{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Crosswalk\n",
    "\n",
    "Meet The Beatles at Abbey Road for Image Processing.\n",
    "\n",
    "Roland Bruggmann, 2018\n",
    "https://github.com/brugr9/Crosswalk"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from skimage.io import imread\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "silhouette = imread('images/beatles-abbey-road-silhouette.jpg', True)\n",
    "cover      = imread('images/beatles-abbey-road-cover.jpg', True)\n",
    "\n",
    "# The Beatles: George Harrison - Paul McCartney - Ringo Starr - John Lennon\n",
    "george = imread('images/beatles-abbey-road-silhouette-1-george.jpg', True)\n",
    "paul   = imread('images/beatles-abbey-road-silhouette-2-paul.jpg', True)\n",
    "ringo  = imread('images/beatles-abbey-road-silhouette-3-ringo.jpg', True)\n",
    "john   = imread('images/beatles-abbey-road-silhouette-4-john.jpg', True)\n",
    "thebeatles = [[george, 'coral'], [paul, 'deepskyblue'], [ringo, 'fuchsia'], [john, 'gold']]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Template Matching"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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OdfZCE41GcfHFFxfEB6tbt24A9jUR+pE2aRr78ssvPfXbkS/sggULEIvFEI1G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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f36c2c968d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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sKch55Vgk/ZwSiQTC4bA7VhUTx3GgKAoWLFhQlHNHIpGCnyNfyk7JkeuefrV3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\nkuikKAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f36c1bc2690>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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t2rVlua5UcoQQeOONN5DNZr3NNZW2+riuC0VRsGDBgopcOxaLlf0aYVC3Sg8A\nb8fW+++/j2g0WjZNNjcP19SpU7F8+fJepkyGYeoXIkImkyn7dVzXhaqqNSc3pE9kWDz++ONQVXXA\nZKtSMajGMl88HoemaVAUpWwTZaD7Hh3HQVNTE7q6urws5JUmnU7jjDPOqMjkfPTo0QBQ82Nj3Zkp\nXNeFbdtwHAfLli3Dr371q1BziABfeKPnxhwwTRO2beOzzz5DY2Mjli9fXtFcNQzDlAdFUUId9CUT\nJkzAsmXLYFkWUqkUbNv2km3WGmEMUnKwGzZsWMFrCSGgaVrFfEDS6TQMw8DYsWOhqmro/p/9KTTS\np6e5uRkvvfRSxeMgERHOPvvsbcbGclidFEXBvvvuWxfuH7X39RVAxswxDAN77rmnlyoibORW074v\nUHbuPffcE62trQDCdXxkGKaylMOpVVVVbNmyBRMmTADwhZ+HTLRZSziOg6lTp5Y8GEprhqIoNbfU\noWkazjjjDKRSqbLFqTnssMO2+b3rurAsC1//+tfx6KOPhn7dfFiWhdtvvx0zZ87stSmnHBARFixY\ngK6urpq28gB1GqfHNE0kEglPWw/zHnLX4DOZDFpaWvD55597yo7ckheJRDyzuDwnQKeq7V7BMLVJ\n2eL0TJkyBatXrw61XiEENm3ahOHDh9f0QCAVsnfffRcHHHBA0XJVxjfKZrPh5x4rMV7NW2+9hYMO\nOsiT32HGqAG6x4tNmzbhW9/6Fp5++mlvKVMqWJqmQQiBdevWYcSIEf7HihDi9Mjdg0cccYTnu5XJ\nZJDJZJBKpTylv1QrjaIo6OrqQiQSKYc1c+jG6SEinHHGGb0UjbARQkDXddi2jTVr1qCzsxPDhw/v\nZcKUP7/yyis1v4bJMMzACCEwevTosnzDO+20Ezo6OkKvN2yEENhpp51w4YUXFl2HHDAffPDBmkvF\ncNBBB5XVwkZE+MMf/oDHH38cmUxmm8jHuq7DcRzceOONMAyjouOFVECfffZZLF26FMuWLUNrays2\nbNiAzs5OWJaFjRs3YtKkSdB1vejrEBEWLVpUk8u3udSNpcd1XWSzWXR2dmL8+PFlNxHruo7W1laM\nHTsWQLeFJ5FIbBN8KR6PY+vWrdB1PUhHZg2JYYJTto9eTnLKUW9bWxsaGhpCrzts0uk0fvazn+FX\nv/pVSfVMmTIFixYtQlNTU0gtQ9EWD9d1scMOO2DFihXhtaUfFEXBoYceimeeeQYA8i5l2rbt3y0j\n5EjU+Wi5aTwOAAAgAElEQVRvb8eYMWOKcvCWVr4ddtgBS5YsKYfT9tCz9Mh14ilTplREk3RdF/Pn\nz/d+VlUVxx577DbXzu3ctbZWzzBMYeR362eWe8ABByCRSPiWQURU1WjHQXAcBy+99FLJ9axatQqJ\nRCKEFpXOunXryhqUL5fcWEfZbBaLFi2qqxUA13VLbu+aNWvY0pOHQBd2HAeGYeDJJ5/E3LlzkU6n\ny7rlUQiBvfbaC2+//banmSuKgsbGRqTTaS9PT1tbm5dPhy09DFNWyiKsDMNAPB7PO2mJRqMwDAPp\ndBqapqGxsdHbRZqPSCSCWCyGDRs2eLmZag3TNCGEQFNTE2zbLtnipWmaV2doFGnxcBwHw4cPRyaT\nQTKZRHt7e3htykE6cOdGYSYiTJs2DWvWrEE8HodhGHj00UdxzDHH+M9GXgFLj8w0cOCBB4aioFuW\nBU3Twnb7GHqWHqC7Ex199NFYvHgxgPJsvcvl/fffh2ma0DTNy6Xyj3/8A5qmIZ1O4+GHH0YymayL\nLMoMw/TPQw89BCD/pMUwDOyzzz7eoLZlyxZfdVuW1Svjei2iqioWLFgQWn25VvJq4zgONm3ahClT\nppQ16rMcHzo7OwF8kUF+9erVnkPzDTfcgP/8z/+suVUBRVHgOA7ee++9kpelFEXBjBkzvODBNUlu\nEs0Kl6JwXZccx6FbbrmF0K3/lq0IIej2228n27a96zqOQ6ZpFtt8STWfOxcu9VpCJZvNkmVZtNde\ne5EQgoQQeeWBYRi9zl+1ahUlk0mKx+N5ZYgQgq644gpyHCfsWwgFx3Fo1KhRocnNSCRC0WiULMva\n5pkVTYk9wDAM0jSt7OPFLrvsQp2dnd51XdctbbwoS8/vjW3b9Prrrxfs/0GKHDNDJDQ5UjfLW95J\nRJ75NRqNer8rF01NTdi8ebMXSVU+OLnFr0hLEy9vMUxwQv3QiQiWZaGhocFLmDgQEydOxKpVq7yZ\nsGma0HUdv/rVrzBv3rwBl4Ryd5nKtDm1hgwBEqa7gKqq4cY/KnGZx3VdXH755bjlllvCac8AyFWA\nXKue9JUpaqyowPKW67oYN24cNm3aFMpYKoTwwhbw8lYIyGjJqqrizDPPRCQSga7rnlIS5nKXEMIT\nUrIzyOvLnxmGqU8cx4GiKL58WD744INeA0IkEoEQAhdffDGmTJnSSy7k4s0uhfCWPmoFy7Lgui5m\nzZrla4u5EAKzZs3yJfdc18Xvfve7msoof9VVV2H48OFeFOhyRIMWQmzjDF6uALphsnnz5tCMB0SE\nQw89tOJJZP1Sl5YeKawsy4KqqvjNb37jZUku9JH17XyF7l8Igf333x8vvvhimJprbX8BDFObhCqs\nDMNAR0eHF5aiP1kgJ1LpdBqu626TT8q2bZimieHDhwPAgH4M0WgUBx98sLeluRYgImzduhWjR4/2\npZzI7fdNTU3QdT2vz4a0isvUGyUTgqVH+tls2rQJ++yzDzZu3Fgw/Ugx40UkEgkvLVIFLD3//d//\njR//+McFfXCCBDBUVRXt7e3eJp8QGNqWHhndUu6E+P73v+8pQ/lIJBJYt24dXn/9dVx//fU4+eST\nkUwm82r8Mluu4zica4thBhGqquK//uu/BhTkcuD+/ve/P2A2cE3TkEgk0N7e7g2s/R1nWRaef/55\nZDKZmgnc5zgOxo0bV1CmSQvWvffei0gkgkMOOaTgOdK6VSv3mmttGTt2LM4//3xflog//OEPeO21\n13DHHXfg7LPPRjKZzLsDL9cFQkZCrlVkHsurrrrKl7FAURQ0Nzf7mvirqlpzqUg8wnQQClhKwnVd\nz0ns1ltvJU3TSFXVAR2rdF2nSy65xDtHOlptv/32ec+Tf3v77bcplUqF5aBVbYdQLlzqsYSK67qU\nSCTyOmSqqkqpVKrgN++6Lr366quUTCYpGo32W5emaXTdddeFfRtFM23atLyyr2+RMteyLN9OwaHd\nb0g9QN5Dc3NzXsddRVEoGo2S67pk2zZZlkVERBs2bCBFUQre9+zZs71r1cJ994fjONTZ2UmKouTt\nB/J+d91114LPLfe7eeONN8JsbmhypO6Wt7yTieC6LhzHQVNTk7c+3R9S+06n04jFYr3iKHR0dGDE\niBEFNfJEIoGtW7d6VqYS4eUthglOqMLKNE0MGzYMmUxmm7/JZa3m5mZs3rzZ9ze/yy67YOnSpegr\nV3NlTmhLPkUi3QOkxaKQT1MsFsPuu++ON998E0B34L1x48aho6Njm/vsDylbS5KbIS3zEBHuuece\nnHfeeXmtG4qi4Mgjj8RTTz21zfky5k4+ZB6qkq0dZVze6urqwgUXXIAHHngg73HJZBK2baOjowOZ\nTAajR4/2ZSXbaaed8MEHH3j+tiUydJe3+vL0008XDIRFRIjFYl6S0FwaGxt9Xce27bI4vjEMUx2I\nKK/wJiK89tprgZxxX3jhhbx/V1UVH3zwge/6woaoO4L8lClT4DiOLyduRVHw8ssv9/r/u+++6+t6\nchdXrTg027aNuXPnFpzkCiFw11139Xv+7bffXvA6ROQF6KtVFEXxYlTlwzRNb7eipmn49re/XXDT\nkBACH3/8sRcDqJaoO6VHCirHcdDV1YXjjz8eRP3780irjKZp+POf/wwi2maHhW3bWLt2LTRNy6vU\nOI6Df//7356JjGGY+sR1XViWhenTp/c76Odmzt5hhx0CbbuWGbT7IuWG67q9FIhqYNs2Wltbfckx\nKT9z/VgikQimTZvmRSHOh+M4WLhwYdV9WwzD8IImxmKxAe9d3u/UqVMxfvz4fv9++umnFxwvVFXF\nxRdfHFr7w8R1XZimiblz5+ZVSIQQiEaj3ioJ0G31ue2227y/D6T45K7E1FpaitpqjU+kafi0007z\ndlT19/CldUYIgWOOOabfuhRFwdixY5FMJgt+mIXMgAzD1D4yjsinn346oIICAF/96le94/1CRPjT\nn/4EAANuYV+3bl0RrQ6PyZMnB5q4zZo1q9/fX3rppb4GtDlz5vi+VrnQNA2u6+K0004rKOcVRcGS\nJUv6/Zsce2688caCz9CPRagayF3P0hCQD8dxcMIJJ/RS8BRFwWWXXVbQ0iOXtWrN0lOXPj2GYcCy\nLAwbNqzguiwAbN26FYlEYsB1dMdx0NnZidGjR8N13QE/ioaGBnR0dNTU+iTDDCFCEVZEhFmzZuEf\n//jHgMdEIhG0t7cX7ZOhqiqi0eg2/kKapkFRFGzZsgW6rlcsNYXcWZbNZr1M2n7TBMh8Y33balkW\nEolEwSUyTdPQ2dlZmn9Lib4ttm1j2rRpaG1tzXucqqo4+eST8cc//rFgfYXeXTweR1dXV034MgFf\npMpYuHAh5syZU9AvSRoM+vYTacWR4RvyBfb8y1/+guOOOy4MH7ah7dNDRPjSl77k69i3334bsVgs\n79q9qqpobGzEyJEjC/oGMQxT3ziO4znl9ocQArqul5QcNB6P9xurRS5zLVmypKLyRA5eRx11lDdp\n9INU3vqz6KiqOqAVKBciwrJlywK3OUxSqVRBhQcAhg8fjvvvv7/gca7r4tprrx3Q0qUoSr8O8tXE\nMAzssMMOnkuIH/q7B9d1