscale 30
|
|
width 30col%
|
|
|
|
\end_inset
|
|
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|
|
\begin_inset space \quad{}
|
|
\end_inset
|
|
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|
|
\begin_inset Graphics
|
|
filename /home/andy/dev/matlab/cv-coursework/data/10_15_s.png
|
|
lyxscale 30
|
|
width 30col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
Example of images with comparable colour information but different shapes
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "fig:sheep-flower"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The act of reducing the dimensionality of most of the descriptors improved
|
|
performance however this only occurs when the optimum level of reduction
|
|
is achieved.
|
|
Looking again to figure
|
|
\begin_inset CommandInset ref
|
|
LatexCommand ref
|
|
reference "fig:pca-colour-texture-map"
|
|
plural "false"
|
|
caps "false"
|
|
noprefix "false"
|
|
|
|
\end_inset
|
|
|
|
only the maxima of the curve represents results that were better than could
|
|
be achieved without reduction.
|
|
Without identifying this range the performance can be worse, 2% appears
|
|
to be a reasonable range to reduce by.
|
|
When using this value for all descriptors a performance increase was generally
|
|
observed indicating that it may be worth considering in most instances.
|
|
\end_layout
|
|
|
|
\begin_layout Section
|
|
Conclusions
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
To summarise, each descriptor has varying efficacy for different applications
|
|
and the context should be identified before selecting one over the other.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
Optimum internal parameters for each are data and query dependedent but
|
|
well performing values can be obtained experimentally.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
Spatial texture techniques were found to perform better than exclusively
|
|
colour based methods such as a global colour histogram.
|
|
While the combination of both colour and texture information didn't provide
|
|
as much of an improvement over either separately as expected, the combination
|
|
of both colour and texture information as part of the descriptor was the
|
|
best performing while using the L1 norm.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The use of appropriate amounts (approximately 2%) of dimensionality reduction
|
|
following principal component analysis provided performance increases over
|
|
the standard L2 norm, however following investigations into difference
|
|
distance measures the L1 norm tended to be best performing method.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Newpage pagebreak
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\start_of_appendix
|
|
\begin_inset CommandInset bibtex
|
|
LatexCommand bibtex
|
|
btprint "btPrintCited"
|
|
bibfiles "references"
|
|
options "plain"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Section
|
|
MSRCv2 Dataset Classifications
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "sec:MSRC-Dataset-Classifications"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\align center
|
|
\begin_inset Tabular
|
|
<lyxtabular version="3" rows="21" columns="2">
|
|
<features tabularvalignment="middle">
|
|
<column alignment="center" valignment="top">
|
|
<column alignment="center" valignment="top">
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Category Index
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Category Classification
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
1
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Farm Animal
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
2
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Tree
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
3
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Building
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
4
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Plane
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
5
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Cow
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
6
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Face
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
7
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Car
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
8
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Bike
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
9
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Sheep
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
10
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Flower
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
11
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Sign
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
12
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Bird
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
13
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Books
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
14
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Bench
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
15
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Cat
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
16
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Dog
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
17
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Road
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
18
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Water Features
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
19
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Human Figures
|
|
\end_layout
|
|
|
|
\end_inset
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34
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36
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|
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|
|
|
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\begin_layout Section
|
|
Spatial Mean Average Precision Tables
|
|
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|
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|
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|
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Colour
|
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|
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LatexCommand label
|
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name "sec:spatial-colour-grid-maps"
|
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|
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|
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|
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|
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6
|
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|
</cell>
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7
|
|
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|
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|
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|
|
</cell>
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8
|
|
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|
|
|
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|
|
</cell>
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|
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9
|
|
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|
|
|
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|
|
</cell>
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|
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|
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|
|
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|
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10
|
|
\end_layout
|
|
|
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|
|
</cell>
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<row>
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0.1345
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0.1336
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0.1326
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0.1319
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2
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0.1213
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0.1179
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0.1424
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0.1551
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0.1527
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0.1537
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0.1547
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0.1538
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0.1519
|
|
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|
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|
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|
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0.151
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|
|
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|
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<row>
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|
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|
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3
|
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|
|
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|
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0.131
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0.1123
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0.1401
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|
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0.1469
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|
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0.148
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0.1477
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|
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0.1513
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|
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|
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0.154
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0.155
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0.1545
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0.1542
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0.1537
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|
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0.1536
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|
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10
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11
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</cell>
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0.1516
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0.1504
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0.1488
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</cell>
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<row>
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14
|
|
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|
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</cell>
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0.1403
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|
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</cell>
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0.1293
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\end_layout
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|
</cell>
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0.1479
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</cell>
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0.156
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0.154
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0.1536
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0.1518
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|
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</cell>
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0.1513
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|
