{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Intro to Convolutions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Set up"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import math,sys,os,numpy as np\n",
    "from numpy.linalg import norm\n",
    "from PIL import Image\n",
    "from matplotlib import pyplot as plt, rcParams, rc\n",
    "from scipy.ndimage import imread\n",
    "from skimage.measure import block_reduce\n",
    "import pickle as pickle\n",
    "from scipy.ndimage.filters import correlate, convolve\n",
    "rc('animation', html='html5')\n",
    "rcParams['figure.figsize'] = 3, 6\n",
    "%precision 4\n",
    "np.set_printoptions(precision=4, linewidth=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plots(ims, interp=False, titles=None):\n",
    "    ims=np.array(ims)\n",
    "    mn,mx=ims.min(),ims.max()\n",
    "    f = plt.figure(figsize=(12,24))\n",
    "    for i in range(len(ims)):\n",
    "        sp=f.add_subplot(1, len(ims), i+1)\n",
    "        if not titles is None: sp.set_title(titles[i], fontsize=18)\n",
    "        plt.imshow(ims[i], interpolation=None if interp else 'none', vmin=mn,vmax=mx)\n",
    "\n",
    "def plot(im, interp=False):\n",
    "    f = plt.figure(figsize=(3,6), frameon=True)\n",
    "    # plt.show(im)\n",
    "    plt.imshow(im, interpolation=None if interp else 'none')\n",
    "\n",
    "plt.gray()\n",
    "plt.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## MNIST Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.datasets import fetch_mldata\n",
    "mnist = fetch_mldata('MNIST original')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys(['DESCR', 'COL_NAMES', 'target', 'data'])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mnist.keys()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((70000, 784), (70000,))"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mnist['data'].shape, mnist['target'].shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((70000, 28, 28), (70000,))"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "images = np.reshape(mnist['data'], (70000, 28, 28))\n",
    "labels = mnist['target'].astype(int)\n",
    "n=len(images)\n",
    "images.shape, labels.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "images = images/255"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAM0AAADKCAYAAAAGucTRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\ngiVI6GTUAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc9cd605f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(images[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "labels[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc9cdda2fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plots(images[:5], titles=labels[:5])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we can zoom in on part of the image"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAM0AAADKCAYAAAAGucTRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc9cd595400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(images[0,0:14, 8:22])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Edge Detection"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will look at how to create an Edge detector:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAANgAAADKCAYAAADHPo59AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc9cd88c4e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "top=[[-1,-1,-1],\n",
    "     [ 1, 1, 1],\n",
    "     [ 0, 0, 0]]\n",
    "\n",
    "plot(top)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.1882,  0.9333,  0.9882,  0.9882],\n",
       "       [ 0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.149 ,  0.6471,  0.9922,  0.9137,  0.8157],\n",
       "       [ 0.    ,  0.    ,  0.    ,  0.    ,  0.0275,  0.698 ,  0.9882,  0.9412,  0.2784,  0.0745],\n",
       "       [ 0.    ,  0.    ,  0.    ,  0.    ,  0.2235,  0.9882,  0.9882,  0.2471,  0.    ,  0.    ],\n",
       "       [ 0.    ,  0.    ,  0.    ,  0.    ,  0.7765,  0.9922,  0.7451,  0.    ,  0.    ,  0.    ],\n",
       "       [ 0.    ,  0.    ,  0.    ,  0.298 ,  0.9647,  0.9882,  0.4392,  0.    ,  0.    ,  0.    ],\n",
       "       [ 0.    ,  0.    ,  0.    ,  0.3333,  0.9882,  0.902 ,  0.098 ,  0.    ,  0.    ,  0.    ],\n",
       "       [ 0.    ,  0.    ,  0.    ,  0.3333,  0.9882,  0.8745,  0.    ,  0.    ,  0.    ,  0.    ],\n",
       "       [ 0.    ,  0.    ,  0.    ,  0.3333,  0.9882,  0.5686,  0.    ,  0.    ,  0.    ,  0.    ],\n",
       "       [ 0.    ,  0.    ,  0.    ,  0.3373,  0.9922,  0.8824,  0.    ,  0.    ,  0.    ,  0.    ],\n",
       "       [ 0.    ,  0.    ,  0.    ,  0.3333,  0.9882,  0.9765,  0.5725,  0.1882,  0.1137,  0.3333],\n",
