computer-vision/edge-detection.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2><center>edge detection</center></h2>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7fa72c19bf50>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import cv2\n",
    "import math\n",
    "import numpy as np\n",
    "from scipy.signal import convolve2d\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "img = cv2.imread('sheep.png')[:,:,::-1]\n",
    "plt.imshow(img)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "sobel filter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7fa72c18dc50>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "kx = np.array([[-1, 0, 1], [-2, 0, 2], [-1, 0, 1]]) / 4\n",
    "ky = np.array([[1, 2, 1], [0, 0, 0], [-1, -2, -1]]) / 4\n",
    "\n",
    "grey = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)\n",
    "\n",
    "blur = convolve2d(grey, np.array([[1, 1, 1], [1, 1, 1], [1, 1, 1]]) / 9)\n",
    "\n",
    "dx = convolve2d(blur, kx)\n",
    "dy = convolve2d(blur, ky)\n",
    "\n",
    "x = np.concatenate((dx, dy), axis=1)\n",
    "\n",
    "plt.imshow(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7fa726fcdc50>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "kx = np.array([[-1, 0, 1], [-2, 0, 2], [-1, 0, 1]]) / 4\n",
    "ky = np.array([[1, 2, 1], [0, 0, 0], [-1, -2, -1]]) / 4\n",
    "\n",
    "grey = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)\n",
    "\n",
    "blur = convolve2d(grey, np.array([[1, 1, 1], [1, 1, 1], [1, 1, 1]]) / 9)\n",
    "\n",
    "dx_grey = convolve2d(grey, kx)\n",
    "dy_grey = convolve2d(grey, ky)\n",
    "\n",
    "dx_blur = convolve2d(blur, kx)\n",
    "dy_blur = convolve2d(blur, ky)\n",
    "\n",
    "dx = np.concatenate((dx_grey, dx_blur[1:-1, 1:-1]), axis=1)\n",
    "dy = np.concatenate((dy_grey, dy_blur[1:-1, 1:-1]), axis=1)\n",
    "\n",
    "x = np.sqrt(dx**2 + dy**2) > 20\n",
    "plt.imshow(x)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}