Lucas-Kanade Python Implementation

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lucas Kanade"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Input Image"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"http://glimpglobe.com/proj/output_j77EBM-2.gif\">\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import cv2\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Displaying Image"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def img_display(img, name):\n",
    "    plt.figure()\n",
    "    plt.imshow(img, cmap='gray', interpolation='bicubic')\n",
    "    plt.title(name)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Get Derivatives"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def derivatives(img1, img2):\n",
    "    \n",
    "    # Convolve the images with a kernel\n",
    "    \n",
    "    kernel = 0.25 * np.array(([-1, 1], [-1, 1]))\n",
    "    kernel2 = 0.25 * np.array(([-1, -1], [1, 1]))\n",
    "    kernel = np.fliplr(kernel)\n",
    "\n",
    "    fx = cv2.filter2D(img1, -1, kernel) + cv2.filter2D(img2, -1, kernel)\n",
    "    fy = cv2.filter2D(img1, -1, kernel2) + cv2.filter2D(img2, -1, kernel2)\n",
    "    ft = cv2.filter2D(img1, -1, 0.25 * np.ones((2, 2))) + \\\n",
    "        cv2.filter2D(img2, -1, -0.25 * np.ones((2, 2)))\n",
    "\n",
    "    return (fx, fy, ft)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Lucas Kanade Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def lucas_kanade(img1, img2,window):\n",
    "    \n",
    "    ## Get derivateives\n",
    "    Idx, Idy, Idt = derivatives(img1, img2)\n",
    "\n",
    "    # It\n",
    "    It = cv2.filter2D(Idx**2, -1, window)*cv2.filter2D(Idy**2, -1, window) - \\\n",
    "        cv2.filter2D((Idx*Idy), -1, window)**2\n",
    "        \n",
    "    It[It == 0] = np.inf\n",
    "\n",
    "    ##A(1,1) + Ix(m,n)*Ix(m,n)\n",
    "    \n",
    "    u = (-cv2.filter2D(Idy**2, -1, window) * cv2.filter2D(Idx*Idt, -1, window) +\n",
    "         cv2.filter2D(Idx*Idy, -1, window) * cv2.filter2D(Idy*Idt, -1, window)) / \\\n",
    "        It\n",
    "        \n",
    "    v = (cv2.filter2D(Idx*Idt, -1, window) * cv2.filter2D(Idx*Idy, -1, window) -\n",
    "         cv2.filter2D(Idx**2, -1, window) * cv2.filter2D(Idy*Idt, -1, window)) / \\\n",
    "        It\n",
    "\n",
    "    return (u, v)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Loading the image"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "img1 = cv2.imread('car1.png', cv2.IMREAD_GRAYSCALE)\n",
    "img2 = cv2.imread('car2.png', cv2.IMREAD_GRAYSCALE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Convert to numpy format"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "img1 = np.float32(img1)\n",
    "img2 = np.float32(img2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculate Lucas Kanade"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "u, v = lucas_kanade(img1, img2, np.ones((3, 3)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Display "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "x = np.arange(0, img1.shape[1], 1)\n",
    "y = np.arange(0, img1.shape[0], 1)\n",
    "x, y = np.meshgrid(x, y)\n",
    "\n",
    "img_display(img1, 'Lucas Kanade')\n",
    "step = 3\n",
    "plt.quiver(x[::step, ::step], y[::step, ::step],\n",
    "           u[::step, ::step], v[::step, ::step],\n",
    "           color='g', pivot='middle', headwidth=2, headlength=3)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"http://glimpglobe.com/proj/LucasKanade.jpg\">\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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