       "       [ 0.    ,  0.    ,  0.    ,  0.3333,  0.9882,  0.9882,  0.9882,  0.898 ,  0.8431,  0.9882],\n",
       "       [ 0.    ,  0.    ,  0.    ,  0.1098,  0.7804,  0.9882,  0.9882,  0.9922,  0.9882,  0.9882],\n",
       "       [ 0.    ,  0.    ,  0.    ,  0.    ,  0.098 ,  0.502 ,  0.9882,  0.9922,  0.9882,  0.5529],\n",
       "       [ 0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ],\n",
       "       [ 0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ],\n",
       "       [ 0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ],\n",
       "       [ 0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ]])"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dims = np.index_exp[10:28:1,3:13]\n",
    "images[0][dims]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "corrtop = correlate(images[0], top)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.1882,  0.9216,  0.9765,  0.7843, -0.2392],\n",
       "       [ 0.    ,  0.    ,  0.    ,  0.    ,  0.149 ,  0.6078,  0.6667,  0.4431, -0.1882, -0.6196],\n",
       "       [ 0.    ,  0.    ,  0.    ,  0.0275,  0.5765,  0.9176,  0.8392, -0.3451, -1.4275, -1.5961],\n",
       "       [ 0.    ,  0.    ,  0.    ,  0.1961,  0.4863,  0.4863, -0.4039, -0.9725, -1.0471, -0.4627],\n",
       "       [ 0.    ,  0.    ,  0.    ,  0.5529,  0.5569,  0.3137, -0.4863, -0.4902, -0.2471,  0.    ],\n",
       "       [ 0.    ,  0.    ,  0.298 ,  0.4863,  0.4824, -0.1216, -0.3098, -0.3059,  0.    ,  0.    ],\n",
       "       [ 0.    ,  0.    ,  0.0353,  0.0588, -0.0275, -0.4039, -0.4275, -0.3412,  0.    ,  0.    ],\n",
       "       [ 0.    ,  0.    ,  0.    ,  0.    , -0.0275, -0.1255, -0.1255, -0.098 ,  0.    ,  0.    ],\n",
       "       [ 0.    ,  0.    ,  0.    ,  0.    , -0.3059, -0.3059, -0.3059,  0.    ,  0.    ,  0.    ],\n",
       "       [ 0.    ,  0.    ,  0.0039,  0.0078,  0.3216,  0.3176,  0.3137,  0.    ,  0.    ,  0.    ],\n",
       "       [ 0.    ,  0.    , -0.0039, -0.0078,  0.0863,  0.6627,  0.8549,  0.8745,  0.6353,  1.1451],\n",
       "       [ 0.    ,  0.    ,  0.    ,  0.    ,  0.0118,  0.4275,  1.1373,  1.8549,  2.0941,  1.6745],\n",
       "       [ 0.    ,  0.    , -0.2235, -0.4314, -0.4314, -0.2078,  0.0941,  0.2392,  0.2392,  0.0706],\n",
       "       [ 0.    ,  0.    , -0.1098, -0.7922, -1.2784, -1.1686, -0.4863,  0.    , -0.4353, -1.2039],\n",
       "       [ 0.    ,  0.    ,  0.    , -0.098 , -0.6   , -1.5882, -2.4824, -2.9686, -2.5333, -1.6863],\n",
       "       [ 0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ],\n",
       "       [ 0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ],\n",
       "       [ 0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ]])"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "corrtop[dims]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAM0AAADKCAYAAAAGucTRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nERogiNAAQf8FqjqkxkDdheQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc9cd5ec4a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(corrtop)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1,  1,  0],\n",
       "       [-1,  1,  0],\n",
       "       [-1,  1,  0]])"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.rot90(top, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAM0AAADKCAYAAAAGucTRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nERogiNAAQf8FqjqkxkDdheQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc9cd5bb2b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "convtop = convolve(images[0], np.rot90(top,2))\n",
    "plot(convtop)\n",
    "np.allclose(convtop, corrtop)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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lX1y9ew+sewEzjb7+ZL2PQXbXZ/T1J7K7G77u6ye3u+Prvn4b8RgWfXMgAADsV64cCAAA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\ngAkUZwAAmEBxBgCACf4NIdf5/MfjwlcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc9cd8e0940>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "straights=[np.rot90(top,i) for i in range(4)]\n",
    "plots(straights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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h72yu0R/DJqx/tNyu1rX2v7c5Rl9/sjmPYZFP1aiq65J8JcmfXPxDkCTd/XJ3b69un0hy\nXVXdsMTcMIfsMirZZURyy+iW+FSNSvJHSb7T3X9wiTFvWY1LVd2+mvfFuXPDHLLLqGSXEcktB8ES\nn6rxa0l+I8lfV9UTq/t+L8mRJOnu+5N8IMlHqup8kp8kuaeXfHH13h1f9wJmGn39yXofg+yuz+jr\nT2R3L3zf109u98b3ff024jEs+uZAAAA4qFw5EAAAJlCcAQBggquyOFfVe6vqu1V1uqo+ue71XK6q\neqCqnq+qb697LXsx5bKr7E5210t2905210t290Zu12sTc3vVvca5qq5J8j+TvCcXPmD90SQf3OWS\nnxurqv5pku0kD3X3O9e9nstVVTcmuXHnZVeT/PpI34N1kN31k929kd31k93LJ7frt4m5vRqfcb49\nyenu/l53/zTJl5PcveY1XZbufiTJD9a9jr1y2dU9k901k909k901k909kds128TcXo3F+aYkz+7Y\nPhMnj7WpC5dd/eUkf7XelQxBdjeI7F4W2d0gsjuZ3G6QTcnt1Vic2RCry65+JcnvdPfL614PTCW7\njEp2GdEm5fZqLM5nk9yyY/vm1X3so9e67Cq7kt0NILt7IrsbQHYvm9xugE3L7dVYnB9NcrSq3lZV\nr0tyT5KH17ymq8qUy66yK9ldM9ndM9ldM9ndE7lds03M7VVXnLv7fJKPJflaLrzI/D9096n1rury\nVNWXkvzXJD9fVWeq6l+ve02X6WeXXf3nVfXE6uuudS9q08nuRpDdPZDdjSC7l0luN8LG5faq+zg6\nAADYi6vuGWcAANgLxRkAACZQnAEAYALFGQAAJlCcAQBgAsUZAAAmUJwBAGCC/wepJTYbNznzsAAA\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc9cdacafd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "br=[[ 0, 0, 1],\n",
