convolution-intro.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "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 cPickle as pickle\n",
    "from scipy.ndimage.filters import correlate, convolve\n",
    "from ipywidgets import interact, interactive, fixed\n",
    "from ipywidgets.widgets import *\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": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "from tensorflow.examples.tutorials.mnist import input_data\n",
    "mnist = input_data.read_data_sets(\"MNIST_data/\")\n",
    "images, labels = mnist.train.images, mnist.train.labels\n",
    "images = images.reshape((55000,28,28))\n",
    "np.savez_compressed(\"MNIST_data/train\", images=images, labels=labels)\n",
    "\"\"\"\n",
    "1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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.imshow(im, interpolation=None if interp else 'none')\n",
    "\n",
    "plt.gray()\n",
    "plt.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(55000, 28, 28)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = np.load(\"MNIST_data/train.npz\")\n",
    "images=data['images']\n",
    "labels=data['labels']\n",
    "n=len(images)\n",
    "images.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f70c9799c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(images[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "labels[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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OSVqzkvac1GNW0pgTspK+nKQ1K0nnpBJZSWtOKpWVNOakElmppXNKa7zCu5+k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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f707da67fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plots(images[:5], titles=labels[:5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAANoAAADICAYAAACOA/9LAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAC9VJREFUeJzt3XuIXPUZxvHvEzUiqNEoXjCaBI1YpRIVNGohEREvFFNE\n0bZg1IIiikKhVYpYtaVV/6pWRaRWVJBU8oeu91jjItZrTWJsNbrCeosaITFYL5Q0vv1jflmGycxe\n5px5dyd5PjDsmT2/nfecTZ49Z878eI8iAjPrrWmTvQFmOwIHzSyBg2aWwEEzS+CgmSVw0MwSVAqa\npL0lLZf0rqRnJM3oMG6LpJWSVkl6pEpNs36kKp+jSboF2BARt0q6Btg7Iq5tM+6riNizwnaa9bWq\nQVsLLIyI9ZIOAAYj4og24/4TEXtU2E6zvlb1Pdp+EbEeICI+B/brMG5XSa9JeknS4oo1zfrOzmMN\nkPQssH/zt4AArmszvNPhcXZEfCZpLrBC0pqIGG5Ty/PBbEqLCHXzc2MGLSJO67RO0npJ+zedOn7R\n4TU+K1+HJQ0CxwDbBM1sqpo3bx5DQ0Nd/3zVU8cB4KKyvAR4tHWApL0kTS/L+wInAW9XrGvWV6oG\n7RbgNEnvAqcCNwNIOk7SPWXMD4B/SloFPAf8MSLWVqxr1lcqXXWsm9+j2VS19dSx2/donhlilsBB\nM0vgoJklcNDMEjhoZgkcNLMEDppZAgfNLIGDZpbAQTNL4KCZJXDQzBI4aGYJHDSzBA6aWQIHzSyB\ng2aWwEEzS+CgmSWoJWiSzpC0VtJ7pTV46/rpkpZKGpL0sqRD6qhr1i8qB03SNOAO4HTgKOCnklrb\ngv8C2BgR84A/AbdWrWvWT+o4oh0PDEXEhxGxGVgKtLb9XgzcX5aX0WhNZ7bDqCNoBwEfNz3/pHyv\n7ZiI2AJskjSzhtpmfWGyLoZ01RvPbLJs2LCh0s/XEbR1QPPFjVnle80+AQ4GkLQTsGdEbKyhtlmK\nffbZp9LP1xG014HDJM0uPfYvoNGTv9ljNHrzA5wHrKihrlnfGPNuMmOJiC2SrgSW0wjuvRHxjqQb\ngdcj4nHgXuBBSUPABhphNNthuPe+2Ti4975ZH3DQzBI4aGYJHDSzBA6aWQIHzSyBg2aWwEEzS+Cg\nmSVw0MwSOGhmCRw0swQOmlkCB80sgYNmlsBBM0vgoJklcNDMEjhoZgmyeu8vkfSFpJXlcUkddc36\nReUuWE29908FPgVel/RoRKxtGbo0Iq6qWs+sH2X13gd3J7YdWFbvfYBzJK2W9LCkWTXUNesblU8d\nx2kAeCgiNku6lMadZdreUeb6668fWV60aBGLFi1K2UCzVoODgwwODo48v+mmm7p+rcoNVCUtAG6I\niDPK82uBiIhbOoyfRuNeaXu1WRfff/99pe0x65Vp06ZNagPVMXvvSzqg6eli4O0a6pr1jaze+1dJ\nOhvYDGwELqpa16yfTLne+z51tKlqsk8dzWwMDppZAgfNLIGDZpbAQTNL4KCZJXDQzBI4aGYJHDSz\nBA6aWQIHzSyBg2aWwEEzS+CgmSVw0MwSOGhmCRw0swQOmlkCB80sQV299++VtF7SmlHG3C5pqDRR\nnV9HXbN+UdcR7T7g9E4rJZ0JHBoR84DLgLtrqmvWF2oJWkS8CHw5ypDFwANl7KvADEn711HbrB9k\nvUdr7c+/jvb9+c22S1m998fthhtuGFl2732bTK2996uorYGqpNnAYxFxdJt1dwPPR8TfyvO1wMKI\nWN8yzg1UbcqaKg1URed7oA0AF8LITTE2tYbMbHtWy6mjpIeARcA+kj4CfgtMp3FXmXsi4klJZ0l6\nH/gGuLiOumb9wr33zcZpqpw6mlkHDppZAgfNLIGDZpbAQTNL4KCZJXDQzBI4aGYJHDSzBA6aWQIH\nzSyBg2aWwEEzS+CgmSVw0MwSOGhmCRw0swQOmlkCB80sQUrvfUkLJW2StLI8rqujrlm/qKuB6n3A\nnyltvzt4ISLOrqmeWV/J6r0PnXs+mm33Mt+jLZC0StITko5MrGs26bJ6778BzI6Ib8stnB4BDm83\n8JRTThlZnjNnDnPnzs3ZQrMWw8PDfPDBBwDstttulV4rJWgR8XXT8lOS7pI0MyI2to5tDprZZJo7\nd+7IH/qZM2fy9NNPd/1aKb33m++FJul4Gh2StwmZ2fYqpfc+cK6ky4HNwHfA+XXUNesXtQQtIn42\nxvo7gTvrqGXWjzwzxCyBg2aWwEEzS+CgmSVw0MwSOGhmCRw0swQOmlkCB80sgYNmlsBBM0vgoJkl\ncNDMEjhoZgkcNLMEDppZAgfNLIGDZpbAQTNLUDlokmZJWiHp35LeknRVh3G3SxqStFrS/Kp1zfpJ\nHc15/gf8MiJWS9odeEPS8ohYu3VAaZp6aETMk3QCcDewoIbaZn2h8hEtIj6PiNVl+WvgHeCglmGL\nKTfAiIhXgRnNvR7Ntne1vkeTNAeYD7zasuog4OOm5+vYNoxm263aWoKX08ZlwNXNLcAn6vnnnx9Z\ndu99m0xTrve+pJ1phOzBiHi0zZB1wMFNz2eV723DvfdtqpiKvff/CrwdEbd1WD8AXAggaQGwKSLW\n11TbbMqrfESTdDLwc+AtSauAAH4DzKb03o+IJyWdJel94Bvg4qp1zfpJ5aBFxD+AncYx7sqqtcz6\nlWeGmCVw0MwSOGhmCRw0swQOmlkCB80sgYNmlsBBM0vgoJklcNDMEjhoZgkcNLMEDppZAgfNLIGD\nZpbAQTNL4KCZJXDQzBI4aGYJUnrvS1ooaZOkleVxXdW6dRgeHnY910tRxxFta+/9o4ATgSskHdFm\n3AsRcWx5/L6GupVtbY7peq7Xa1m99wFUtZZZv6qtJTiM2nsfYEHp+/gp8KuIeLvdaxx44IF1btKo\n9thjD9dzvXGZMWNGpZ9XRNSyIaX3/iDwu9a24GXd9xHxbbmF020RcXib16hnY8x6JCK6OjOrJWil\n9/7jwFOjtAVvHj8MHBcRGysXN+sDKb33m++FJul4GgF3yGyHkdJ7HzhX0uXAZuA74Pyqdc36SW3v\n0cyss0mdGSJpb0nLJb0r6RlJbS/tSNpSPuheJemRLuqcIWmtpPckXdNm/XRJS8vN7F+WdEg3+zOB\nekskfdH0Af4lFWrdK2m9pDWjjLm97NtqSfO7rTWeenVPThjPhIgyrpZ97NkEjIiYtAdwC/DrsnwN\ncHOHcV9VqDENeJ/GqewuwGrgiJYxlwN3leXzgaU9rrcEuL2m3+GPaHyksqbD+jOBJ8ryCcArPa63\nEBio8f/IAcD8srw78G6b32dt+zjOehPex8me67gYuL8s3w/8pMO4Kh92Hw8MRcSHEbEZWFrqdtqO\nZcCpPa4HNX2AHxEvAl+OMmQx8EAZ+yowo/niVA/qQY2TE2J8EyJq28dx1oMJ7uNkB22/KHf+jIjP\ngf06jNtV0muSXpLU7j/taFpvVP8J2/7iRsZExBZgk6SZE6wzkXoA55TTnIclzeqyVjfbs67D9tRp\nQTnNf0LSkXW96CgTInqyj+OZgDHefax1Zkg7kp4Fmv+6iMaVyXbntZ2uzMyOiM8kzQVWSFoTEb2c\nUdrr6WIDwEMRsVnSpTSOplWOolPJGzT+vbZOTngE2GZywkSVSQ/LgKvLkaanxqg34X3s+REtIk6L\niKObHj8sXweA9VsP8ZIOAL7o8Bqfla/DNGafHDOBTVgHNF/caHej+k8oN7OXtBOwZ3T/Od+Y9SLi\ny3JaCfAX4Lgua413ew4ebXvqFBFfR8S3ZfkpYJcKZwfAyISIZcCD0TLrqKh1H8eq180+Tvap4wBw\nUVleAmyzU5L2kjS9LO8LnAS0nSfZwevAYZJml9e5oNRt9lipD3AesGICrz/heuWPylaLmdj+tCM6\nH4UHgAtL3QXApq2n672o16PJCaNOiKD+fax/AkZdV4e6vMIzE/g7jSs7y4G9yvePA+4pyycCa4BV\nwJvARV3UOaPUGAKuLd+7EfhxWd4VeLisfwWYU3G/xqr3B+BfZZ+eAw6vUOshGhO1/wt8BFwMXAZc\n2jTmDhpXQt8Ejq24b6PWA65o2reXgBMq1jsZ2ELj6u0qYGX5/fZkH8dTr5t99AfWZgkm+9TRbIfg\noJklcNDMEjhoZgkcNLMEDppZAgfNLMH/AVxfpJwpw1R/AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f707d721410>"
      ]
     },
     "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": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMYAAADFCAYAAAAPD43zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nxCf7gzWvTgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f707d705dd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "r=(0,28)\n",
    "def zoomim(x1=0,x2=28,y1=0,y2=28):\n",
    "    plot(images[0,y1:y2,x1:x2])\n",
    "w=interactive(zoomim, x1=r,x2=r,y1=r,y2=r)\n",
