Horn-Schunk Python Implementation

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Horn-Shunk"
   ]
  },
  {
   "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": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import cv2\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "import time"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Display Image"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "averageKernel = np.array([[ 0.08333333,  0.16666667,  0.08333333],\n",
    "                          [ 0.16666667,  0.        ,  0.16666667],\n",
    "                          [ 0.08333333,  0.16666667,  0.08333333]], dtype=np.float32)\n",
    "\n",
    "def average(img):\n",
    "    return cv2.filter2D(img.astype(np.float32), -1, averageKernel)\n",
    "\n",
    "\n",
    "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": [
    "### Horn-Shunk"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def hornShunckFlow(img1, img2, alpha):\n",
    "    img1 = img1.astype(np.float32)\n",
    "    img2 = img2.astype(np.float32)\n",
    "    \n",
    "    [Idx, Idy, Idt] = derivatives(img1, img2)\n",
    "\n",
    "    u = np.zeros_like(img1)\n",
    "    v = np.zeros_like(img1)\n",
    "\n",
    "    for iteration in xrange(100):\n",
    "        u0 = np.copy(u)\n",
    "        v0 = np.copy(v)\n",
    "\n",
    "        u_av = average(u0)\n",
    "        v_av = average(v0)\n",
    "\n",
    "        u = u_av - 1.0/(alpha**2 + Idx**2 + Idy**2) * Idx * (Idx * u_av + Idy * v_av + Idt)\n",
    "        v = v_av - 1.0/(alpha**2 + Idx**2 + Idy**2) * Idy * (Idx * u_av + Idy * v_av + Idt)\n",
    "        \n",
    "    return u, v"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Load Image"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "img1 = cv2.imread('taxi1.png', cv2.IMREAD_GRAYSCALE)\n",
    "img2 = cv2.imread('taxi2.png', cv2.IMREAD_GRAYSCALE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Convert to numpy format"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "img1 = np.float32(img1)\n",
    "img2 = np.float32(img2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculate Horn-Shunk"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "[u,v] = hornShunckFlow(img1, img2, 0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "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, 'Horn-Schunk')\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/HornSchunk.jpg\">\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}