Image Gradients.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Image Gradients"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*OpenCV provides three types of gradient filters or High-pass filters, <b>Sobel, Scharr and Laplacian</b>. We will see each one of them.*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Sobel and Scharr Derivatives\n",
    "\n",
    "Sobel operators is a joint Gausssian smoothing plus differentiation operation, so it is more resistant to noise. You can specify the direction of derivatives to be taken, vertical or horizontal (by the arguments, yorder and xorder respectively).<br> You can also specify the size of kernel by the argument ksize.If ksize = -1, a 3x3 Scharr filter is used which gives better results than 3x3 Sobel filter."
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The derivative of a matrix is calculated by an operator called the Laplacian, in honor of Laplace, a famous mathematician.\n",
    "\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "\n",
    "Unfortunately the partial derivatives can not be solved analytically but must be treated with the numerical calculation using approximations.<b> So if you want to calculate a Laplacian, you will need to calculate first two derivatives, called derivatives of Sobal, each of which takes into account the gradient variations in a certain direction: one horizontal, the other vertical.</b>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [],
   "source": [
    "import cv2\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f6af17c62b0>"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "img=cv2.imread('assets/grid.png')\n",
    "plt.imshow(img,cmap='gray')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Horizontal Sobal derivative (Sobal x)"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": "iVBORw0KGgoAAAANSUhEUgAAAJUAAAA0CAYAAACD4noEAAAG7UlEQVR4Ae2dd8g0NRCHHyv23gt27BULNlTEXlCxoaIoYgHFhogKFhQRBbGAf4gNFWzYsCAqolhBVMSCivrZsffeeSR5Wde7++623eXdHTj23WQzmUxmJ8nkl30hHToH+Dv32zYd8RuX9LGcrtRdRzkNaFT+OiqmgcaMatZi8iVdamHgaODhiloxN3A7cCSwErByRXyHZWP9BwAvALMPW6jO59pmVPMBxwJfA6tVpNjLgKuAq4EZwHnAYhXxls28wJ4D+B0PfAxs2BnVAC3VmPUDcAHwVkV1RC/xSIbf+8BBmfuyfy4ArDeAyUXA8wPyG89qm6eqWsEbAz+GCXHk/QXQ6gVEZ1TRFIpdnZ/9lSv6B2B6a2kiJnYlte/8ZZ2Z8Hgd+GQmzxTJnqVHIXVaZqW1CrB8hu8iYQGQ9X6/A09lnpmoP9viqcp08qAO+wqYM/fAXMC3ubSqb+tqTyVyTgdP5RzGQN846DVgUUCPFTt66ZJe5G3AXyT5rTXGNkY5hr62xVPlFaI3qaLtXwI3A1uFCmYDdgBuyVdY873tkapoU2BV/DIdPNUordejnA04b7kR2Bv4HHhyFCa5Z48DTgLmAfYNIYsPc8/UeWv96wOXZNrzUJ0VTifebd2mcSW5TwUdGYfnClgNZjER7nKwiK3PNfp/Z0pa6Iwqpd5KRNbOqBLpqJTE7Iwqpd5KRNbOqBLpqJTE7Iwqpd5KRNZ+caolgM1DPOdp4FlgOUDoyDeJtK0TsxkNbAAslKlqRt6ozLwYeBcQfPYgsFNIM1Isg9Tp1LA3ZxRchMEZAeRWtF1iqm4AxFT9DHwH3F2UWYFyBwNirtxUXwo4C3i1AJ8yRZRhP+DQPBNhsK8Aa+czQsT4nh7pTSZVEfzcK4douBJ4sWQjRH36wkV6AFg93lRwHYT8tK+M4kcSBeoOgWXyVGfw8zrA378U51S+bfcB1/axcofAx2OhhK+7AOdn5L8teF9hxkWoF/LzJUDjrYoGIT93DNtCsS6x8kKB1o0JDV23Ax6NdcXh77QwLl4eM3LX94DPcmkp3p6bU/gywC9h2CrSnn7Izy2LMCtQRu/gVCWS7ZH0VmXJTfEDh2CyIrACMLXfGI3qkLAVIGqxFxUFuJ04xFv7JnBUr0prSPOAgL9IYsmdO/4ZE0a8jhv56aLprozMtsdpShY6k8me6Z8OmycA4t7Vk574QuB04Kc+pQUP2oefxnyNyoLu2j8RE8N1SWDNTJqVWHgUuhTwVycVRX56rOlX4MwSwk0S8nOjsGJ3YVWUxNvfC7iYcUrgIsZTQv0Mynr+M/SZ4JxK7yQ8VWxQL7oG2D4A/Hvlp5CWn6RuEk6oOMkt6qVs96QgP4Ufe5bRfjLsU4a0BT2W2LDFeyBb87yd103Np8zUU8nEibjhguxRI93Z9yE+5ST+o8DNsION8M14A3D+cFPW/WVq3Q2wAweRLryMNxsV+SmKUvxR9FD7hyFDrzUqTQLy05jiEcAxAX3qca45Ch7b0phOBk4Jp8Gdg14R7tVznowYGMbI2s3UiVbHUQ3nVuCDTEnTfZOfy6RtHVzk4SEQ6pDYr0PuB/xNCvkyGAJQCfEIvYdKXQUWoSzy0+lDRH7qMZqg+YE7gqcQfCgZr7JvipDDX5zfrhpibocNYLQz4IslPGeK4kTdZfDuwPXAO5lJmgJbKHsMyTFX2gzQkusG+YfqKrkYpHO4z55Mebkk53EiP+0zX/ptMm2wPxxhypInufvRgiF2qZc0DOXQq0MqvNuyaxhz48R+j4aw0VUEP/spaZLTHZLUcVnKzyvL8utbPnqqvg/kMnS3xi48i+YJFmGuusysJ8sV6W5LaiCuyEqyaa74qEalW/3f/k5z4nY1paCBuE2TgqydjIlooDOqRDoqJTE7o0qptxKRtTOqRDoqJTE7o0qptxKRtY1GJbLAYN0zFfWRG/LimOTpyrhKLNUwIkZMl59Lyn+BZpjyrX6miuCnSt8CEAeVxSGVUew4kZ/KbXt8UQxuxg919GpPY8HPtnmq38LmeVXB2uglshuqTSI/NR7BAP32XnsZV+1pbTOqqhXaD/npvmhrqTOqcl0/buRnOelrKj3qNk1NYpRiWxT5WarSUFjkZx79qU7LzF+6b35W0TMN8CjTyYPEE/mZnxx7XzccqK72DGrr0HnTwVONivwcWjlDPCjWTCSsq0oXAVL3zc+giLZd9CZVzCcj8tPTuVJEfnbf/AwKactF1KcQYhGLfvNTOHSZY+IiP/3e5hrAsmP45uemoT2icGN7svDvtvRroXZWEfwsVPGYCyWH/KxiCBizzqd99ckhPzujmvY22XwDUzMqjyG5nI6/7KmY5rU32TXm/91tY9L+A6moP94sJhVFAAAAAElFTkSuQmCC"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is obtained through the convolution  * of the image I with a matrix  $ G_{x} called kernel which has always odd size. The kernel with size 3 is the simplest case:\n",
    "\n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'\\nddepth means desired depth of the destination image\\n\\nIt has information about what kinds of data stored in an image, \\nand that can be unsigned char (CV_8U), signed char (CV_8S), unsigned short (CV_16U), and so on...\\n'"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "sobx=cv2.Sobel(img,cv2.CV_8U,1,0,ksize=5)\n",
    "plt.imshow(sobx,cmap='gray')\n",
    "\n",
    "'''\n",
    "ddepth means desired depth of the destination image\n",
    "\n",
    "It has information about what kinds of data stored in an image, \n",
    "and that can be unsigned char (CV_8U), signed char (CV_8S), unsigned short (CV_16U), and so on...\n",
    "'''"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Vertical Sobal derivative (Sobal x)\n",
    "\n",
    "Vertical Sobal derivative (Sobal y). It is obtained through the convolution * of the image I with a matrix $ G_{y} $ called kernel which has always odd size.\n",
    "\n",
    "\n",
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f6af16bae48>"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "soby=cv2.Sobel(img,cv2.CV_8U,dx=0,dy=1,ksize=5)\n",
    "plt.imshow(soby,cmap='gray')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Combining the Sobel along both X and Y directions we get :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Clipping input data to the valid range for imshow with RGB data ([0..1] for floats or [0..255] for integers).\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f6af1b6c438>"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "res=cv2.add(sobx,soby)\n",
    "plt.imshow(res,cmap='gray')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using the Laplacian Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f6af17975c0>"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lap=cv2.Laplacian(img,cv2.CV_8U)\n",