oSgKrrzySliWlbeuU045hS09OQS+sG3bcF0Xn332GXbeeWdkMpl+H7g0\nrem6jvb2ds+0OZC2SURIpVJwHAejRo2C67rb1CujQKdSKdi27WVlLnK9ki09DBOckoSVbduwLAvJ\nZLKg0L/qqqtw9dVXF32tVCqF5ubmvDtKZUZzaf0pN67rQtd13/410m8llUr1G1XYcRyk02mMHj06\nb9LlaDSKAw44AE8++SSIqLiAdUVaPOQz3nnnnbFq1aoBj9N1HZZl4eWXX8a+++7rpTgaCPkM5eaY\ngZ6p67ro6upCMpmsWhoK27aRyWQwbtw4zzcnH7quw3Ec7LPPPnjppZcGtNAZhuG5heT7nt566y3s\nsccepfbzoWnpkQ92++23z/ugVVWF67o46qijvOMKPexEIgFd1zF+/PhtHNSkc5vrumhsbPQ80ms9\ntDjDML0599xz8/5dWnl+9rOf+drZNBAy6OlAckfXdYwdO9aTVeWGiHDBBRcEOkfXdcyePXtAn0m5\n7X3EiBF5Bz3DMPD2229j4cKFVck0f/XVV2PVqlV55bW0Ruy3336+dunKZ/Lb3/6233tXFAWKong7\nnqrtyD1y5MhAaSEURcHrr7+eV/nrm6JpoGP23XffgsdVlDCD/gQsvnAchwzDoM7OTrJtmzRN8xUc\nSQaWChocKpVKUSQS6bdOmTG5ubmZUqkUpdNpchyHbNsOdA2q3jPnwqWeS1G4rkvpdJq6urqooaEh\nbxA2TdNo+vTp3jmlXHPp0qWk6/qAARBVVaV9992XDMMoPRt3HizLonQ67TsIoSyapvnKDC8D3BWq\nT1VVevLJJ8kwDMpms8FuImAPyGaz5LouPf7449TU1OSrbTNnzgzWJuoen/IFahRCkKZp1NHRQZZl\nBQ9WWELPd12XMpkMffvb3+41fuV736qqkqIo9IMf/MBX/bquFxyPhRC0ZMkSL8BjkYQmR2re0iO1\n80Qi4TsEtq7r2HHHHZFOp0HkX7uUS2CFtPJsNosDDzzQSzpYa1vyGIb5AvldjxgxIq/1RgrFhQsX\nAkBJPj22bWPixIn9OoLmtmvRokU4/PDD0dnZGUhW+cVxHKiq6u0oC8Jee+3l67hoNOorAJ2iKDj+\n+ONx8MEHlz0ZpaqqmD9/Po4//nhfiV4VRdkmUagfhBCYO3fugH8n6l5lGDVqVFnebz5M08T8+fPx\nwAMP+LJeSevUN77xDdx8880FjxdCYMKECb7aMm/evNpZGQlTgwpY8uK6LjmOQ6ZpkmVZpOt6wdlE\nNBolTdOopaWF0uk0maYZSLOWIdbPPffcvNeS2vvXvvY1chyHHMcJqsFXe8bMhUs9lqKwLIv++Mc/\netac/r5pTdNIURQaOXIkZTKZklMIyPMNw6BkMplXlqiqSieeeCIZhuGdGxau61IqlSJFUUhRFF9W\ncl3XSVVVsm3bl/XJtm1atGgRxWKxgjN++fO8efN8WZE8fPYA+ezuu+++AdOB9PfuW1tbg7WnB8uy\naOXKlQXvW9M0mjRpkmft8P2Oi+j5lmWRbds0f/58X89AWqqi0SjNmTOHbNv29Swsy6IbbrjBVyqT\neDwe3LrXm9DkSE0LMPnRJZNJX+bTeDxOkUiETNOkbDYbOE+WVLQ+++yzgsJB13XSNI22bt3qKT0B\nrlXtwYMLl3osReE4DsXj8YLf80knnRR4olQIwzBo1KhRAy4tyN+rqko33XQTmabpKT9hYNs2vfnm\nm9soHYXK7rvvTul02tezkMv70WjU1zU0TSNN0+idd97x7xrgswe4rktbt24tmItRlkQiQYsXL/Zk\nf1Bs2ybbtn3dsxCC/u///i9Y/yqi56fTafrb3/4W6H1EIhE644wzAl1HLsn6uYaiKEU93xxCkyM1\nK8DkeuQHH3zgaaJ+FBGphEhtNajSI69b6FoySVtjY6OnXLHSw4VLWUsgLMsix3HoBz/4QcHvORaL\neTKjROHci0wmQytXriRN0/LOuqV15frrry/GcrwNjuN4VgW/Fo9c2SZ9Yvw+C9u2acGCBb4UDVVV\nSQhBkUiEDMPwNzn12QMMw6CJEyd6g3m+NmiaRkcccYQnu4t57/K8YcOG+Rov5KTcNwF6vrTwPPHE\nE56RIJ+xQP5NVVX65z//6SlwQbAsy1efEkLQhg0bAtXdh9DkSM0KMOnA7DcLcCQSobPOOqsYBaTf\na7e0tPgWEg888IBvk2