{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "

Week 10: Unsupervised Learning (Part II)

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CSCI-UA 9473 - Introduction to Machine Learning

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Partial Solutions

\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Exercise 1. White matter, Gray matter and cerebrospinal fluid\n", "\n", "For this exercise, you will need to install nibabel. You can do this by typing the line 'pip install nibabel' in your terminal. \n", "\n", "We consider the MR image shown below. We want to segment this image into the white matter, gray matter and cerebrospinal fluid. \n", "\n", " - Start by plotting the historgram of all pixel values (you can do this with 'numpy.histogram'). How does the distribution look like ? \n", "\n", "- Use your histogram to initialize the E-M algorithm (means and variance). The plot the resulting distributions on top ofthe histogram. Does your algorithm correctly capture the three clusters?" ] }, { "cell_type": "code", "execution_count": 214, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import nibabel as nib\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "img = nib.load('T1.nii')\n", "plt.imshow(img.dataobj[:,80,:], cmap = 'gray')\n", "\n", "np_array = np.asarray(img.dataobj[:,80,:])\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#### Exercise 2. Spectral clustering\n", "\n", "pixel_list = np.reshape(np_array,np.shape(np_array)[0]*np.shape(np_array)[1])\n", "\n", "pixel_list2 = np.delete(pixel_list, np.argwhere(pixel_list==0))\n", "plt.hist(pixel_list2, bins=np.linspace(np.min(pixel_list2), np.max(pixel_list2),100), density=True)\n", "plt.title('Original pixels histogram')\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQoAAAD8CAYAAACPd+p5AAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8vihELAAAACXBIWXMAAAsTAAALEwEAmpwYAAAaSElEQVR4nO3de3SU9b3v8fc3QXLBEElABOUSBbGCCCpK4Uhpu7WoIJZWD/RYsVovbZVa91JKT2W3UltqFVf1nI3F1ssWFRQPFVkoW6hVXEuRi24Ft0C8ElGCgEiUJIR8zx8zYICECZOZ+c3l81pr1sz8ZuZ5vs8a8uF5fs8zv5+5OyIih5IXugARSX8KChGJSUEhIjEpKEQkJgWFiMSkoBCRmJIWFGY2yszWmVmlmf0yWesRkeSzZFxHYWb5wHrgHKAKWAFMcPe3Er4yEUm6ZO1RnAlUuvu77l4PzAHGJmldIpJk7ZK03GOBjU2eVwFntfRmM9PloSLhferuXZp7IVlBYc207RcGZnY1cHWS1i8ih++Dll5IVlBUAT2aPD8O2NT0De4+C5gF2qMQSXfJ6qNYAfQ1swozaw+MBxYkaV0ikmRJ2aNw9wYzuw5YDOQD97v72mSsS0SSLymnRw+7CB16iKSDVe5+RnMv6MpMEYlJQSEiMSkoRCQmBYWIxKSgEJGYFBQiEpOCQkRiUlCISEwKChGJSUEhIjEpKEQkJgWFiMSkoBCRmBQUIhKTgkJEYlJQiEhMCgoRiSlZg+uKtNpFF11Et27d4vrs22+/zfPPP5/giuRACgpJucLCQvr377/v+dSpUxk8eHBcy1q4cCGff/75fm3r169n586dbapR9qcxMyVlCgoKOOKII+jfvz+vvPJK0tZz/vnns2zZsv3aampqkra+LNLimJkKCkmZv/3tb1xxxRUpX29jYyOFhYXs3r075evOMC0GRdyHHmbWA/gP4BigEZjl7n82s98AVwFbom/9lbsvinc9kpmGDRvGokX7f+1FRUVBasnLy2PLli37ta1YsYJzzjknSD2ZKO49CjPrBnRz99VmVgKsAi4CLgFq3P2Ow1iW9igyzKRJk/jBD37Q4uslJSWcfPLJKazo8NTU1LB27VdTzUycOJF169YFrCgtJH6Pwt0/Bj6OPt5pZv9NZHJiyWK33XYbxcXFjBgxgtNOOy10OXE78sgjOeusr+bNnjp1KtXV1axatYrZs2cHrCw9JeSsh5n1BgYDy4HhwHVmdhmwEvhXd9/ezGc0SXEG6N27N6effvq+55MmTeLII48MWFFy7N07WrZsGbt27drXvnDhQurq6kKVlTba3JlpZkcCLwC3ufv/M7OuwKdEZi+fRuTw5JA9WDr0SC+9e/fe93jChAn8/ve/D1dMYEOGDGHNmjXU1taGLiUVknPWw8yOABYCi919RjOv9wYWuvuAGMtRUASUl5dHXl7kIl0zY+fOnRQUFASuKn2MGjWKpUuX4u7s2bMndDnJlPgpBc3MgL8B/900JKKdnHt9F1gT7zokNSZPnkxdXR11dXXU1tYqJA6waNEi6urqePrpp0OXEkxbznr8D2AZ8CaR06MAvwImAIOIHHq8D1wT7fg81LK0R5ECF1xwATNnzjyovWPHjpSWlgaoKLPU1tayZcsW3J0+ffpk43UZuuAq1xQWFvL444/v19a9e/f9OiYlfgsXLsTduf3223nppZdCl5MoiT89Kunlqquuory8fN/z9u3bM2bMmIAVZbfRo0cDkesxCgsLWbJkSeCKkktBkYF69uy535kJgF//+tf07NkzTEE5bMKECRQUFPDpp5/y+uuvhy4naXTokSHKysqI9B/DTTfdxOTJkwNXJE299tpr+y4J37ZtG+nwdxUH9VFksvbt21NbW7svKCS9lZaWHvTT9wyhPop0YWZs376d9u3bH/bnJDN88sknnH322axatSp0KQmjoEig8847jz/+8Y8x39exY0f94WexoqIi5syZwy233MKcOXNCl5MQCooEuOWWW+jVqxcnnHACp5xySuhyJA306dOHSZMm0bFjR2bNmhW6nDZTUMShc+fOXHDBBfueX3nllfTq1StgRZKOvv71r5OXl0ddXR2NjY08/PDDoUuKmzozD8Nxxx1HaWkpAwcO5NFHHw1djmSQhoYGBg8ezNtvv01DQ0Poclqisx5tUVhYCMAjjzzCuHHjAlcjmayiooIPP/yQxsbG2G9OPQVFvPLy8qitreWII44IXYpkiVGjRrF48eLQZTQn8b8ezQXHHHMMn3zyiUJCEmru3LlUV1czb9680KW0moKiGT/+8Y95/vnnefLJJ+nSpUvociTLlJaW0qVLF771rW/x5JNPhi6nVRQUB7jyyiv50Y9+xMiRIxk2bFjociSLderUiXPPPZdp06aRn58fupxDUh9FE9/+9reZMWMGAwcODF2K5JixY8eydOlSvvjii5BlqDMzlu7du/Pmm29SVlYWuhTJUXsv+246uG+KqTPzUIqLi/noo48UEhLUsmXLuOiii0KX0aycD4qTTjqJzz77LHQZImktZ4Ni2rRpbNiwgcWLF+v0p6SNu+66i9/+9rehyzhIzv3W48EHH6SwsJAhQ4Zw/PHHhy5HZD9du3bl6KOPDl3GQdoUFGb2PrAT2AM0uPsZZlYGzAV6ExmF+5LmZgpLpW7duu279HrChAmHPRaESCoNGDCASy655KDBkUNq6wRA7wNnuPunTdpuB7a5+3Qz+yXQyd0POW5bMs96dO3alTFjxnDfffclaxUiCbd69eoQI6an9KzHWOCh6OOHiMxwHkRRURFXXHGFQkIyTn5+PiUlJaHL2KetexTvAduJTPbzF3efZWafuftRTd6z3d07xVhOUvYo5s+fn7anm0RiqampSXVYJG3MzOHuvsnMjgaeM7O3W/vBZM9m/sYbb/C1r30tWYsXySltOvRw903R+2pgPnAmsHnv/KPR++oWPjvL3c9oKcHaqqSkhHbtcu6kjmSR4uJili9fzpFHHhm6lDZNUtzBzEr2PgbOJTIh8QJgYvRtE4Gn2lqkSC7Ky8vjzDPP5I477gg+1GJb/svtCsyPjibdDnjU3Z81sxXA42Z2JfAhcHHby2w9M2PcuHF06NAhlasVSZprrrmGDz74gCeeeILKysogNWTdj8Ly8/Opq6tL+5/tihyu3/3ud9xzzz1UVzd7NJ8IufPrUQWFZLMnn3yS8ePHJ2uAXgWFSLaorKykb9++yVh0bvzMvHv37rz//vsKCclqFRUVvPfee+Tlpe7PN6uCol27dhx33HGhyxBJqvz8fHr16sVTTz1FeXl5StaZVUEhkivMjNGjR++bcybZsiYoysvLGTp0aOgyRFJq6NChKRmZLWuCYtiwYcydOzd0GSIpNW/ePM4991yKi4uTup6sCQqRXPXYY48xZcqUpK4jK4Ji2rRpGTXrkkimyYqgaN++vUatEkmijA+KyZMnc95554UuQySoMWPGcNNNNyVt+Rn/O+zzzz+fU045JXQZIkGdeuqpFBQUsHHjRubMmZPw5Wf0HsVJJ52kX4mKRJ100kncfffdSVl2Ru9RvPTSSym7Mk0kl2X0HoWIpIaCQiSLdO7cmerqagoKChK63IwMioKCAv75z39SWloauhSRtGJmdOnShejIcwmTkX0UeXl5fOMb3whdhkjOyMg9ChFJLQWFiMQU96GHmfUjMhnxXscDU4GjgKuALdH2X7n7onjXIyLhxR0U7r4OGARgZvnAR0QmAfoRcJe735GIAkUkvEQdenwbeMfdP0jQ8lp04oknsnbt2mSvRkSaSFRQjAcea/L8OjN7w8zuN7NDTlB8uNq3b09FRUUiFykiMbQ5KMysPXAh8ES0aSZwApHDko+BO1v43NVmttLMVra1BhFJrkTsUZwHrHb3zQDuvtnd97h7I3AfkYmLD5LsSYpFJHESERQTaHLYsXcm86jvEpm4WEQyWJuuzDSzYuAc4Jomzbeb2SDAgfcPeE1EMlCbgsLdvwTKD2j7YZsqEpG0oyszRSSmjAuKTZs2ceONN4YuQyQt1dTUcP3117N79+6ELjcjZzMvKiriyy+/TFY5Ihlry5YtHH300fF+PDdmMxeR5MjYoEj0rpWItCwjg2LXrl0UFhaybdu20KWI5ISMDAqAxsZG0qF/RSQXZGxQiEjqKChEJCYFhYjEpKAQkZgyOigSPXeBiDQvI4Ni75WZZWVloUsRyQkZGRQQCQsRSY2MC4pjjz2Wv/zlL6HLEMkpGRcUnTp14oc/1JAXIqmUcUEhIqmXUUGRn59PYWFh6DJEck5GBcVll13GihUrQpchknMyKihEJAwFhYjEFDMootMCVpvZmiZtZWb2nJltiN53avLaFDOrNLN1ZvadZBUuIqnTmj2KB4FRB7T9Eljq7n2BpdHnmNnJROYh7R/9zL9HZzoXkQwWMyjc/UXgwKGkxgIPRR8/BFzUpH2Ou9e5+3tAJS1MKSgimSPePoqu7v4xQPR+77C/xwIbm7yvKtp2EE1SLJI52jRTWDOa+zlns+PVufssYBYc/nD9IpJa8e5RbN47GXH0vjraXgX0aPK+44BN8ZcnIukg3qBYAEyMPp4IPNWkfbyZFZhZBdAXeLVtJYpIaK05PfoY8DLQz8yqzOxKYDpwjpltIDKb+XQAd18LPA68BTwL/Mzd9ySq2LfeeovZs2cnanEi0koZN6XggAEDePPNN5NZjkjG0pSCIhKMgkJEYlJQiEhMCgoRiSnjgmLTpk3ceOONocsQySkZd9YDvhquX0T2p7MeInJIu3bt4t13303KshUUIlli+fLlDB06NCnLVlCISEwKChGJKdE/MxeRAObMmcOdd96ZtOVn5B5FQ0MD06ZNY9euXaFLEUkLlZWVrFyZvDGgMjIodu/ezdSpU3WKVCRFMjIoROQrO3bsSPp/muqjEMlwEyZM4JlnnknqOrRHISIxZXRQDBs2jFWrVoUuQySYb37zmyxbtizp68nooFi/fj1ffPFF6DJEgtmwYQM1NTVJX09GBwXA008/zRtvvBG6DJGUcnf++te/puw/yozvzLzjjjvo0qULAwcODF2KSErU19ezZs0arrnmGhobG1OyzngnKf6Tmb1tZm+Y2XwzOyra3tvMdpnZ69HbvUmsfZ/6+nrq6upSsSqR4Kqqqjj99NNTFhIQ/yTFzwED3H0gsB6Y0uS1d9x9UPR2bWLKPLRbbrmFiy++OBWrEslJcU1S7O7/6e4N0aevEJkRLKhnn32WU089NXQZIkm1YMECTjvttJSvNxGdmVcATa/2qDCz18zsBTM7OwHLb5Xdu3fz2WefpWp1IkHU19ezY8eOlK+3TUFhZv8baAAeiTZ9DPR098HAjcCjZtaxhc8mfDbz7du3M2XKlJQeu4mkytNPPx1spry4g8LMJgKjgf/l0YE33b3O3bdGH68C3gFObO7z7j7L3c9oaYy+eOzcuZM//elPpMM4oCKJ9o9//IOnnnoq9huTIK6gMLNRwGTgQnf/skl7FzPLjz4+nsgkxckZxE8kh2zevJmdO3cGW3/M6yiikxSPBDqbWRXwb0TOchQAz5kZwCvRMxwjgFvNrAHYA1zr7tuaXXAS7dmzh/z8/FSvViQpGhsbufDCC3n11VeD1ZCRw/XH0q5dOyorK+nVq1ciFysSROfOndm6dWsqVpVbw/U3NDSon0KyRkNDQ+w3JVlWBgXAtddeG3RXTaStamtrGTduXFqM5Jbxv/VoyeLFi+nevTu1tbWMGDEidDkih62hoYH58+eHLgPI4qAAeOCBB6itraWsrIwBAwaELkek1WpqatJqjzgrOzMPdNZZZ7F48WJKS0uTuRqRhKivr+fll19m5MiRqV51bnVmHmj58uVUVFSELkOkVe6///4QIXFIOREUELm8u6SkJC06hkRacsUVV3DDDTeELuMgORMUEDnuGz58OBs2bAhdishBxo0bx9///ve0HFslJ/ooDnTxxRdTXl7O0KFDmThxYipXLdKs66+/ntmzZ4f+BXSLfRRZfdajJU888QQAa9asoby8nNGjRweuSHJVbW0t8+bN4957702LC6takpN7FE2dcMIJPPPMM/Tt2zdUCZKDtm7dytatW/n0008ZPnx46HL2yu2zHofyzjvvMHDgwLQ8LpTs1NDQwN13302/fv3SKSQOKScPPQ5UW1tLUVER1dXVdO7cOXQ5kuUuvPDCpE8BmGg5v0exl7vTv39/unXrxt133x26HMlSgwYNYunSpaHLOGw530fRnD59+nD88cdTXl7Oo48+GrocyQINDQ2MHj2a559/nvr6+tDltERnPQ5HZWUllZWVlJSUcOuttwIwadIkjjrqqLCFSUbatm0bf/7zn1m8eHHoUuKmPYpWevjhh+nWrRs9e/bUGRJplXXr1lFVVUVVVRWXX3556HJao8U9CgXFYbr66qu59dZbycvLo0uXLqHLkTRUXV2NuzNlyhQeeOCB0OUcDgVFopWWlrJ9+/Z9z6Njh0qOc3dKS0uDDoTbBrqOItF27NhBUVHRvtt9990XuiQJbOfOnRQVFWVqSByS9igS5JhjjuGoo46ioqKCRYsWhS5HUmj27NncdtttNDY2sn79+tDltEWLexS4+yFvwP1ANbCmSdtvgI+A16O385u8NgWoBNYB34m1/L1zB2XLrWPHjn7ppZf6pZde6jt27HDJbvfcc4+fccYZwf/dJei20lv4G23N6dEHgf8D/McB7Xe5+x1NG8zsZGA80B/oDiwxsxPdfU8r1pMVPv/8833Tvp166qmUlJQwZMiQIBPLSnLNmTOHhx56iJUrEzYrZtqKGRTu/qKZ9W7l8sYCc9y9DnjPzCqBM4GX4y8xc910000A/OQnP+Hqq69u9ef69etHUVFRssqSNmhoaGDNmjUA3HzzzWzcuDFwRanRlguurjOzy4CVwL+6+3bgWOCVJu+pirYdxMyuBlr/15PBZs6cycyZM1v9/hdffJHTTz99v7bi4uJElyWHac+ePXzwwQcMHjw4dCkpF+9Zj5nACcAgIjOY3xltb+4cYbMdlZ6ESYqzxYgRI+jQocO+W6dOnTShURpYsmQJffr0CV1GEHEFhbtvdvc97t4I3Efk8AIiexA9mrz1OGBT20qU+vp6ysvLKSsro6ysjOnTp4cuKedMnz6d73//+6HLCKelXk7f/6xEb/Y/69GtyeNfEOmXgEgn5n8RmcC4gshM5vmtWH7o3t6MuvXo0cOHDx/uY8aMSVpvvnzl5z//uffo0SP4956CW/xnPVqYzXykmQ2KLvx94BoAd19rZo8DbwENwM88h854pMrGjRvZuHEjxcXF3HzzzfvaJ0yYkJPHz8l06623Mn/+/JzptGyJLrjKIr/4xS/2TZ/Yrl07jQXaBo2NjSxYsIDLL7+cHTt2hC4nVfRbj1xTXFzMW2+9tV9bhw4dNIJXDDU1NWzdupX6+nr69euXa53IGo8i13z55Zf07t17v7bvfe97zJ07t9n3mxl5ebn705/Gxkbcnfnz53PZZZeFLiftaI8ihxwqDEaOHMmSJUtSXFH6GDJkCK+99hruTmNjY+hyQtGhhxxaQUEBxxxzzH5tM2bMYNy4cYEqSo6f/vSnzf5o7+OPP07nIepSRUEhh++0006jZ8+eVFRUMGPGjCA1TJ8+neXLlydsea+++iqbNunSnhaoj0IO3+rVq1m9ejXdu3fn2GObvRIfgLy8PG644YZWDd6zZs2awxo78pFHHtn32woJR3sU0mZ5eXm88MILreoMXbhwIX/4wx9SUJXEQYceIhKThsITkfgpKEQkJgWFiMSkoBCRmBQUIhKTgkJEYlJQiEhMCgoRiUlBISIxKShEJCYFhYjEpKAQkZhiBoWZ3W9m1Wa2pknbXDN7PXp738xej7b3NrNdTV67N4m1i0iKxDVJsbv/z72PzexOoOkwxe+4+6AE1SciaaBNkxRbZKSSS4BvJbguEUkjbe2jOBvY7O4bmrRVmNlrZvaCmZ3dxuWLSBpo61B4E4DHmjz/GOjp7lvN7HTg72bW390/P/CDuTSbuUimi3uPwszaAeOAfRNFuHudu2+NPl4FvAOc2NznXbOZi2SMthx6/AvwtrtX7W0wsy5mlh99fDzQl8hExSKSwVpzevQx4GWgn5lVmdmV0ZfGs/9hB8AI4A0z+y9gHnCtu29LZMEiknoaXFdE9tLguiISPwWFiMSkoBCRmBQUIhKTgkJEYlJQiEhM6TKb+afAF9H7XNCZ3NjWXNlOyI5t7dXSC2lxHQWAma3Mlcu5c2Vbc2U7Ifu3VYceIhKTgkJEYkqnoJgVuoAUypVtzZXthCzf1rTpoxCR9JVOexQikqaCB4WZjTKzdWZWaWa/DF1PokVHKX8zOir5ymhbmZk9Z2YbovedQtcZjxZGaG9x28xsSvR7Xmdm3wlTdXxa2NbfmNlHTUadP7/Jaxm7rc0JGhTRQW7+L3AecDIwwcxODllTknzT3Qc1OX32S2Cpu/cFlkafZ6IHgVEHtDW7bdHvdTzQP/qZf987yFGGeJCDtxXgruh3O8jdF0FWbOtBQu9RnAlUuvu77l4PzAHGBq4pFcYCD0UfPwRcFK6U+Ln7i8CBAxO1tG1jgTnR4RLfAyqJfP8ZoYVtbUlGb2tzQgfFscDGJs+rom3ZxIH/NLNV0QGFAbq6+8cA0fujg1WXeC1tW7Z+19eZ2RvRQ5O9h1lZt62hg8Kaacu20zDD3f00IodXPzOzEaELCiQbv+uZwAnAICIj0N8Zbc+6bQ0dFFVAjybPjwM2BaolKdx9U/S+GphPZBd0s5l1A4jeV4erMOFa2ras+67dfbO773H3RuA+vjq8yLptDR0UK4C+ZlZhZu2JdAAtCFxTwphZBzMr2fsYOBdYQ2QbJ0bfNhF4KkyFSdHSti0AxptZgZlVEBmh/dUA9SXM3kCM+i6R7xaycFuD/nrU3RvM7DpgMZAP3O/ua0PWlGBdgfmRmRdpBzzq7s+a2Qrg8eiI5h8CFwesMW7REdpHAp3NrAr4N2A6zWybu681s8eBt4AG4GfuvidI4XFoYVtHmtkgIocV7wPXQOZva3N0ZaaIxBT60ENEMoCCQkRiUlCISEwKChGJSUEhIjEpKEQkJgWFiMSkoBCRmP4/ZnO1aXWwKnQAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# finding the mask\n", "\n", "mask = 0*np.ones(np.shape(np_array))\n", "\n", "for