    "plt.imshow(lap,cmap='gray')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# IMPORTANT NOTE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In our last example, output datatype is cv2.CV_8U or np.uint8. But there is a slight problem with that.<b> Black-to-White transition is taken as Positive slope (it has a positive value) while White-to-Black transition is taken as a Negative slope (It has negative value)</b>. So when you convert data to np.uint8, all negative slopes are made zero. In simple words, you miss that edge.\n",
    "\n",
    "If you want to detect both edges, better option is to keep the output datatype to some higher forms, like cv2.CV_16S, cv2.CV_64F etc, take its absolute value and then convert back to cv2.CV_8U. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Original"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f6af13612e8>"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "img=cv2.imread('assets/blackandwhite.jpg',0)\n",
    "plt.imshow(img,cmap='gray')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Using Sobel with Unsigned-Integer( np.uint8 / CV_8U )\n",
    "\n",
    "   As you can see below by using uint8 we are unable to recognize multiple edges for both horizontal and vertical directions.<b>So when you convert data to np.uint8, all negative slopes are made zero. In simple words, you miss that edge.\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Along X\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Along Y\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sobx=cv2.Sobel(img,cv2.CV_8U,1,0,ksize=5)\n",
    "soby=cv2.Sobel(img,cv2.CV_8U,0,1,ksize=5)\n",
    "\n",
    "print('Along X')\n",
    "plt.imshow(sobx,cmap='gray')\n",
    "plt.show()\n",
    "print('Along Y')\n",
    "plt.imshow(soby,cmap='gray')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Converting data to a higher type\n",
    "   \n",
    "   As you can observe the lost edges in the above images along X and Y directions are retained respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Along X\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Along Y\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sobx=cv2.Sobel(img,cv2.CV_64F,1,0,ksize=5)\n",
    "soby=cv2.Sobel(img,cv2.CV_64F,0,1,ksize=5)\n",
    "\n",
    "print('Along X')\n",
    "plt.imshow(sobx,cmap='gray')\n",
    "plt.show()\n",
    "print('Along Y')\n",
    "plt.imshow(soby,cmap='gray')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reverting to lower dtype without edge loss\n",
    "\n",
    "   But this seems to be on a overlay of gray.To convert it to a Black/White image we need to retain the negative gradients too.We can do this by <b>taking the asbolute values and then converting the datatype tp uint8</b>.Demonstrated below :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Taking absolute values for sob in float 64 form and then converting to uint8\n",
    "sobx8 = np.uint8(np.absolute(sobx))\n",
    "soby8 = np.uint8(np.absolute(soby))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Along X\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Along Y\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "print('Along X')\n",
    "plt.imshow(sobx8,cmap='gray')\n",
    "plt.show()\n",
    "print('Along Y')\n",
    "plt.imshow(soby8,cmap='gray')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## END"
   ]
  }
 ],
 "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": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}