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|
</cell>
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<cell alignment="center" valignment="top" usebox="none">
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|
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0.1507
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|
\end_layout
|
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|
|
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|
|
</cell>
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<cell alignment="center" valignment="top" usebox="none">
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|
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0.1477
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|
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|
|
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|
|
</cell>
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</row>
|
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<row>
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<cell alignment="center" valignment="top" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
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|
|
15
|
|
\end_layout
|
|
|
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\end_inset
|
|
</cell>
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<cell alignment="center" valignment="top" usebox="none">
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|
|
|
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|
|
0.1413
|
|
\end_layout
|
|
|
|
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|
|
</cell>
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<cell alignment="center" valignment="top" usebox="none">
|
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|
|
|
|
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|
|
0.1312
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
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<cell alignment="center" valignment="top" usebox="none">
|
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|
|
|
|
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|
|
0.1494
|
|
\end_layout
|
|
|
|
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|
|
</cell>
|
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<cell alignment="center" valignment="top" usebox="none">
|
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|
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|
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|
|
0.1557
|
|
\end_layout
|
|
|
|
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|
|
</cell>
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<cell alignment="center" valignment="top" usebox="none">
|
|
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|
|
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|
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|
|
0.1515
|
|
\end_layout
|
|
|
|
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|
|
</cell>
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<cell alignment="center" valignment="top" usebox="none">
|
|
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|
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|
|
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|
|
0.1503
|
|
\end_layout
|
|
|
|
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|
|
</cell>
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|
|
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|
|
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|
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0.15
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|
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|
|
|
|
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|
|
</cell>
|
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<cell alignment="center" valignment="top" usebox="none">
|
|
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|
|
|
|
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|
|
0.1489
|
|
\end_layout
|
|
|
|
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|
|
</cell>
|
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<cell alignment="center" valignment="top" usebox="none">
|
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|
|
|
|
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|
|
0.1495
|
|
\end_layout
|
|
|
|
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|
|
</cell>
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<cell alignment="center" valignment="top" usebox="none">
|
|
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|
|
|
|
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|
|
0.1464
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
</lyxtabular>
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Subsection
|
|
Texture
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "sec:spatial-texture-grid-maps"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\align center
|
|
\begin_inset Tabular
|
|
<lyxtabular version="3" rows="9" columns="9">
|
|
<features tabularvalignment="middle">
|
|
<column alignment="center" valignment="top" width="0pt">
|
|
<column alignment="center" valignment="top" width="0pt">
|
|
<column alignment="center" valignment="top" width="0pt">
|
|
<column alignment="center" valignment="top" width="0pt">
|
|
<column alignment="center" valignment="top" width="0pt">
|
|
<column alignment="center" valignment="top" width="0pt">
|
|
<column alignment="center" valignment="top" width="0pt">
|
|
<column alignment="center" valignment="top" width="0pt">
|
|
<column alignment="center" valignment="top" width="0pt">
|
|
<row>
|
|
<cell alignment="center" valignment="top" bottomline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
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|
|
Grid Size
|
|
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|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" bottomline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
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|
|
1
|
|
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|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" bottomline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
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|
|
2
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" bottomline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
3
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" bottomline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
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|
|
4
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" bottomline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
5
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" bottomline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
6
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" bottomline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
7
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" bottomline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
8
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
1
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
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|
|
0.1637
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
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|
|
0.1688
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
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|
|
0.1836
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
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|
|
0.163
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
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|
|
|
|
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|
|
0.1669
|
|
\end_layout
|
|
|
|
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|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
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|
|
0.157
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
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|
|
0.1488
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.141
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
2
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
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|
|
0.1881
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
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|
|
|
|
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|
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0.1928
|
|
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|
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0.2182
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|
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0.1982
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0.1922
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0.1817
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0.1695
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0.1638
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|
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<row>
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<cell alignment="center" valignment="top" rightline="true" usebox="none">
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3
|
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0.1946
|
|
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|
</cell>
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<cell alignment="center" valignment="top" usebox="none">
|
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0.2084
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|
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0.2203
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|
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0.2031
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|
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|
</cell>
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<cell alignment="center" valignment="top" usebox="none">
|
|
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|
|
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|
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0.1954
|
|
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|
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|
</cell>
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<cell alignment="center" valignment="top" usebox="none">
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|
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0.1908
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|
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|
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|
</cell>
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<cell alignment="center" valignment="top" usebox="none">
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|
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0.1772
|
|
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|
|
|
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|
|
</cell>
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|
<cell alignment="center" valignment="top" usebox="none">
|
|
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|
|
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|
|
0.1772
|
|
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|
|
|
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|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" rightline="true" usebox="none">
|
|
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|
|
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|
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4
|
|
\end_layout
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|
|
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|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
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|
|
|
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|
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0.1886
|
|
\end_layout
|
|
|
|
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|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
