{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "|Item|Description|\n",
    "|:---|:---|\n",
    "|Created |Jan 24, 2021|\n",
    "|Author|BIMALKA PIYARUWAN|\n",
    "|GitHub|https://github.com/bimalka98|"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Corner Detection\n",
    "\n",
    "## Quantities to be evaluated over a window.\n",
    "\n",
    "The function E(u,v) is minimum when the displacement is zero. Function is non zero for any ohter displacement.\n",
    "\n",
    "### $E(u,v) = \\Sigma{(I(x+u, y+v)-I(x,y))}^{2}$\n",
    "### $E(u,v) = \\Sigma{(I_{x}.u+I_{y}.v)^{2}}$\n",
    "### $E(u,v) = \\Sigma{(I_{x}^{2}.u^{2}+2.I_{x}.I_{y}.u.v + I_{y}^{2}.v^{2})}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import cv2 as cv\n",
    "import matplotlib.pyplot as plt\n",
    "%config IPCompleter.greedy=True\n",
    "%config Completer.use_jedi = False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "img0 = cv.imread('chess1.jpg', cv.IMREAD_GRAYSCALE)\n",
    "img = cv.GaussianBlur(img0, (3, 3), 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Gradient calculation using sobel or more accurate Scharr function \n",
    "Ix = cv.Scharr(img,cv.CV_64F,1,0)\n",
    "Iy = cv.Scharr(img,cv.CV_64F,0,1)\n",
    "\n",
    "#Taking sigma equals to convolve with a filter of ones\n",
    "windim = 7\n",
    "window = np.ones((windim,windim))\n",
    "\n",
    "#Calculating second moment matrix's components over window for each pixel\n",
    "sigma_Ixx = cv.filter2D(Ix*Ix,-1,window)\n",
    "sigma_Iyy = cv.filter2D(Iy*Iy,-1,window)\n",
    "sigma_Ixy = cv.filter2D(Ix*Iy,-1,window)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Computing eigen values is expensive. Therefore calculate corner response function\n",
    "\n",
    "## $R = det(M) - alpha* trace(M)^2$\n",
    "### $det(M) = \\Sigma(I_{x}^{2}).\\Sigma(I_{y}^{2}) - (\\Sigma(I_{x}.I_{y}))^{2} $   \n",
    "### $trace(M) = \\Sigma(I_{x}^{2})+ \\Sigma(I_{y}^{2})$\n",
    "## alpha = [0.04,0.06]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "det_M = sigma_Ixx*sigma_Iyy - sigma_Ixy**2\n",
    "trace_M = sigma_Ixx + sigma_Iyy\n",
    "alpha = 0.045\n",
    "CornerResponse = det_M - alpha*trace_M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[(47, 52), (47, 98), (47, 153), (47, 197), (47, 253), (47, 297), (47, 353), (53, 46), (53, 104), (53, 147)]\n"
     ]
    }
   ],
   "source": [
    "# Thresholding\n",
    "CornerResponse = CornerResponse/np.max(CornerResponse) # Normalizing the corner response to ease the thresholding\n",
    "#print(np.min(CornerResponse), np.max(CornerResponse))\n",
    "threshod = 0.9\n",
    "cornerList = []\n",
    "thrshldCorners = np.zeros(img.shape)\n",
    "x_range, y_range = CornerResponse.shape\n",
    "for x in range(x_range):\n",
    "    for y in range(y_range):\n",
    "        if CornerResponse[x][y] > threshod:\n",
    "            thrshldCorners[x][y] = 1\n",
    "            cornerList.append((x, y))\n",
    "\n",
    "print(cornerList[0:10])            "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "106192640.0 105165716.0 -13643046.0\n",
      "105983042.0 105671174.0 13718014.0\n",
      "106156693.0 105665549.0 -13715589.0\n",
      "106171148.0 105688076.0 13603154.0\n",