    "w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 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.    ],\n",
       "       [ 0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ],\n",
       "       [ 0.    ,  0.    ,  0.    ,  0.3529,  0.5412,  0.9216,  0.9216,  0.9216,  0.9216,  0.9216],\n",
       "       [ 0.    ,  0.    ,  0.549 ,  0.9843,  0.9961,  0.9961,  0.9961,  0.9961,  0.9961,  0.9961],\n",
       "       [ 0.    ,  0.    ,  0.8863,  0.9961,  0.8157,  0.7804,  0.7804,  0.7804,  0.7804,  0.5451],\n",
       "       [ 0.    ,  0.    ,  0.149 ,  0.3216,  0.051 ,  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.    ]], dtype=float32)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "k=w.kwargs\n",
    "dims = np.index_exp[k['y1']:k['y2']:1,k['x1']:k['x2']]\n",
    "images[0][dims]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "corrtop = correlate(images[0], top)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 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.    ],\n",
       "       [ 0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ,  0.    ],\n",
       "       [ 0.    ,  0.    ,  0.3529,  0.8941,  1.8157,  2.3843,  2.7647,  2.7647,  2.7647,  2.7647],\n",
       "       [ 0.    ,  0.549 ,  1.1804,  1.6353,  1.1608,  0.6039,  0.2235,  0.2235,  0.2235,  0.2235],\n",
       "       [ 0.    ,  0.3373,  0.349 ,  0.1686, -0.3843, -0.6118, -0.6471, -0.6471, -0.8824, -1.4235],\n",
       "       [ 0.    , -0.7373, -1.4118, -2.1765, -2.2196, -2.3255, -2.3412, -2.3412, -2.1059, -1.5647],\n",
       "       [ 0.    , -0.149 , -0.4706, -0.5216, -0.3725, -0.051 ,  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.    ]], dtype=float32)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "corrtop[dims]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMYAAADlCAYAAAAIo4jFAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nCYoBJCgGkKAYQIJiAAmKAST+C2jpey2QKzvpAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0aa7ba7a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(corrtop[dims])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMYAAADFCAYAAAAPD43zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n8T87q+KmGathOwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0aa7d041d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(corrtop)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1,  1,  0],\n",
       "       [-1,  1,  0],\n",
       "       [-1,  1,  0]])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.rot90(top, 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMYAAADFCAYAAAAPD43zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAADU1JREFUeJzt3U1sVWUaB/D/H6EqrdgP4FZbvlqVLkSJmXEDCydjDJkN\nxsXEOAu/Ylw44ySzAJ0NiXGhLEgmk7hRx+BkjJmZxAETI2hmVYxDM3wUZ9oi0g9a2gsGBOpHA+WZ\nxT0wl/Z54X6dc8+9/n9Jw+Xfw3nfU3g49773nOfSzCAi11pQ7QmIpJEKQ8ShwhBxqDBEHCoMEYcK\nQ8RRVmGQ3ERykORRklsrNSmRamOp72OQXADgKICfAzgJoA/A42Y2OGc7vVEiqWVm9PKFZezzQQBf\nmtkoAJB8H8BmAINzN9yyZQsAoLe3Fxs3bixjyNJo3Podt5wxt2/fHvxeOU+lOgCcyPv9eJSJ1Lxy\nzhgF6+3tBQCMjY1hbGwMK1euTGJYkWtc+fdXiHIKYwJA/r/wziib58qprlpFUa1C1LjpGnPlypXX\nbP/ZZ58Fty3nqVQfgLtIriLZAOBxALtvNLFq0Lj1O25cY5Z8xjCzWZK/BrAXuQJ728wGKjYzkSoq\n6zWGmX0MYG2F5iKSGnrnW8ShwhBxqDBEHCoMEYcKQ8ShwhBxqDBEHCoMEYcKQ8ShwhBxqDBEHCoM\nEYcKQ8ShwhBxqDBEHCoMEYcKQ8ShwhBxqDBEHCoMEYcKQ8RRVpcQkiMAzgG4DOCimT1YiUmJVFu5\nLTovA3jIzM5WYjIiaVHuUylWYB8iqVPuP2oDsIdkH8nnKjEhkTQo96nUBjObJLkMwCckB8ysd+5G\nV7qdA/Mb64okJalu5zCzyejX0yQ/QO7DZOYVRjU+xERkrkS6nZNcTLIpetwI4BEAX5S6P5E0KeeM\nkQHwQfQZewsB/MXM9lZmWiLVVc7HAAwDWF/BuYikhpZaRRwqDBGHCkPEocIQcSTyccY/Jq2trUXl\nt99+u5svWrTIzWdmZtz83Llzbp7NZt3822+/dXPJ0RlDxKHCEHGoMEQcKgwRhwpDxJG6VamWlhY3\n7+jocPN169a5+YoVK9w8tDpUKaHVoW+++cbNL1y44Oazs7Nu3tDQ4OZNTU1u3tjY6OYjIyNu3t/f\n7+ZHjx5188uXL7t5rdMZQ8ShwhBxqDBEHCoMEYcKQ8RRtVWp0CpTqFFCJpNx89HRUTfPb8CQ78yZ\nMwXMrnSh1aRiczNz8wUL/P/LQvltt93m5qtWrXLzW265xc27urrc/Pjx4/Oyelip0hlDxKHCEHGo\nMEQcKgwRxw0Lg+TbJLMk+/OyFpJ7SQ6R3EPSv9tGpEYVsir1DoA/Ang3L3sJwKdmtp3kVgAvR1nB\nQneQDQ4OuvnBgwfd/MSJE27+3XffuXmxKybT09NufvLkSTefmJhw89C1UsUqdpVp7dq1bh46rtD2\noWux1qxZMy8bHh52t62l1aobnjGiXrRz2/xvBrAzerwTwKMVnpdIVZX6GmO5mWUBwMymACyv3JRE\nqq9Sb/D570ZF1O1c0iCJbudZkhkzy5JsB3Dqehur27mkQRzdzhl9XbEbwFPR4ycB7CpqhiIpd8Mz\nBsn3ADwEoI3kGIBtAF4D8DeSzwAYBfDL6+3Du+6nr6/P3da79gYo/g6yixcvFjyX6wmtxoSu9brv\nvvvcfMmSJUWNGxJaTZqamnLzoaEhNz9//rybh67d6uzsdHPv5xnqlXX2bO18VOMNC8PMngh86+EK\nz0UkNfTOt4hDhSHiUGGIOFQYIo6q3cEXWuUIrQLde++9bn7zzTe7eXNzs5vfdNNNBcyu9oS6oE9O\nTha1n9C1Z0uXLi14H6FO7bVEZwwRhwpDxKHCEHGoMEQcKgwRRyKrUiTnZaH+Re3t7YnPpR6EVudW\nr15dkf2HPsuvXumMIeJQYYg4VBgiDhWGiEOFIeKo2rVS9bo6VC2ha5lCd9OFnDrl374f6gN26623\nFrzv0N2T33//fcH7SIrOGCIOFYaIQ4Uh4lBhiDhK7Xa+jeQ4yQPR16Z4pymSrFK7nQPADjPbUfkp\n1bbQ3WvLl/vtfUN3Jvb09Lj5smXL3PzcuXNuHurKfuTIETcPdWUPdY8P3YnpCfUAO3bsWMH7SEqp\n3c6BazsTitSVcl5jvEDyEMm39MExUm9KfYPvDQCvmJmRfBXADgDPhjZWt3NJg9i7nZvZ6bzfvgng\nw+ttr27nkgaxdzuPWv9f8RiAL4qboki6ldrt/Gck1wO4DGAEwPMxzrGqQp95l8lk3Pzuu+9281C3\n8zNnzrj5Rx995Oaha5lC3d2LzUNC1znt27evqP14Qitt1VRqt/N3YpiLSGronW8RhwpDxKHCEHGo\nMEQcVbuDr1pC/Ze6u7vdPLTK1NbW5uahN5D279/v5sPDw24eumYpdLdbqEv5+Pi4m4e6vnd1dbl5\n6OdQ7B2CtUJnDBGHCkPEocIQcagwRBwqDBFH3a5Khe6YC626hK6J+uqrr9w8dC3T4OCgm4+OjhaV\nX7hwwc1/+OEHNw8d75133unm99xzj5uHrukK9QGbnp52c09oJayhoaHgfSRFZwwRhwpDxKHCEHGo\nMEQcKgwRR92uSoW6cw8NDbl5qC/T4cOH3fzAgQNuPjMz4+bNzc1u/sADD7h5aJWptbXVzUMrO6Fu\n5MWuBIVWny5dulTwPkKrUmmkM4aIQ4Uh4lBhiDhUGCKOQrqdd5L8J8n/kDxC8sUobyG5l+QQyT1q\n0yn1pJBVqUsAfmdmh0g2Afg3yb0AngbwqZltJ7kVwMsAXopxrq5Qv6OBgQE3n5ycdPPQNVGhVaD7\n77/fzYu9FqtSQtcyhX4+s7OzRW0fWuUL7cezePHigrettkK6nU+Z2aHo8TSAAQCdADYD2BltthPA\no3FNUiRpRb3GILkawHoAnwPImFkWyBUPAH/hXaQGFfwGX/Q06u8Afmtm0yTnnnP9czDU7VzSoeLd\nzkkuRK4o/mxmu6I4SzJjZtmoybPfVBXqdi7pEEe38z8B+K+Z/SEv2w3gqejxkwB2zf1DIrWqkG7n\nGwD8CsARkgeRe8r0ewCvA/gryWcAjAL4ZZwTLVZ7e/uNN8pzxx13uPnChf6PKLR9SGjVKG4LFvj/\n94U+Dy+0yhTqc+UJXRMVujswjQrpdr4PQOjqr4crOx2RdNA73yIOFYaIQ4Uh4lBhiDhq/g6+0GrP\nokWL3HzFihWxjlstPT09br506dKi9tPX11f2XEJ3DdYSnTFEHCoMEYcKQ8ShwhBxqDBEHDW/KhWS\ntlWjuB0/ftzNQ5/xF+oHNTExUdS43nVRTU1NRe0jjXTGEHGoMEQcKgwRhwpDxKHCEHHU7apUvQp1\nTQ/dqRe6I6+/v9/Nz58/7+ahOxk7OzvnZfWwIqgzhohDhSHiUGGIOFQYIo5Sup3/Jsq3kRwneSD6\n2hT/dEWSUWq380+i7+0wsx3xTe/HK7SyU+xn54VWmULXSjU2Nrp5aDWsHq6L8hTSV2oKwFT0eJrk\nAICO6Nu1vy4n4ii12/m/ougFkodIvqUPjpF6Uk638zcAvGJmRvJVADsAPOv9WXU7lzRIpNu5mZ3O\n2+RNAB+G/ry6nUsaJNLtPGr9f8VjAL4obpoi6VVOt/MnSK4HcBnACIDnY5xn3Qp95l2oG/ng4KCb\nhz5DMPTUoaWlxc27u7uL2r4erovylNPt/OPKT0ckHfTOt4hDhSHiUGGIOFQYIg7dwVdjZmZm3Dz0\n+Xbr1q1z80wmU9R+6nX1KURnDBFHooVR6NvxGrc8X3/9dVXGrcbxxjWmCqMOx1VhlE9PpUQcibz4\n7ujI3b6xZMmSq4+TlOZxQ5eEhPLQx3hNT09ffZzNZtHV1QUg/KK5ra3NzUM3KhXy4rsaP+e4xmTo\nL6BiA5DxDiBSBjNzKz72whCpRXqNIeJQYYg4VBgijkQKg+QmkoMkj5LcmsSY0bgjJA+TPEhyf8xj\nvU0yS7I/L2shuZfkEMk9lW4YERgz9n5fTq+xF6M87uNNrseZmcX6hVzxHQOwCsAiAIcA9MQ9bjT2\ncQAtCY21EbkOKv152esAtkSPtwJ4LYExtyHXByzOY20HsD563ARgCEBPAscbGrfix5zEGeNBAF+a\n2aiZXQTwPoDNCYwL5PpeJXJWNLNeAGfnxJsB7Iwe7wTwaAJjAjH3+zKzKTM7FD2eBjAAoBPxH683\nbiw9zpL4R9MB4ETe78fx/4OJmwHYQ7KP5HMJjZlvuZllgauN65YnNG5i/b7yeo19DiCT1PHG3eOs\n3l98bzCznwD4BXI/uGr38UniTaM3AHSb2XrkOkjG1kJ1bq8xzD++WI7XGbfix5xEYUwAyO+w1hll\nsTOzyejX0wA+QO5pXZKyJDPA1XZDp+Ie0MxOW/QkHLl+Xz+NYxyv1xgSON5Qj7NKH3MShdEH4C6S\nq0g2AHgcwO64ByW5OPqfBSQbATyC+HtfEdc+190N4Kno8ZMAds39A5UeM8F+X/N6jSGZ402mx1mc\nqxd5qwmbkFtB+BLASwmNuQa5FbCDAI7EPS6A9wCcBDADYAzA0wBaAHwaHfteAM0JjPkugP7o2P+B\n3PP+Sh/rBgCzeT/fA9HfcWvMxxsat+LHrGulRBz1/uJbpCQqDBGHCkPEocIQcagwRBwqDBGHCkPE\n8T87q+KmGathOwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0aa78bdc90>"
      ]
     },
     "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": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6wWmnnTbQGsx/ctRIlSO7F1100cC27+DBg3r7298+sPmboPTnxllnndXX/VZ7dlfiuVH6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\nQAMAAAAJaKABAACABP8PMtOjLKq/PbAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0aa7ba7250>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "straights=[np.rot90(top,i) for i in range(4)]\n",
    "plots(straights)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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AEtBAAwAAAAlooAEAAIAENNAAAABAAhpoAAAAIAENNAAAAJCABhoAAABIQAMNAAAAJKCB\nBgAAABLQQAMAAAAJaKABAACABDTQAAAAQAIaaAAAACBB7Qba9gbb99v+he1HbN84z5gttk/afrja\nPlm3br8mJiYGOn9EFD3/5OTkQOdfqhq9KCm7Tfi6DHr+Qb+2Bz1/ipKyO+jnjdfG8OfvVUm5laSp\nqamBzl96vyCtrOPuXDnegf6LpI9HxGslvUnSR21fOs+4H0TEG6rtXzPU7cv3v//9YZUuwqAPGEtV\no0fFZLcJX5dBz7/CDuTFZHfQx1xeG8OfP0ExuZWW1fO2bK2w4+5ZajfQEfGbiDhc7f9e0mOS1s8z\n1HVrATmRXZSK7KJE5BZNsibnZLZfLukySQ/Mc/Nm24ckHZf0zxHxaM7ay8VLX/pSvexlLxvY/MeP\nHx/o/Oedd54uuOCCgc2/VDVS5cjuIB9TE74ug55/enp6YHMvZyv9uMtrY/jz92O5H3OlwT9vpfcL\nK15EZNkknS/pZ5K2d7ntvGp/q6SpLnMEG1uOjeyylbqRXbYSN3LLVurWb9/ryHCSue01ksYlfSsi\nPt/D+MclXR4Rz9QuDtRAdlEqsosSkVs0Ra6PsfuKpEe7vRhsX9Sxf4Uk82LAMkF2USqyixKRWzRC\n7XOgbb9F0nslPVKdsxSSbpa0STNvje+T9A7bH5Z0StKfJL2rbl2gLrKLUpFdlIjcokmynMIBAAAA\nrBRD/UuEtl9k+z7bk7a/Y3tdl3Gnqw9UP2T7nh7mvcr2UdtTtm+a5/a1tvfbPmb7x7Y39rH2xWpc\na/vpjg+D/0DC3LfbPmH7yAJjbqnWf9j2ZX2sf8EadT/MvpcPzK/zOIb9gfylZneQua3uP9Dsktv6\nyG7X+cluzfk55vZdg36hxOz2+9uHOTZJn5X0L9X+TZI+02Xc7xLmXCXpl5r5kdDzJB2WdOmcMR+W\n9F/V/rsk7U9cdy81rpV0S5/Py99q5uN9jnS5faukg9X+GyX9ZAA1tkg6UONre7Gky6r98yVNzvMc\n9f04epy/1mNoWnYHndulyC65Jbtkd2Vmt8TcLkV2B51bstt9G+o70JK2S7qj2r9D0t93GZfyoepX\nSDoWEb+KiFOS9ld1utW9W9KVCfP3WkPq88PgI+KHkp5dYMh2SXdWYx+QtM4dv3iRqYZU48Pso7cP\nzO/7cfQ4vzS4D+QvMbsDza00+OyS2yzI7jzIbpb5JY65/dSQ6BeKy+6wG+gLI+KENPMAJV3YZdzz\nbf/U9o9szxe8TuslPdFx+Umd+0TNjomI05JO2n5xwrp7qSFJb69+1PAN2xsS5k+tP92lfl2bqx+D\nHbT9mn4ncfcPzM/yOBaYX8r0GOZRYnaHndv51jCI7JLbhZHd/pDdxeeXOOb2U0OiX5BUVnaz/iXC\n+dj+rqTO7xKsmd+8ne/8km6/0bgpIp6y/QpJ99s+EhGP51xmxrnOOCDprog4Zft6zXwHm/qd6zA9\npJnn/Y+2t0q6R1IrdRLb52vmu/aPVd/5ZbXI/LUewwrNLrlV2bmt5ie7ZLe47K7Q3EpkV1J52R34\nO9AR8daIeF3H9jfVvwcknTjzFrztiyU93WWOp6p/H5c0Ien1C5ScltR5kv+G6rpOT0q6pKq7WtIL\nIu1zJhetERHPVj+ukaTbJF2eMH8v9S9ZqH5dEfH7iPhjtf8tSc9L/K77zAfm3y3paxFx7zxDaj2O\nxeav+xgamN1h5/bMGgaWXXI7OwfZJbvFZbeBue2pBv1Cmdkd9ikcByRdV+1fK+mcB2X7hbbXVvsX\nSHqzpEcXmPNBSa+yvam637urOp3GqnqS9E5J9yeue9Ea1Qv8jO2LrHk+VvfvdA9Iel9VZ7Okk2d+\ntJWrhvN8mP2CH5iv+o9jmB/IX2J2lyK30uCzS27rIbvdkd0a83PM7a8G/YKkErMbff7WZI5N0osl\n/bdmfiPyPkkvrK6/XNK+av9Nko5IOiTp55Ku62Heq6o5j0n6RHXdHknXVPvPl/SN6vafSHp5H2tf\nrMa/Sfrfat3fk9RKmPsuSccl/VnSryW9X9IOSdd3jPmCZn6z9+eS3tDH+hesIemjHev/kaQ3Js7/\nFkmnNfMbx4ckPVw9Z1keRy/z130MTczuIHO7FNklt2SX7K7M7Jaa20Fnd9C5JbvdN/6QCgAAAJBg\n2KdwAAAAAEWhgQYAAAAS0EADAAAACWigAQAAgAQ00AAAAEACGmgAAAAgAQ00AAAAkOD/Ad2u+upZ\n1ka8AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0aa7ec5f90>"