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|
|
|
|
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|
|
0.2121
|
|
\end_layout
|
|
|
|
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|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
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|
|
|
|
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|
|
0.2308
|
|
\end_layout
|
|
|
|
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|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
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|
|
0.2137
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
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|
|
0.1986
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.1954
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.1889
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.1836
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
5
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.1982
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2076
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2176
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2033
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.1911
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.1831
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.1765
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.1656
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
6
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.1792
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.1957
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2138
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.1885
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.1799
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.1774
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.1654
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.1595
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
7
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2086
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2182
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2262
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2019
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.1935
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.182
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.1694
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.1614
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
8
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.1999
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2102
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2179
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2003
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.1839
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.1818
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.1658
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.1563
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
</lyxtabular>
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Subsection
|
|
Colour and Texture
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "subsec:Colour-and-Texture"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\align center
|
|
\begin_inset Tabular
|
|
<lyxtabular version="3" rows="9" columns="9">
|
|
<features tabularvalignment="middle">
|
|
<column alignment="center" valignment="top" width="0pt">
|
|
<column alignment="center" valignment="top" width="0pt">
|
|
<column alignment="center" valignment="top" width="0pt">
|
|
<column alignment="center" valignment="top" width="0pt">
|
|
<column alignment="center" valignment="top" width="0pt">
|
|
<column alignment="center" valignment="top" width="0pt">
|
|
<column alignment="center" valignment="top" width="0pt">
|
|
<column alignment="center" valignment="top" width="0pt">
|
|
<column alignment="center" valignment="top" width="0pt">
|
|
<row>
|
|
<cell alignment="center" valignment="top" bottomline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Grid Size
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" bottomline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
1
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" bottomline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
2
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" bottomline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
3
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" bottomline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
4
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" bottomline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
5
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" bottomline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
6
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" bottomline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
7
|
|
\end_layout
|
|
|
|
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8
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<row>
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0.1848
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0.211
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|
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|
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0.2052
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0.2021
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|
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<cell alignment="center" valignment="top" usebox="none">
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|
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0.1928
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|
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|
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|
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</row>
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<row>
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|
<cell alignment="center" valignment="top" rightline="true" usebox="none">
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|
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|
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|
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3
|
|
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|
|
|
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|
</cell>
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|
<cell alignment="center" valignment="top" usebox="none">
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|
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0.2008
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|
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|
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|
</cell>
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|
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|
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|
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0.1881
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|
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|
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|
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|
</cell>
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|
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|
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|
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|
0.2102
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|
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|
|
|
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|
</cell>
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<cell alignment="center" valignment="top" usebox="none">
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|
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|
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|
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|
0.2146
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|
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|
|
|
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|
</cell>
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|
<cell alignment="center" valignment="top" usebox="none">
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|
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|
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|
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|
0.2047
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|
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|
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|
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|
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|
<cell alignment="center" valignment="top" usebox="none">
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|
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|
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|
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|
0.2
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|
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|
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|
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|
</cell>
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|
<cell alignment="center" valignment="top" usebox="none">
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|
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|
|
|
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|
|
0.1991
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|
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|
|
|
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|
|
</cell>
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|
<cell alignment="center" valignment="top" usebox="none">
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|
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|
|
|
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|
|
0.196
|
|
\end_layout
|
|
|
|
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|
|
</cell>
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|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" rightline="true" usebox="none">
|
|
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|
|
|
|
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|
|
4
|
|
\end_layout
|
|
|
|
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|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
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|
|
|
|
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|
|
0.2113
|
|
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|
|
|
|
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|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
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|
|
|
|
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|
|
0.1953
|
|
\end_layout
|
|
|
|
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|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
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|
|
|
|
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|
|
0.217
|
|
\end_layout
|
|
|
|
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|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
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|
|
|
|
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|
|
0.2149
|
|
\end_layout
|
|
|
|
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|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
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|
|
|
|
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|
|
0.2134
|
|
\end_layout
|
|
|
|
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|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
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|
|
|
|
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|
|
0.205
|
|
\end_layout
|
|
|
|
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|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