    "    [ 0, 1,-1.5],\n",
    "    [ 1,-1.5, 0]]\n",
    "\n",
    "diags = [np.rot90(br,i) for i in range(4)]\n",
    "plots(diags)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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EITWOq+te0x8Iq3G1Ald7aDKkpF0i2GtPw6lFMHv2bKxduzY3tm7dOsQYD6EH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\nY4wxxpja8v9i029ma30TLQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fca00481860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rots = straights + diags\n",
    "corrs = [correlate(images[0], rot) for rot in rots]\n",
    "plots(corrs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "eights=[images[i] for i in range(n) if labels[i]==8]\n",
    "ones=[images[i] for i in range(n) if labels[i]==1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc9cd703128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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3HwQKev/hyDAAAACixTAMAACAaDEMAwAAIFoMwwAAAIgWwzAAAACixTAMAACAaDEMAwAA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\nNSiMAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc9cd5216d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plots(eights[:5])\n",
    "plots(ones[:5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def normalize(arr): return (arr-arr.mean())/arr.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "filts8 = np.array([ims.mean(axis=0) for ims in pool8])\n",
    "filts8 = normalize(filts8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAArwAAABqCAYAAABeQoJYAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nHzN8h1mcMyu+AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc9cd8e6da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plots(filts8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pool1 = [np.array([pool(correlate(im, rot)) for im in ones]) for rot in rots]\n",
    "filts1 = np.array([ims.mean(axis=0) for ims in pool1])\n",
    "filts1 = normalize(filts1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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UOeHMHKMOdIwM80ADfMzMnjazn5rZah/tziVS5oEGeW0EcpqTDPNAg7zmIsPc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\nIXKgDrQQQgghhBA5+P+DE9hOFpm8qAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0aa6ef2b50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plots(filts1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def pool_corr(im): return np.array([pool(correlate(im, rot)) for rot in rots])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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0yGu1erWPOo3IgQMHvFarV/uo04jU19d7rVavecTKRYSxq0CBQpxhIcmTQd4J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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0aa77da8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plots(pool_corr(eights[0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def sse(a,b): return ((a-b)**2).sum()\n",
    "def is8_n2(im): return 1 if sse(pool_corr(im),filts1) > sse(pool_corr(im),filts8) else 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(126.77776, 181.26105)"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sse(pool_corr(eights[0]), filts8), sse(pool_corr(eights[0]), filts1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[5223, 287]"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[np.array([is8_n2(im) for im in ims]).sum() for ims in [eights,ones]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[166, 5892]"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[np.array([(1-is8_n2(im)) for im in ims]).sum() for ims in [eights,ones]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def n1(a,b): return (np.fabs(a-b)).sum()\n",
    "def is8_n1(im): return 1 if n1(pool_corr(im),filts1) > n1(pool_corr(im),filts8) else 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "[np.array([is8_n1(im) for im in ims]).sum() for ims in [eights,ones]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "[np.array([(1-is8_n1(im)) for im in ims]).sum() for ims in [eights,ones]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python [conda root]",
   "language": "python",
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