      ]
     },
     "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": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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wGnoG0DQHpt2pvhwXdEzQ9Ecua/oNbVnTb6h1kZlci9D0ac17/5L3ftv08qsA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\nGIZh9DT2wGsYhmEYhmH0NP8ftk3LGQVxi5wAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0af8bbab50>"
      ]
     },
     "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": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0aa733bd50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def pool(im): return block_reduce(im, (7,7), np.max)\n",
    "\n",
    "plots([pool(im) for im in corrs])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "eights=[images[i] for i in xrange(n) if labels[i]==8]\n",
    "ones=[images[i] for i in xrange(n) if labels[i]==1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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HH3007Rjjx4/PekzbT759+3ZVjxkzJm3MYleMWQkraN9dex2B5bPnbrH07PpKYk7se02L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\nMwBPAxiZ+tuOnVd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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0aa75e2b10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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XL17s1a+//rpX33nnnV798MMPp9gdiiK59luS5s+f79XnnXeeV99+++1evWbNmvQbQ+79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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0aa7f8c2d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plots(eights[:5])\n",
    "plots(ones[:5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pool8 = [np.array([pool(correlate(im, rot)) for im in eights]) for rot in rots]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "len(pool8), pool8[0].shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0aa7ea3550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plots(pool8[0][0:5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def normalize(arr): return (arr-arr.mean())/arr.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "filts8 = np.array([ims.mean(axis=0) for ims in pool8])\n",
    "filts8 = normalize(filts8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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RSCTo6uri+9//PqBexxORB9Ai8hug7D1BEflC1H1NJpLJJNOmTSv8/8Mf/jD/\n+q//OqzpB6jXIFRVVY24JVjcSAXUaVCKc/XjH/84jzzyiHqNQE1NDfPnzx/2tSNHjqjTiKTTaWbP\nHnrG6p577uHrX/+6eo2A5mplSCaTw67o33fffTz44IPqdRwxKo1UjDHvA54FDtpfekpE/i7qvicy\nfhqpqNdg+Gmkok6D46eRinoNhp/mFOo0OH4aqajXYGiuVgY/jVTU69gyKo1UbLaIyEdj2N+koVwj\nFRv1GoByjVRs1GlAyjVSsVGvPvHTnMJGnQakXCMVG/XqE83VylGukYqNeh0jRquRCsDkfZw+BD4b\nqYB69Y3PRiqgTgPhs5EKqFff+GxOAeo0ED4bqYB69Y3mamXw2UgF1OuYMVqNVADWGmO2G2OeM8Ys\nj3O/E50SjVRAvYaiRCMVUKehKdFIBdRrKEo0pwB1GpoSjVRAvYZCc7UylGikAup1zBitRiqvAfNF\npMfu3f4MsMRtO86Tb9iC/8UPNIRl//79sWyno6Mj1HoiUhjkzZ49262Rim+vcTRSOXr0aOB13Hjm\nmWcib6PE9IuSOJ164Nupcw512ML0n/vc5wKv48bvfve7WLbjbGIShPwT44ODg7S2tro1UvHtNZvN\nFt6HbaRS4ta8bzo7OyNvAyj14bckziYKHsdB307zd17AmsYUpsb+5s2bA6/jxqJFi2LZTtimEplM\npvBatGiR23ZCHVfD5mqJu4u+2bJlS+RtwPjIVecYIOxxNa5cjasOfdjGUs7zlUfTn1C5mk6nQ3kN\ne35wEtfvJuwYIF+NKw5GpZGKiHSJSI/9/nkgZYxxvXemBf9HYoxhzZo1I74exKs2UhmOczqHkyBO\ntTD9EPmC/+l02rWRShCv2kjFwtlEwa3gfxCn9fX1hddkb1Dl9HrrrbeOWK65Gpw4c1WPqyMxxnD7\n7beP+HoQr1OnTi28JrPX/JSjODpdj0ojFWPMTMf7NYARkXa3WGWI/CdPrwOzeg2OOq0Mvb29JBIJ\nz4L/6jU45ZooqNNw9PX1kUgkPE+e6jU4mquVQc9X45tRaaQC/IEx5nPAINALfDLqfic6zmkGuVyO\nTZs2AcOLqKNeA1HsNI86jYaz4H9nZydPP/00oF6jUNxEIY86jUZ+6kYikaC7u5sf/ehHgHqNguZq\nZSg+X/3bv/0boF7HE6PSSEVEHgIeirqvyUTxfLpbbrmFp59+elgRdfUaDLc5ivbDhOo0Aslkctg8\nzrvvvpvzUR+zAAAOKklEQVTvfOc76jUCxU0UwJrzq06jkUwmmTJlSuH/n/zkJ3nooYfUawQ0VytD\n8fnqU5/6FN/85jfV6zgi8hQOY0zaGLPNfgp0pzHmAZeYamPME8aY/caYl4wx86Lud6IjIuRyucJr\n9+7dI2LUazCKnbo9TKhOgyMidHV10dnZSWdnp1dzCvUagLzT/MvtgRl1GhwRobu7u/B6+eWXR8So\n12BorlaG4vPVtm0ji5up17EljjrQ/cDNIrIKq4Td7fZcHCd/ArSLyGLgH4GvRd3vRCf/6TP/cMrp\n06fdwtRrAIqdelTjUKcBMcZQX1/PlClTaGho4NixY25h6jUAeacNDQ3U19eTyWTcwtRpQIwx1NXV\nUV9fT11dnVdlIfUaAM3VylB8vjp8+LBbmHodQ2J5iDD/FCiQxpoWUjwyuQv4vv3+SWDkY/rKCJy3\nbzwGe+o1ID6elFenIdBcjR91WhmcXj3KcqnXgGiuVgb1Or6Jq4xdwn6AsA3YKCKvFIXMBo4BiEgW\nuOBVakUZIn8LR0SYMWOGW4h6DYjTqQfqNAQiQmdnJxcvXmT2bLdGpOo1KM6pMc6a4w7UaQjy0zi6\nurqYO3euW4h6DYjmamVwnq80V8cfsTRSEZEcsMoY0wg8Y4xZLiK7SqzieRlwcHCw8D5sI5WJyPHj\nx/2EeXqNo5HKJMXT6YULFwrvwxb8nyhks1lSqRQiwoEDB/ys4um1qELKpK2vm81mSSaTiMiw42IJ\nPEU5mzCFbaQyUXB69dksS3O1DHHmqh5X3dm3b5+fME+vzoZuYRupTATGXSOVPCJyEfh34LaiRceB\nuQDGmCqg0atWoTZSGSI//ymRSHh1V/TtVRupWDidepzsfDvVgv9DJJPJwgezpUuXuoX49qrNKSyc\nTj0GvL6daiOVIZLJZGEAsWzZMrcQzdWAxJmrelwdwnm+uvrqq91CfHvVRioW46qRijGmyRgz1X5f\nC3wQ2FMU9lPgPvv9J4BNUfc70RFHC08R4cyZM25h6jUAxU49pnGo04A4p8SICCdOnHALU68BKHbq\n8WCWOg1IsVePB17VawA0VytD8fnK44FX9TqGxHEFugX4d2PMDmAb8IKI/NwY8xVjzJ12zKNAkzFm\nP/CXwN/EsN8Jj3P+08yZVsMh9RoNp9P8FSN1Gg3n/Meurq7CHGj1Gh7nPN3u7u7CvFJ1Gg0Roaen\nh+7ubnp6epg3z6r6pV7Do7laOZznq/xdaPU6fohjAL0PqwuOYM2/SQKIyAMi8jM75h7gJqATqAZu\niWG/k4r8XDv1Gj/qNBrFt68dV03Ua0gSCfdDszqNRrFXPa5GR3N1dNBcHX+MVh1ogCdEZLX9+m7Y\n/fmZ/L1rV6nnF/3HeNRdDBxTouKDZ4zPOtAQk9fe3t6yMdu3b48l5tSpU5GWQzxOS2wjFqd9fX1l\nYzZv3hxLzKuvvhpLjMft15IxPutAQ0xe/fzuDx48GEvMW2+9FWk5RHNaprYuxOR0YGCgbMyRI0di\nidmzp3iGX7iYsF591IGGUczVt99+O3JMW1tb2W34ibkUctXPcTWuXB1PY4AS+xk1r34eZCwX4+f8\n7ifGz1gwrocFvRitOtBQ4unQIHjU7RyGW9e+MDFj+ccDvmpAQkxe/fzxxDWALncg93Ogj8NpCUbN\n6UQYQMPo5upoDqDLfdD280H8UnDqp3LCeBtAhz2B+qgDDaOYq36q1pSLGcsBNIy/c1VcuRpXzKUw\nBnDrIFlMHAPouHJ1wgygfdSBBvi4MWaHMebHxpg5cex3ouOc/+RRBxrUayCcTkugTgMi5etAg3oN\nhHNuuUdtXVCngXHO2fWorQvqNRCaq5XBeb7SXB1/jFYd6PXAD0Vk0BjzWazOOa4dc1auXFlyX8eO\nHSuVSADU1tYyfXrpWuJ+YhoaGmhpaYkc09LSUmpQAcCJEyc8Y7LZLGfPnnVb5NvrNddcU3L/e/fu\n9So/VqC6upqGhobIMZdddplXWT4ADh06VHI5xOP07bffprOzs3hRbE737dvHkiVLSsbERTKZLFue\n0E/MzJkzaW1tLRlz+PBhz5hMJuN1+82319WrV5fcf6nfa56Ghgaam5sjxUybNo2amhqmTZvmGVNu\nOUBzc3PZfD5y5IhnTCaTYdeuXW7TLHw7vfbaa0vu/+DBgyxcuLBkTDqdZtasWSVjpkyZUjbmwIED\nXH755SVj6urqysbE4dVjatyo5mp9fX2pCyS+YqZOnVrWhZ/j6njI1TiOqyISS67GFRPH+cpZH9tB\nbF7379/P4sWLS8bU1dXR1NQUKabc+R/852r+IWAvjh49WjbmN7/5TcnlpTB+bi0E2qAx/w3oFpF/\n8FiewOrdfpnLsni/mQmIiLjerlGv4VGnlUG9xo86rQzqNX7UaWVQr/Hj5bQcka9AG2OagEER6XDU\ngf77ophmEclParkLcJ04GPaHmIi4eH0B9RoJdVoZ1Gv8qNPKoF7jR51WBvU6/oljCkcL8H37008C\n+JHYdaCBV+xyK180xnwUq9xdO3B/DPud6KjX+FGnlUG9xo86rQzqNX7UaWVQr+Oc2KdwKIqiKIqi\nKMqERux2kWPxAqYBG4C9WLcnpjqW3YbVEnwfkANeB7YDz9jLq4HNwADQC/xPl+3/2l63117/P7rE\nvAVk7JiVLsvfB3RgFSrvxao08kWXuDnAMaDfjvuqS8wH7H312DG/KlqeBl4GztvbOQbMK4q5Dzhj\n/zxeP1MUr3cCF22vRzz234v1ibfXbf8+vf6BYxu9wM8q4dSOaQDOAX1AN/APLjElvWquaq5qrmqu\naq5qrl7KuVrk9K+BrNOrT6eTMlddf8ZyAZV8AV8FvmS//2vg7+33CeBtYD6Qsn/JVxWt+3k7qecD\n99oJVxzzd8APgTc89n87sBWrAcx+4Lcefzwv5BPA/kXsddnXvcCL9vub7F9kccz7gOfs91XAb4E1\nRTFfBP6PvXw/sMHll/zNSni1l58BHrOXH85/v0X7/4ntLIrXu4HNo+T0c8DD9vt7gLMuMSW9aq5q\nrmquaq5qrmquXqq56uJ0B9AVwumkzFW3Vyx1oCNwF1bZFex/P2a/XwPsF5EjIjKI9enirqJ1PwO8\nJSJHgB9hJURxzH6sT1Kl9v8NrCTpBaYaY2a6xA2IyA4AEekCdgPF9WbeC/yTHbPZ/p6vdtlWvnK/\nV9OZO7BcpLES+d0u2yj3QEBYr2vsbT9kL/82VnIW04blrNT+y3ltx/pEPxpO7wIetd//DJjqEgOl\nvWquaq5qrlpormqu5r8fzdUhxnuuFjt9AsuZEz9OYXLm6gjGegA9Q0ROA4j1JGm+0OVsrMv2eaqA\n/2yM2WqMyf8yZwEH7XWzQBfgVsj0NmCxR5Hx4v2cYOQvEGCtMWa7MeY5Y8wHsD5VbfPaljGmFeuX\n6NZOZ60xpgfrD+N1Gdl0ZjbwHXvdjcBZY0xxwepyhdPDep1tfy0fcwzIuO0f+Dkwz2P/Qb1uwjpI\nVNLpcWM1+zmJ9Ufr1tqrlFfNVc1VzdUhNFc1VzVXPbY1TnO1+Gc9DiSNMS87vPp1OhlzdQQVH0Ab\nYzYaY95wvHba/37UJdztEwHAXwI/Bv4Q+EdjzAKfu18P3ID1KfSXDH0iC8JrwHwRWYWV1D8D/sL+\nxDQCY0wD8CTW7Yhej23VYd1G+LQxZrnLZm7FmvtzPdacpOKfqRV4B1gH7I7LK0MHr1Lk938H1h9X\nGKdguwBuxPpZqbBTsX+Hc4AaoLhrzHqsT8AJhrxqrmquguZqMZqrFpqrmqsjuMRy9XsisoahXK3y\niHPb/0TM1VYRWYnPXKn4AFpEPigi1zpeK+x/1wOnjX1Z3xjTjDVPDKxPK872MQ3ACRE5hDXBfZUd\ns8het8qOOVi07/NYl/zBSvzrir69E4CzreEc+2vObXSJSI8xJgn8GdYE9BddftQTWMnwJPA41i/I\ndVv2+/+LNTH+7qLtHAfmishF+2edLiLtzp9JRAZF5INYjrIxep2KNdcs72QukHTbv/3fdkY6ze+n\nrFesW2tPAg8BAy6fsmN1ar/vxrrd856i7ZwXkQ+IyLUMedVcRXNVc1VzVXNVc3UC5Gqx0zlYHyxw\neO3Ch9MJnKv5n8stV0Yw1lM41jNUt/A+4Fn7/SvAlcaY+caYK4BPAeuNVVh8HVax8B8Ay40x87E+\ndQza2ytgJ46xX25FxtcDf2QvrwMuiH3bw7GN/Lyd72LP2XEmc9G2HrT3sc1jW8uMMVPt9zcCtVhP\nv+aXN2HdsrnPWIXTP4X1NGjxz5THq3B6WK/rsT6p/rkxphrrYLHFY/8G68TgtX8/Xr9rr/8SVknF\nYq+RndpsAv6T/f5erKd193j8XOCdK/fb7zVXNVc1VzVXNVc1V4u3NZ5z1em0Guuq8/OO/a7Dusrv\nxylMvlwdiQR44jDuFzAd61L5XqySK5fZX78Oa37NXqz5L6dsIW3A/7Jj0lgHoXy5la/aX/8KcKf9\n/i2sBMhhlS/5G6yD12cd38M+rE+oOXs/f+yMAf4c6xOYYH1y2YuV0LcVxd1gbyNfbmW3S8x/t5f1\n2Nv6lvN7BlbYP2e+hM1RrFslzp/pfwBv2nG/ApbE7PUjDJVb8tr/BYfXk8XOfHr9uu20B+tT755K\nOLXfr3Y47QYedIkp6TWiU81VzdWyTjVXNVfRXNVcrWyufgErz/ZjVfp4w/6ZD2INuP04nZS56vbS\nRiqKoiiKoiiKEoCxnsKhKIqiKIqiKJcUOoBWFEVRFEVRlADoAFpRFEVRFEVRAqADaEVRFEVRFEUJ\ngA6gFUVRFEVRFCUAOoBWFEVRFEVRlADoAFpRFEVRFEVRAqADaEVRFEVRFEUJwP8HQBu3zWz3uDQA\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f0aa754ba50>"
      ]
     },
     "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": {
    "collapsed": false
   },
   "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": false
   },
   "outputs": [],
   "source": [
    "def pool_corr(im): return np.array([pool(correlate(im, rot)) for rot in rots])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "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": {
    "collapsed": false
   },
   "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": {
    "collapsed": false
   },
   "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": {
    "collapsed": false
   },
   "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": false
   },
   "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": false
   },
   "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": {
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