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|
|
|
|
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|
|
0.2014
|
|
\end_layout
|
|
|
|
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|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
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|
|
|
|
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|
|
0.1977
|
|
\end_layout
|
|
|
|
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|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" rightline="true" usebox="none">
|
|
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|
|
|
|
\begin_layout Plain Layout
|
|
5
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
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|
|
|
|
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|
|
0.2125
|
|
\end_layout
|
|
|
|
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|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
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|
|
|
|
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|
|
0.1928
|
|
\end_layout
|
|
|
|
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|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
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|
|
|
|
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|
|
0.2073
|
|
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|
|
|
|
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|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
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|
|
|
|
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|
|
0.2056
|
|
\end_layout
|
|
|
|
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|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
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|
|
|
|
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|
|
0.2004
|
|
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|
|
|
|
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|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
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|
|
|
|
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|
|
0.196
|
|
\end_layout
|
|
|
|
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|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
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|
|
|
|
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|
|
0.1922
|
|
\end_layout
|
|
|
|
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|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
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|
|
|
|
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|
|
0.1849
|
|
\end_layout
|
|
|
|
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|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" rightline="true" usebox="none">
|
|
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|
|
|
|
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|
|
6
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
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|
|
|
|
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|
|
0.2044
|
|
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|
|
|
|
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|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
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|
|
|
|
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|
|
0.1857
|
|
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|
|
|
|
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|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
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|
|
|
|
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|
|
0.2047
|
|
\end_layout
|
|
|
|
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|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
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|
|
|
|
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|
|
0.2035
|
|
\end_layout
|
|
|
|
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|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
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|
|
|
|
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|
|
0.197
|
|
\end_layout
|
|
|
|
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|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
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|
|
|
|
\begin_layout Plain Layout
|
|
0.1919
|
|
\end_layout
|
|
|
|
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|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
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|
|
|
|
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|
|
0.1878
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
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|
|
|
|
\begin_layout Plain Layout
|
|
0.1828
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
7
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2134
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
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|
|
|
|
\begin_layout Plain Layout
|
|
0.1912
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2095
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2062
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2029
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.1977
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.1883
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.1828
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
8
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2081
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.1898
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2059
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2049
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.1999
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.1939
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.1883
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" usebox="none">
|
|
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|
|
|
|
\begin_layout Plain Layout
|
|
0.1836
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
</lyxtabular>
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Section
|
|
Principal Component Analysis MAP values
|
|
\begin_inset CommandInset label
|
|
LatexCommand label
|
|
name "sec:pca-map"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\align center
|
|
\begin_inset Tabular
|
|
<lyxtabular version="3" rows="47" columns="2">
|
|
<features tabularvalignment="middle">
|
|
<column alignment="center" valignment="top" width="0pt">
|
|
<column alignment="center" valignment="top" width="0pt">
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Percentage Energy Reduction
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
Mean Average Precision
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.1208
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.1
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.1498
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.1656
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.3
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.1885
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.4
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2017
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.5
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2067
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.6
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2217
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.7
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2222
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.8
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2329
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.9
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2414
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
1
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2377
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
1.1
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.234
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
1.2
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2425
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
1.3
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2462
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
1.4
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.251
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
1.5
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2465
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
1.6
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2463
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
1.7
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2448
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
1.8
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2425
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
1.9
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2423
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
2
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.244
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
2.1
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2434
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
2.2
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2409
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
2.3
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2379
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
2.4
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2352
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
2.5
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2353
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
2.6
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2274
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
2.7
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.229
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
2.8
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2271
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
2.9
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2261
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
3
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2173
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
3.1
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2172
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
3.2
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.218
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
3.3
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2114
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
3.4
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2234
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
3.5
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2129
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
3.6
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2137
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
3.7
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2134
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
3.8
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2132
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
3.9
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2133
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
4
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2172
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
4.1
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.217
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
4.2
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2161
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
4.3
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2161
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
4.4
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.2058
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
4.5
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
0.1944
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
</lyxtabular>
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_body
|
|
\end_document
|