      "105983042.0 105671174.0 -13718014.0\n",
      "105880014.0 105325606.0 13450292.0\n",
      "106156693.0 105665549.0 -13715589.0\n",
      "105464774.0 106031058.0 -13738002.0\n",
      "105629039.0 105979035.0 13745757.0\n",
      "105762569.0 105467617.0 -13577153.0\n"
     ]
    }
   ],
   "source": [
    "#Get the Ixx, Iyy, Ixy values over a window to plot the Error function surface.\n",
    "for i in range(10):\n",
    "    corner = cornerList[i]\n",
    "    print(sigma_Ixx[corner[0]][corner[1]],sigma_Iyy[corner[0]][corner[1]],sigma_Ixy[corner[0]][corner[1]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Non-maximum suppression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 1440x1440 with 9 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Place rectangles at the corners\n",
    "annotatedImg = cv.cvtColor(img, cv.COLOR_GRAY2RGB)\n",
    "offset = 2\n",
    "for i in cornerList:\n",
    "    x1 = i[0] - offset\n",
    "    y1 = i[1] - offset \n",
    "    x2 = i[0] + offset + 1\n",
    "    y2 = i[1] + offset + 1\n",
    "    annotatedImg = cv.rectangle(annotatedImg, (x1,y1), (x2,y2), [255,0,0], 1)\n",
    "\n",
    "# Plotting\n",
    "fig, axes  = plt.subplots(3,3, sharex='all', sharey='all', figsize=(20,20))\n",
    "img_dict = {'BlurImg':img, 'Ix':Ix, 'Iy':Iy,\n",
    "            'sigma_Ixx':sigma_Ixx, 'sigma_Iyy':sigma_Iyy,'sigma_Ixy':sigma_Ixy,\n",
    "            'Corner Response':CornerResponse, 'Threshold Corners':thrshldCorners,'Annotated Image':annotatedImg}\n",
    "i =0\n",
    "for key in img_dict.keys():\n",
    "    plt.subplot(3,3,i+1),plt.imshow(img_dict[key], cmap='gray')#, vmin = 0, vmax = 255)\n",
    "    plt.title(key),plt.xticks([]),plt.yticks([])\n",
    "    i+=1\n",
    "    \n",
    "plt.show()\n",
    "#plt.savefig('Corner Detection.eps')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Ctrl + ] indent.\n",
    "#Ctrl + [ dedent.\n",
    "# Using built-in functions\n",
    "#harrisCorner =\tcv.cornerHarris(src, blockSize, ksize, k[, dst[, borderType]])\n",
    "source_window = 'Source image'\n",
    "corners_window = 'Corners detected'\n",
    "\n",
    "img0 = cv.imread('chess1.jpg', cv.IMREAD_GRAYSCALE) # input 8-bit single channel\n",
    "img = cv.GaussianBlur(img0, (3, 3), 0)\n",
    "thresh = 230\n",
    "# Detector parameters\n",
    "blockSize = 7 # neighbourhood\n",
    "apertureSize = 3 # for gradient operator\n",
    "k = 0.045\n",
    "# Detecting corners\n",
    "dst = cv.cornerHarris(img, blockSize, apertureSize, k)\n",
    "# Normalizing\n",
    "dst_norm = np.empty(dst.shape, dtype=np.float32)\n",
    "cv.normalize(dst, dst_norm, alpha=0, beta=255, norm_type=cv.NORM_MINMAX)\n",
    "dst_norm_scaled = cv.convertScaleAbs(dst_norm)\n",
    "# Drawing a circle around corners\n",
    "for i in range(dst_norm.shape[0]):\n",
    "    for j in range(dst_norm.shape[1]):\n",
    "        if int(dst_norm[i,j]) > thresh:\n",
    "            cv.circle(dst_norm_scaled, (j,i), 5, (0), 2)\n",
    "# Showing the result\n",
    "cv.namedWindow(corners_window)\n",
    "cv.imshow(corners_window, dst_norm_scaled)\n",
    "cv.waitKey()\n",
    "cv.destroyAllWindows()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.9.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}