i in np.arange(np.shape(np_array)[0]):\n", " for j in np.arange(np.shape(np_array)[1]):\n", " \n", " if np_array[i,j] >0:\n", " \n", " mask[i,j]=1\n", " \n", " \n", "plt.imshow(mask,cmap = 'gray')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 98, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import cv2\n", "\n", "kernel = np.ones((5,5), np.uint8)\n", "\n", "img_erosion = cv2.erode(mask, kernel, iterations=2)\n", "#img_dilation = cv2.dilate(mask, kernel, iterations=1)\n", "\n", "# for display\n", "kernel2 = np.ones((4,4), np.uint8)\n", "img_erosion2 = cv2.erode(img_erosion, kernel2, iterations=1)\n", "border = img_erosion - img_erosion2 \n", "\n", "#image_contour = np.zeros(np.shape)\n", "color_tmp = np.zeros((np.shape(np_array)[0], \\\n", " np.shape(np_array)[1], \\\n", " 3))\n", "\n", "for i in np.arange(3):\n", " \n", " color_tmp[:,:,i] = np_array[:,:]/np.max(np_array)\n", "\n", "border_c = np.squeeze(np.where(border==1))\n", "\n", "for k in np.arange(len(border_c[0,:])):\n", " \n", " color_tmp[border_c[0,k],border_c[1,k],0:1] = 0 \n", " color_tmp[border_c[0,k],border_c[1,k],2] = 1 \n", " \n", "plt.imshow(color_tmp)\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": 99, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(2, 16900)" ] }, "execution_count": 99, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ind1 = np.squeeze(np.where(img_erosion==1))\n", "np.shape(ind1)" ] }, { "cell_type": "code", "execution_count": 100, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "cropped_image = np.zeros(np.shape(img_erosion))\n", "\n", "for k in np.arange(len(ind1[0,:])):\n", "\n", " if img_erosion[ind1[0,k], ind1[1,k]]==1:\n", " cropped_image[ind1[0,k], ind1[1,k]] = np_array[ind1[0,k], ind1[1,k]]\n", "\n", "plt.imshow(cropped_image, cmap = 'gray')\n", "plt.show()\n", "\n", "\n" ] }, { "cell_type": "code", "execution_count": 223, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "\n", "pixel_list = np.reshape(cropped_image,np.shape(cropped_image)[0]*np.shape(cropped_image)[1])\n", "\n", "pixel_list2 = np.delete(pixel_list, np.argwhere(pixel_list==0))\n", "plt.hist(pixel_list2, bins=np.linspace(np.min(pixel_list2), np.max(pixel_list2),100), density=True)\n", "plt.title('Original pixels histogram')\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": 195, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0.5, 1.0, 'Reconstructed Image')" ] }, "execution_count": 195, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# optional median filter \n", "from scipy import ndimage, misc \n", "filtered_image = ndimage.median_filter(cropped_image,[2,2])\n", "\n", "plt.figure()\n", "plt.imshow(filtered_image, plt.cm.gray)\n", "plt.title('Reconstructed Image')" ] }, { "cell_type": "code", "execution_count": 200, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pixel_list = np.reshape(filtered_image,np.shape(cropped_image)[0]*np.shape(cropped_image)[1])\n", "\n", "pixel_list2 = np.delete(pixel_list, np.argwhere(pixel_list<100))\n", "plt.hist(pixel_list2, bins=np.linspace(np.min(pixel_list2), np.max(pixel_list2),50), density=True)\n", "plt.title('Original pixels histogram')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 254, "metadata": {}, "outputs": [], "source": [ "import copy \n", "\n", "\n", "# Initialization\n", "\n", "mu1 = 100\n", "mu2 = 200\n", "mu3 = 300\n", "\n", "mu = np.asarray([mu1, mu2, mu3])\n", "\n", "sigma1 = 20\n", "sigma2 = 20\n", "sigma3 = 10\n", "\n", "sigma = np.asarray([sigma1, sigma2, sigma3])\n", "\n", "phi1 = .8\n", "phi2 = .1\n", "phi3 = .1\n", "\n", "phi = np.asarray([phi1, phi2, phi3])\n", "\n", "\n", "num_clusters = 3\n", "\n", "criterion = 10\n", "\n", "maxIter = 500\n", "\n", "criterion_mu = np.zeros((maxIter,))\n", "criterion_sigma = np.zeros((maxIter,))\n", "criterion_phi = np.zeros((maxIter,))\n", " \n", "\n", "for kk in np.arange(maxIter):\n", "\n", " # E-step \n", " \n", " gamma = np.zeros((len(pixel_list2), num_clusters))\n", " numerator = np.zeros((len(pixel_list2), num_clusters))\n", " denominator = np.zeros((len(pixel_list2),))\n", " \n", " for j in np.arange(num_clusters):\n", "\n", " numerator[:,j] = np.squeeze(np.exp(-np.power(pixel_list2- mu[j], 2.) / (2 * np.power(sigma[j], 2.)))*phi[j])\n", " denominator+= numerator[:,j]\n", "\n", " for j in np.arange(num_clusters):\n", " \n", " gamma[:,j] = np.divide(numerator[:,j],denominator)\n", "\n", " # M-step \n", " \n", " mu_old = copy.deepcopy(mu)\n", " sigma_old = copy.deepcopy(sigma)\n", " phi_old = copy.deepcopy(phi)\n", " \n", " for j in np.arange(num_clusters):\n", "\n", " \n", " tmp = np.dot(gamma[:,j],pixel_list2)\n", " mu[j] = tmp/np.sum(gamma[:,j])\n", "\n", "\n", " tmp = np.dot(gamma[:,j],(pixel_list2 - mu_old[j])**2)/np.sum(gamma[:,j])\n", " sigma[j] = np.sqrt(tmp)\n", "\n", "\n", " phi[j] = np.sum(gamma[:,j])/len(pixel_list2)\n", " \n", " \n", " criterion_mu[kk] = np.sqrt(np.sum((mu.reshape(-1,1)-mu_old.reshape(-1,1))**2))\n", " criterion_sigma[kk] = np.sqrt(np.sum((sigma.reshape(-1,1)-sigma_old.reshape(-1,1))**2))\n", " criterion_phi[kk] = np.sqrt(np.sum((phi.reshape(-1,1)-phi_old.reshape(-1,1))**2))\n", " " ] }, { "cell_type": "code", "execution_count": 255, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.semilogy(criterion_mu+criterion_sigma+criterion_phi)\n", "plt.title('Convergence of the EM Algorithm')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 256, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import scipy.stats as stats\n", "import math\n", "\n", "numClasses = 3\n", "plt.hist(pixel_list2, bins=np.linspace(np.min(pixel_list2), np.max(pixel_list2),100), density=True, alpha=0.5)\n", "\n", "for i in np.arange(numClasses):\n", " \n", " \n", " x = np.linspace(mu[i] - 3*sigma[i], mu[i] + 3*sigma[i], 100)\n", " plt.plot(x, stats.norm.pdf(x, mu[i], sigma[i]))\n", " \n", "plt.title('Recovered Gaussian Mixture')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To recover the independent regions, we take for each pixel the Gaussian that returns the highest probability\n" ] }, { "cell_type": "code", "execution_count": 259, "metadata": {}, "outputs": [ { "data": { "image/png": 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FBQUoKSkJdhf9IikpCYcPH8bhw4d9Dk3eu3cv0tLSJLft3r0bOTk56OzsFNLSA0FWVhYOHz6MgwcPut33hRdeEEVdWq1WHDlyRLRuwcNxHI4cOeLTSGD//v1OrlZ/jjcfYIbCDZRSfOMb38Dy5cuRnJwMAJI/pNlGFIQQJCcnY8eOHUHtK090dDSef/55r9/Hq1Pv2bMHGo0GANDV1YWPPvrIo/dXV1djcHBQchv/lKWUYnx83KuKX7m5uZJuSf64nqpqz5x6KBQK7Nmzx2WglOOaRl5enlNMyaVLl9DX1yc6XkVFhcspGMdxuHDhQsCFhOcCtpg5C3q9Hv/xH/+BRYsWISYmRvhCRUZGoqioCI6CwIsXL541WUoul/s1PfAGf8+l0Wiwbt06Ye7tqSvWYDBIPp15Fi9ejJSUFBgMBjx48EAyDmTmguOyZcuQnZ3tkyCOJ/AG0R1KpdKpD47XGxkZiTVr1rg93uTkJB4+fIi8vDxJXYz5il+GghDSAWACgA2AlVJaRAiJB/BbADmwq3B/XKpS2HzHYDCgra0NAwMDWLt2rehppFQqkZmZKTIUnkT1BZPs7GxhUS8QPyp/ApZ0Oh2ePHniVO0rPj4e8fHxMJlMToFoQ0NDkouGiYmJQfEaqFQqZGdne7Rveno64uPjndqzs7PR2dkJuVyO7Oxsl9XNZjI4OAiFQgGZTPbUxFoEYkRRTil1HEt9G8B5SukPCCHfnn79rQCcZ84wGo148uQJmpqaPI4i5N2Lnj6h3MEHBsnlciHleTa8ze4cHR0VpkoREREBfWL39/fDZrO5/OGoVCqnz7WlpQWdnZ2w2WxCOnuwUKlUSE1NxerVqyW38wljPHl5eUIWqiMFBQXgOA5hYWHIz8/3qg+82O+zZChmcgDA9um/fwGgGk+JoeB/mI8fP0ZTU5NX721qaoLVasXmzZs9fg8/bHWcI/PD/YaGBrS3tyMmJgbl5eUBTTjiOA7nz58XDEV+fj4KCwsDkhU629RjNvLy8pCXlweDwYATJ0743Q9XyOVy5OTkuFTNAuxGmi+YzD/5XTFTe9MbKKWwWq1PRTKZvz2kAM4QQiiAtyml7wBI4Qv+UEp7CSHJ/nZyrnjttdewfv36OdMXqKmpgVKpFD1dq6qqhL8zMzOxatUqHDt2DC+//HLQ+tHU1ITh4WGPXLHuuHHjBqKjo4OSaxEINm3a5NX+FRUVHoWR+8LAwABOnTolJJnNZ/w1FM9RSnumjcFZQohn8cSYP9XMe3p6BMm4mQV0ZyMsLAwHDx5EVVWVz09Rd5mZPT09olX1YJGfn4/k5GScOnUKFRUVPh9nz549UKvV6Ovrw/DwME6ePIm9e/d69N76+nqMj49jzZo1ovabN29i2bJlfj+5KysrwXEcNm/ePOtwX6vV4vbt25DJZHjppZcCor6t1+sFl3AwDU8w8ctQUEp7pv8fIIQcBbAJQD9ff5QQkgZAMnZ5evTxDmAvKehPP3zh6NGjuH37NqampoSFNUcNSU9w/BI5zlFlMhnKy8vdRiq6G3JyHCcq8usLly5dwrp160Rh0DKZDDt27MDVq1dhNpvR1dWFJ0+eeBSFCdhHQmNjY0hKShLN8xUKBTZu3IjHjx9jaGjIqxR1m82Gvr4+USg53+6P9J7ZbMbVq1cxNTWF4uJitzVHOI6D1WqFTCYLiJHo7+/HvXv3hIfJlStXRPdTJpPh+vXreOONN4IqCOQvPhsKQkgkABmldGL67+cB/C2ASgCfA/CD6f+PBaKjgaSpqQkNDQ1oaWkRtcfGxgo/3vHxcXR3d6OwsNCjY85cxJRaJZ9LOI7DvXv3MDQ0JDniiY+Px6pVq4QUc8A+f6+rq3Py8swkNTUVk5OTTj9qwD6c1ul0UCgUXnuCrFark+cjNzfXY2+CFHK5HFlZWcjKykJycrJHP36lUhkw6T+1Wi3S4Hj48KHT/ZhZoGg+4s+IIgXA0ekvlALAe5TSDwkhtwH8jhDyRQBdAD7mfzcDx61bt9DT0wO5XO7kx3a06JOTk2hpaRE8DqmpqX4vOvHn5NOpgwnHcYIh7O/vh