3637 lines
64 KiB
Plaintext
3637 lines
64 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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abstract
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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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viusal 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 composed of the extraction and comparison
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of these descriptors.
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It 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 to form part of
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a spatial colour descriptor due to it's 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 for each pixel.
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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 a 3D point of three 'binned'
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values, a full RGB colour space has been reduced to three colour histrograms,
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one 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 by count.
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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 similiarity can be computed using a suitable
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distance measure (L1 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 calculating descriptors that are discriminative
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between colour and shape information in different regions 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 the 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 approprate method however
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a main consideration should be the dimensionality of the final descriptor.
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This can be calculted 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 desciptor 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 divisions.
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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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dimenions, 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 value.
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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 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 in the middle
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of an image surrounded by 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-desciptor 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 greyscale 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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|
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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 angle 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 applcation.
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\end_layout
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\begin_layout Standard
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Once a thresholded edge maginute 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 histograms of 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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|
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\begin_layout Standard
|
|
\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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\end_inset
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|
|
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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 $q$
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\end_inset
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refers to the number of edge histogram bins.
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\end_layout
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\begin_layout Section
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Principal Component Analysis
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\end_layout
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\begin_layout Standard
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|
When extracting a descriptor from an image an important design factor is
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keeping the dimensionality as low as appropriate.
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|
This is so as to reduce the effect of the 'curse of dimensionality', a
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set of adverse phenomena which arise when analysing high dimensional data.
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Each additional dimension exponentially increases the volume of the feature
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space, a higher dimensional descriptor requires a longer time to extract,
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process and store.
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|
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.
|
|
In doing so redundant, low variation dimensions can be identified and removed.
|
|
The resulting dataset has a lower dimensionality and complexity but retains
|
|
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 80col%
|
|
|
|
\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 varied and measured.
|
|
\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.
|
|
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 points Euclidean distance.
|
|
\end_layout
|
|
|
|
\begin_layout Subsection
|
|
Mahalanobis Distance
|
|
\end_layout
|
|
|
|
\begin_layout Section
|
|
Test Methods
|
|
\end_layout
|
|
|
|
\begin_layout Subsection
|
|
Dataset
|
|
\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 evaulation of implemented visual search techniques the classification
|
|
of each image is done by referencing the group index they are named with.
|
|
As such, occurences 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 similar and measure negatively for the performance of the method.
|
|
\end_layout
|
|
|
|
\begin_layout Subsection
|
|
Precision and Recall
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
When comapring 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 accuracy 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 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 able to 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 with perfect system performance
|
|
being,
|
|
\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 Subsubsection
|
|
Category Response
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The category response aims to control for a descriptor's varying performance
|
|
at each of the dataset's categories by looping through each category and
|
|
using a preselected image from each as the query image.
|
|
Each category iteration has precision and recall values calculated for
|
|
all
|
|
\begin_inset Formula $n$
|
|
\end_inset
|
|
|
|
to allow the mean average precision to be calculated.
|
|
This mean value is calculated from the 20 category iterations for the MSRCv2
|
|
dataset.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
Completing one 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 this is approximately the mean category size.
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
The completed confusion matrix allows the main category confusions to be
|
|
identified and discussions to be made.
|
|
\end_layout
|
|
|
|
\begin_layout Section
|
|
Results
|
|
\end_layout
|
|
|
|
\begin_layout Subsection
|
|
Global Colour Histogram
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Float figure
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
\align center
|
|
\begin_inset Graphics
|
|
filename ../data/colourHistogram/pr-curves-n-5-avg.png
|
|
lyxscale 30
|
|
width 60col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
Mean precision recall curve for histogram
|
|
\begin_inset Formula $n=5$
|
|
\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
|
|
|
|
\end_layout
|
|
|
|
\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
|
|
Mean average precision values for varying numbers of bins
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Subsection
|
|
Spatial Colour
|
|
\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/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:glo-col-hist-map-surfaces"
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Subsection
|
|
Spatial Texture
|
|
\end_layout
|
|
|
|
\begin_layout Standard
|
|
\begin_inset Float figure
|
|
wide false
|
|
sideways false
|
|
status open
|
|
|
|
\begin_layout Plain Layout
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
|
\align center
|
|
\begin_inset Graphics
|
|
filename ../data/edgeThresholds/10_14_s.png
|
|
lyxscale 30
|
|
width 20col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\begin_inset space \quad{}
|
|
\end_inset
|
|
|
|
|
|
\begin_inset Graphics
|
|
filename ../data/edgeThresholds/10_14_flower_edge.png
|
|
lyxscale 30
|
|
width 20col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
Image 10_14_s from the flower category followed by visualisation of detected
|
|
edges
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\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/edgeThresholds/5_15_s.png
|
|
lyxscale 30
|
|
width 20col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\begin_inset space \quad{}
|
|
\end_inset
|
|
|
|
|
|
\begin_inset Graphics
|
|
filename ../data/edgeThresholds/5_15_cow_edge.png
|
|
lyxscale 30
|
|
width 20col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
Image 5_15_s from the cow 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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\begin_layout Plain Layout
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\end_layout
|
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|
\end_inset
|
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|
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|
|
\begin_inset Float figure
|
|
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%
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|
|
\end_inset
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|
|
\begin_inset space \quad{}
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\end_inset
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|
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\begin_inset Graphics
|
|
filename ../data/edgeThresholds/cow-t-0.01.png
|
|
lyxscale 30
|
|
width 20col%
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|
|
\end_inset
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|
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\end_layout
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|
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\begin_layout Plain Layout
|
|
\begin_inset Caption Standard
|
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|
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\begin_layout Plain Layout
|
|
Angle magnitude images after threshold = 0.01
|
|
\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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|
|
\begin_inset Float figure
|
|
wide false
|
|
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%
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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/cow-t-0.08.png
|
|
lyxscale 30
|
|
width 20col%
|
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|
|
\end_inset
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|
|
\begin_inset Caption Standard
|
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|
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\begin_layout Plain Layout
|
|
Angle magnitude images after threshold = 0.08
|
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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
|
|
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{}
|
|
\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
|
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|
|
\begin_layout Plain Layout
|
|
Angle magnitude images after threshold = 0.2
|
|
\end_layout
|
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|
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\end_inset
|
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\end_layout
|
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|
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\end_inset
|
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|
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|
|
\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 80col%
|
|
|
|
\end_inset
|
|
|
|
|
|
\begin_inset Caption Standard
|
|
|
|
\begin_layout Plain Layout
|
|
Mean average precision values for varying numbers of bins, grid size 4x4,
|
|
threshold 0.08
|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
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|
|
\end_layout
|
|
|
|
\begin_layout Plain Layout
|
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|
|
\end_layout
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Subsection
|
|
Spatial Colour and Texture
|
|
\end_layout
|
|
|
|
\begin_layout Subsection
|
|
Principal Component Analysis
|
|
\end_layout
|
|
|
|
\begin_layout Section
|
|
Discussion
|
|
\end_layout
|
|
|
|
\begin_layout Section
|
|
Conclusions
|
|
\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
|
|
</cell>
|
|
</row>
|
|
<row>
|
|
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
|
|
\begin_inset Text
|
|
|
|
\begin_layout Plain Layout
|
|
20
|
|
\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
|
|
Coast
|
|
\end_layout
|
|
|
|
\end_inset
|
|
</cell>
|
|
</row>
|
|
</lyxtabular>
|
|
|
|
\end_inset
|
|
|
|
|
|
\end_layout
|
|
|
|
\begin_layout Section
|
|
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\end_document
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