AP1R48uHCpxxIIKUMKWYml0A9T2ZHYtk2GYdDw4cMLKh/S6vPXv/61VKdP\nIuoekN944w2KxWKBsqknk8minKoty6LGxsaCDrO59xuJRDw3hrz47AHLli3zlQFeLmeaplnMRpRe\nOI5DjzzyiO/M8yeffHLoFi6i7r723HPPUSKRKNjnhRDecq5t25TJZIq6b9d1fd23oij0+9//vpRv\nLDQ5UnMCTCostm3TWWed5TuNfSwWo0wmU5S22l8b/vKXvxRcowa+mKHJWaU8vwDVHjy4cKnHEgjL\nsmjVqlUFBwBd14vbWeMDKc86OjoG3BXaV5YJIWjBggUlKWFSkZB+PH6VHiEEvfPOO0UpXZZlUUdH\nhy9XBHmthoYG2n777Qtfr0APkJNOOcD6ec6/+93viIhC2TUnn7Wfwb/veFHKfRORN17+z//8jy/f\nV6Dbf2fEiBHU2dlZ7A5kz5ro512rqkqTJ08Oahzo70mUXGpOgMkH+c4771A0GvX1AhOJBD333HOh\nCS7XdSmbzXqCIl8b5Ba/Aw88kAzD8NuGag8eXLjUYwmEbdu0995755UdmqbRmDFjQvfl6YtlWTR8\n+HBfAwTQ7Z9YynKA4zj08ssv+76eVEJ0XS964igtBt/73vd8zf77+jPlpUAPyGQytMsuu3gWnELX\nHTNmTCjWNInjOJ6CWWiiLp2aU6lUycoeUXeYlTvvvJMikYgv5VYqXq2trdTV1VXyffvtW5qmleKz\nFpocqSkBJmdFXV1dnhOWH6VHWnnCUnocx6FsNuuZCQvFNpAdfd26dX7X46s9eHDhUo/FF1KOZLNZ\nX/LjzTff9M4rF7ZtU2trq28rSDQapWHDhhW9VG/bNrW0tPhecpGy7Cc/+Qlls9mirB9SUXJdN5CC\nJ9vY1dU18P3m6QGu69Inn3ziTYALDfxCCFq9enWoy5mu69IvfvEL387imqbRW2+9VbgNBXq+67p0\n+OGH9/LPKXTthoYGT/ko9Rn4ceKWzxyA53dUBKHJkZpKQyGT4h1++OF4+eWXC8ZykJEu169fj+HD\nh3uxIsKIB+C6Lj7//HNMnjzZS9RWCE3TkMlk/MSsqJGABQxTV/gSVjKR4llnnYVHH300b2JNRVFg\n23bZY4iYpgnHcdDU1ARd133nZbryyivxs5/9zFeclVyIyFfE3Fyi0ShSqVTga/Wlq6sLiqJg+vTp\naGtr6zcH2UDX37hxIxoaGrZ9H/2kYyAiL2N4Q0MDXNctmEQ1Ho8jk8nAdV04jlPyvea2JZPJoKGh\nwffzVhQF2Ww2f5TqAdJQyLFy2LBhXh1dXV0Fr9nc3IxPPvkEI0aMCKXPB32Gy5cvx6RJk4qJzD34\n0lA4joNsNovPP/8cr732mq8XIl+6fIFhhfomIti2jbFjx2LkyJG+69V1Hc8995zvTs8wTPhEIhHo\nuo6HHnqooBypVHoARVEQi8Xw1FNPFcxuDcBL8nnTTTcVlaH6r3/9K1RVDRRgcccddwx8nf6Ix+OI\nRCJYs2aN70zuQHdAx+HDh/uWn0QEXdex++67ezK7EJlMxsvZGELmbw/XdRGNRnHooYf6fua6ruPn\nP/954GsRERzHQUNDA9LpNGzb9qXw6LqOP/zhD2hubg70XsJk/vz5oT73ogjTbBSw9MJ1XWpvb/f8\nePKZCXP/1t7e7jlyhY3ruvTpp58Gim8BwM92+WovE3DhUo/FF47j0GGHHVbwu41EIvTAAw+UdVmr\nL3Lp3q8s0XWdWlpaem1Bl/fYn8yTsc2kL5PfXVRCCProo49K9vHIRab+iEQipOt6wXbIAIrxeHzb\npZd+eoAML9LfuDDQPUqfpXJh27avDTB9x4sB25Rz33J7/7/+9a9e/q5+/Ih0XafZs2eHGgNKLkVu\nv/32vh3lt9tuu2K/t9DkSM1YegBg9uzZXhoIovzavrTyNDQ0lM087bouxo4dG+gcIQTuueee0NvC\nMIw/TNPEs88+W/A427ZxxBFHFJQ1YRKLxXDvvff6Pp6IsH79eqRSqV4zZCFEvxmzZVqcRYsWQVXV\nQPc2derU0JZ7AHhpepYuXeqrHYqiQFVVtLS0+E7v09TU5P3s5xorVqwo61Km4zhoaWkJdM6ll17q\n6141TcODDz6IvfbaK9DKhqZpSCQSeOaZZ0K1bMolwquuusp3vRs3bqx+OoowNaiAxdMWN2/eTOl0\n2ncUTel9vn79ek9rLNd2U8dx6JVXXvGtycp7kE55A1DtGTMXLvVY8iJ3D5155pm+v9fPP/+8opYe\n6cgZiUR8p4SYNm0adXZ2kmmatGnTJjrllFNI13VKJpN08cUX92q/jE0kA/T5KUIIOvfcc0vZTpwX\n0zTpT3/6k2fJ6U+eK4pCyWSSxo4d621I6fVecnqADCB5zjnn+LaqqKpK8XjcX0ygErBtm9LptO+U\nH/K4AZPb5tz3cccdF8gxXYY/0HW9rPdsWZZ3LT9tGvJb1qU5Vgbv8vNS5Qdv27YnRMql9Egv94Ey\nJQ+k+Dz++OOs9HDhEm7Ji23b1NHRQdFo1PcS0rp16yqq9MhgeMuWLfM1SMTjcS9tg6ZpveKwnHDC\nCV7k5NxnYFlWoCV5VVXL6iYg5fPxxx/fb7vkgHndddf1Ch0wkNIjd/jKVEB+J8qLFy8u21ghkcuO\nDQ0Nvp+/oih022239V9hzn1feeWV1NjYGEiZ1TTNi19XLlzX9ZQrP/fa2tpazGVCkyNVFWBynTqb\nzfqa+ci/CyFozZo1xTy4onAchy677LK8H1cymSRVVWnnnXf2On6ejlbtwYMLl3oseTFNs2A6gL4C\neNWqVRVVeiSGYdCOO+7oO3pxXwXhhBNO6Nc/w3Eceu+993wpAlJh2GWXXcpi4emL9Hfpe89CCPrq\nV7/qxTmTE9lecc96eoCciD7xxBO+rDzyWs3NzRV9z+l0Ou87kMrrmDFj8gcHzOn52Ww2UF+JRCL0\n4osvlv1eXdelXXfd1fc39+CDDxZzmdDkSFV9eogIXV1daG5u9uV5L4nFYhg5ciSIqIyt+wJFUXDd\nddflPcY0TZx99tl47733QES+16QZhgkHuQU4yPH9+cVUiqVLlwb2odE0Da+88goefPDBfnfBKIqC\n9957z/s5n/+EbdswDAP/+te/fG+hL5X169f3+/s33ngD0WgUuq5jxx13xEUXXYRYLIZkMrnN2PDC\nCy/ghBNOCPSuX3jhhZLaHRRN0+A4zoB/tywL+++/P1atWgUAvvxcYrEYGhoaCh4nw7Z8+ctfxsyZ\nM323uRQuvPBC3746f//738vcmgKEqUEFKa7remuf8GmqU1WVotEorVq1qqzmur44jkOpVIqSyaQX\njLBv+3Rdp1gsRueccw7Ztu0lPpWzFbmWnM1mqdzPlguXQVryIs3sfmSJ9CN58sknQ43MG5S77ror\nrwyMRCIUi8U8P0YZdDEfmUyGHnroIS+zvBCC4vG492wURem1+ycSidBnn31GpmmW9VnIpaX99tsv\nUC6wXEtPZ2enl9/Lz7mKopCmaZTNZiv6nru6umiPPfYYsJ0ycvTee+9Ntm1TW1ubZ8WS/kymaXr3\nveuuuwYKfBiNRr3xp9zYtk3t7e1eXyvUvokTJxYTSDg0OVI1Aea6Lj3yyCO+lR5ZYrFY2T/OvkgH\nv0suuaTgBybTUjQ3N9MVV1xB99xzD82dO5disRgtXLiQUqkUlfvZcuEySEteDMOg22+/3ZcMaWpq\noh//+MehZDQvhULLINIvo7W11XcyZembs379errkkkuoo6ODLMuiTCZDH374IQkhPB9FTdOoubmZ\nNE2jO+64o6yDpFxCa2tr8738tu+++3af3NMDpk6d6st3JPf5vfzyy0REFZ0oS7+jQu1TVZVUVaVk\nMklXXHEF3XXXXXTRRRdRLBbrXprquW+5lOfX+f3TTz8l13UrNk7KxL5+XFRUVS3Gtyo0OVI1AeY4\nTuDsv4lEglasWFEVQSU178suu6ygs3Xui5fr5tIJkS09XLgUXfLiui4ZhuFrMO3o6ChUXUUwTbPf\nRKSRSISOPfZYf/mZAiB3Pu24446etUtRFIpEInTqqacWtCKFwUAWful/I1MQHXnkkWQYRi9Lj998\njLlyOMzYQ36RfjodHR2k67rvuHNy8iz7qbzvr3/9677i1yUSCTrqqKMqquDJa/ndWSaEKCbJaWhy\npGpOJ0SERx99FI2Njb6Ol+uUY8eODS3VRBCICADQ2NgIIvJ9fdd1oaoqRowYgfb2dq8ehmHCxXEc\n3HnnnQWPa2xsRCKRqIlvUQiBefPmbeOf4zgOrr76asRisVBlnRACtm1j8eLFsG0b6XQalmUhk8lU\nLL5YNBrF9ttv78nxvvLcNE1Eo1EsWLBgm3N32223QLFmXnnlFcRisVDaHQTLsrwUGYA/nx2JpmkY\nNWoUOjo6vN/Nnz8fmqYNWI+qqrj33nsxY8YMPPbYY6U1PiCKosCyLEyePNn3OVIBqQphalBBityq\nHo1GSdf1vNqw3Nkl1z0rsdNgIO66665ebZVrs3LtWJor5RbTuXPn0qpVq6irqyu33dWeMXPhUo8l\nL47j0M4775x3hinN69OnTyfTNMk0zarKE2m1njlzJgGgpqYmAkBbt24ta2yVaiKX2uLxOEUiEdI0\njaZMmUKRSIQURaEJEyZQJpPpfVJPD0in0xSPx3tt3e+vqKpKM2bM8Cxb1cK2bc9yBaCXZU1abnIt\nbt/61re88SL3vomI/uM//sPz08ot0WiUWlpaKu63JJFWm6uvvtq3pUduow/wfkKTI1VLONrjyIxI\nJIIZM2ZgzZo1yGaz6NseIQQSiQTa2trgOA6i0WhVLD1At4JoGAaSyaQ321AUBa7r4ve//z2+9KUv\nYcaMGdA0Dbquw3Vd6LoO0zShqioURZE7ujjhKMMEJ6+wIurOxTTQrhkpM+SM+fLLL8dPf/pTEFGo\nkYiDYNs2FEVBJpPB//7v/2LVqlW48cYbIYSApmmDcgeojKCfK0OlTCciZLNZqKoKTdO+sID1SMxs\npnuMGDlypJfEtT+mTZuGJUuWQFGUqr5fx3EQj8d7Jc+Wu4EPOuggzJgxA/F43Ou3crzQdb373eck\nHCUiJJPJbXbaqaqKRCKBjRs3es+tkkhl4s0338TBBx8MIUTeZOFCCMRiMVxwwQW45ZZbvO+2AOGN\nmVCg4vcAAASbSURBVGFqUAELEX2Rv8NxHDr11FP7jb3Q3NxMb7zxBpmmSZlMplcAq0oi/XpaWlo8\na080GqVTTjnli7Vnf1R7xsyFSz2WvGzYsCHQxghpnT333HO9XZYF4msx1aJPD7Asi7Zs2eKtFKCP\nb0xzczNlMhnPqlQtZ3XTNOmAAw7wgmXquk5f/vKX/fsZ5dy3bdt01VVX9evXJKM6V7PvOo7Ta7XD\nzzcYiUSovb3d++6y2ayXzaDPOwtNjlTN0oOcWZvU+A3DwPe+9z3cc889XzRQCCSTSViWBcdxMH78\neHz00UeexaeiDe5pk+M428xOiKhgXIwc2NLDMMHJK6zS6TRGjRrVK35LoRxF0vrqui6mTJmCjz76\nyPs9U0P0sXg4juPJ4UQiAdd1e71nTdPgui6EEHj44Ydx4oknAqj8e3Ucx/PtkRYYad3zlW08574B\nIJvNenHt+vbrk046CQ8//HDV+q7rukgkEnAcx3tHhYhEIrAsyxvrVVXFYYcdhieffLLvik5oY2ZN\nfNlS8MTjcdx2222wbRsHHnigZ97t6uqC67pQFAXr1q3D3Xff7Qm2SiptMuCgruvecpX8naqq1U+k\nxjBDmHg8jq6uLjz77LMYPXo0Vq9ejaamJm/Akd+tRJrUZfC71atX47nnnqtK2xn/yKU/GczQsiys\nXbsWI0eORDQaBQBvEkpEOOmkk+A4TlXks6qqiMVi0HXdG8T79sMgxGIxbN68Gbque/1X1vvYY49B\n0zQcdNBBgYL9hoUMDmqapveOCmGapjeGExFc18Xzzz+Pjo6Oso3tNWHpyUVmWJe7nqQ/jNTqpa9M\nrjZbh8pG3TWYYWqAvMJKygjTNHvNINvb27HddtttM/OUA6YQAlOnTsXHH38MwzBKGpSYMtHH4tGX\n3HGMiDxLSDQa9d5pXUbJ7+e+bdvGypUrsdtuuwGA5z8jrSUAcM899+DMM8+sZEt7IQ0Zfb+5gcbq\n3PcnI6VHIpGyWHpqTukZIrDSwzDBKUlm2LYNx3FgGAYsy8Lw4cM9oVqHE6ehRQGlZ9CS574//vhj\n7LTTTojH4146FanYvfXWW9hrr70q184ciAhNTU1IpVJem+TvhRCIRCKehUdaqQ4//HAcd9xxOOec\nc6AoSn9WIlZ66hyWsAwTnJJkhrQg17mVeGjCSs82SMvm008/jbfffhvr168HEeEXv/iF5+tUDYgI\n9913HzZu3AhN0zBt2jRMnToVY8aMQXNzs2cFyvXNisfj3v+l60gfWOmpc1jSMkxwhrLMGNqw0jPU\nCW3MrE7wAoZhGIYJCk8XmRKppqWHYRiGYRimYtSZKzvDMAzDMExxsNLDMAzDMMyQgJUehmEYhmGG\nBKz0MAzDMAwzJGClh2EYhmGYIQErPQzDMAzDDAlY6WEYhmEYZkjASg/DMAzDMEMCVnoYhmEYhhkS\nsNLDMAzDMMyQgJUehmEYhmGGBKz0MAzDMAwzJGClh2EYhmGYIQErPQzDMAzDDAlY6WEYhmEYZkjA\nSg/DMAzDMEMCVnoYhmEYhhkSsNLDMAzDMMyQgJUehmEYhmGGBKz0MAzDMAwzJPj/UjUB+TUyJvwA\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f36c1a7a190>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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o6XQauq5j+/btFTmuVHSk31Q2m0UsFqtKhLBMU7B8+fIBOXY8Hq/4McqlZhQf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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f36c193f290>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from skimage.feature import match_template\n",
    "\n",
    "def matchandplot( image, template, color ):\n",
    "    \"Match a template using [...] normalized correlation. \\\n",
    "    The output is an array with values between -1.0 and 1.0. \\\n",
    "    The value at a given position corresponds to the correlation coefficient between the image and the template. \\\n",
    "    [...] Matches correspond [...] to the top-left corner of the template.\\\n",
    "    To find the best match one must search for peaks in the response (output) image.\"\n",
    "    \n",
    "    response = match_template(image, template)\n",
    "    # search for peaks in the response.\n",
    "    ij = np.unravel_index(np.argmax(response), response.shape)\n",
    "    x, y = ij[::-1]\n",
    "    \n",
    "    # plot\n",
    "    fig = plt.figure(figsize=(12, 2))\n",
    "    ax1 = plt.subplot(1, 2, 1)\n",
    "    ax2 = plt.subplot(1, 2, 2, adjustable='box-forced')\n",
    "\n",
    "    ax1.imshow(template, cmap=plt.cm.gray)\n",
    "    ax1.set_axis_off()\n",
    "    ax1.set_title('Template')\n",
    "\n",
    "    ax2.imshow(image, cmap=plt.cm.gray)\n",
    "    ax2.set_axis_off()\n",
    "    ax2.set_title('Image')\n",
    "    # highlight matched region\n",
    "    h, w = template.shape\n",
    "    rect = plt.Rectangle((x, y), w, h, edgecolor=color, facecolor='none', lw=2)\n",
    "    ax2.add_patch(rect)\n",
    "    \n",
    "    plt.show()\n",
    "    return\n",
    "\n",
    "for member in thebeatles:\n",
    "    matchandplot( silhouette, member[0], member[1] )"
   ]
  },
  {
   "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": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}