8FgQEREhOiJqlKpRE83m82GlpYWJCQkID093eX1ZmZmYnh4GENDQ07X0tbWBovFErDpZFpamlCVzBcUCoVXGZxqtRqLFi1yKmvoK1FRUaIU9vHxcUxNTWF8fFww0JRS3LhxA0VFRfN2WuJPkeI2AGsk2ocBzLtqKbxY7E9+8hNs2rQJWVlZTrJnM5mamhKCgvbu3Sv5w4mMjMTExIQQKCSTyZyk7nnCwsKwdetWnDp1yuUTxFE52tXx+Mpas32pCCGIjIyEwWAQchEyMzOxdetWYZ/a2lrJdZmbN2+irKwMCQkJktfMJ4uNjY0JuSCO/V68eDGWLFnism/zmcTERL8Mkzt4IaKWlhY0NDQIId0/+clP8NZbb81bd+n898sEiMnJSbz22msA7JWpNmzYMKuhcAw5nm0Y/vzzz+PcuXOCOI1arXa7IDjb9qNHj4qGpjOPRylFc3MzhoaGsG3bNpfHkcvl2Lt3LyorK0XZlTMjHwE4aVlyHIfLly9j48aNyM7Odrr+GzduYGRkBOnp6di6dSsopTh69Khg/HjV6u3bt/uUsemqXwuJvLw8REVF4fLly0KbzWZz+30LFc+MofCW1NRU7N27FydPnvQrUSrQXL16FX19fULeiTv279+PCxcuYGRkBFqtVlTHk/9hL1++XLQWc+TIEXAch9u3b2N4eNhJjq+8vFz0hSaE4NChQ8L2pqYmPHjwAMePH8dLL73k87VWVFTMWdj7fOCb3/wmvva1r83LBEIyHxZRioqKqGM4dDDQ6/X4whe+ILzmi9XOFnlJKYXJZHIbtWg2m4UnNV8w11eMRiOuXr0qLOrNPB5/Ll6WjRCCiooKl4bs9OnT0Ov1kiMJwB5XkJ6eLlrkMxqNqK6uhl6vh0KhkFwALCgocDkis1qt6OvrQ21trcdl+O7fvy8EuRFCsHfvXkRERMzLp2ug4EsTOGbTlpaWory83C93sK8QQmoppZKuqmdiRKHVavHzn/9c1Ga1WvHkyRNQSkXVuR0hhHgU2uyvYIsjERERoh89pVRyHYHjOI/iPgwGg0sjAQDh4eFOhsCxD1arVdJrMpsrVaFQICkpCRs2bMDVq1dRXFzs0YgsPj5e8Da4WudZSMhkMkmhnq6uLlitVqxduzY0HZNgfoyng8zk5KSkAIvRaIRWq/U6XDuYNDU1eRX45Q28zuby5cuFNq1W6zI13BXZ2dlu4xGUSiWSkpLQ29uLxsZGj1Wo0tLSXGpaLHQWL16M6OhoTE5OQqvVCnKL84FnYkQxG2azGQ8fPkR8fDwSEhJCvhbx6NEjryM9BwcHkZiYOGvAjkajQVZWFgoLC4UCOENDQxgdHUViYqJT2Hp8fLwgj2ez2URK4vHx8R6tHchkMiQmJuLRo0dQq9VITU11OS3TaDQLZpoxNDQESik0Go3bESkhRPCyrFixQhhJ8TJ6cXFxSExMDPlns+BHFBaLxW1tDY7jUF1djcnJSZjN5jkvwssz21M3PDxc+DfTIFy+fFnQRjCbzaJ/PHl5ecKCJSEE27ZtQ1RUFNasWSNZlGfjxo0oLy9HeXk5Nm7cKJwbsKt5zawgJkVYWBjKy8uhUqlQU1OD3t5el/suXrx41kStp4lbt27h0qVL6OzsdGv0lUql8Dmr1WrRVM9ms6G6uloo8RhKFvyI4vTp0/jv//5vj/b98MMPAQCrVq0SDc/nAovFgsrKSsltMplMtCj46NEjJ7l9wB4X4ckPmMdTFayYmBjh/MeOHfNaUPjFF1/0StHqaWfv3r04f/48Hjx4gNHRUVHsijtqa2sRFhYmWjf76le/itdffz2k0v8L3utRVVXlsaHgcaxbSQjBwYMH52ToZ7PZUFlZKTxRMjMzhWxHx1EEpRQcx8FsNgsp2TKZzKUc3/bt2wM2fOVHWzKZzKvjcRyHO3fuQCaTOS0eX758GSkpKV5rOsxnzp8/j5GREZc1UFesWCEqFcDHofAjh/j4eEE68ejRowCAz372s3jhhReC1udn3uvhLZRS0fTjzJkzKCsrC5ocG4/UGoNUGyFEqE7Fw3EcVq1aJbkQGMj5v6+JS3wRYCmkKq4/7WzevBn19fXo6uqSnMo+fvwY3d3dwuuZUxTHqcbOnTtx48aNkE4/FtbdmcGHH37oUubdG8bHx+fsJq1fv144lzu1rLCwMFGGZnJy8rwOUHJlaOdzn31Fo9EgLy8PCoUCbW1tTttnriHNRnR0NFauXImWlhacOXPGJ+Fkf1nQhuLBgwdoaWmBUqkUnrSdnZ3zOlPPUx1HwP50D1Z18GcZi8WCnp4er+6FFAkJCSCEuHzImEwmSb0RjUbjlPORnp6Ouro69Pb2IiYmxisltUCwYA1Fb2+vEI8QFRWFjRs3ArCPDmYOBXkJeVdER0eH3G3KmDtMJhNqamoQGxuL6Ohov6ZtvKCwFP39/ZKGIiUlRZTmPj4+DkopLBYLOjs78atf/YoZikDxxhtvSNZPmFmJCrAv0B07Ji2bQQjB888/H3I/NmNu4TgOZ86cwb59+6BUKl0u3jpmDfuCXC53enBxHCdqO3/+vM8qaoFiwRoKb5DL5Th8+HCou8GYh/BepcLCQkkxm5s3b0qqintCSkoK9u7di+PHj4va29vb0d7e7luHg8SCG09TSvHqq69iZGQk1F1hPKVoNBq8+OKLwuvi4uJZXbft7e2orKzEyZMnvTrP4OAgTp8+7XX/BgcH8aUvfWlO19oWpKGY6aXQ6XS4evVqCHvFCCRXrlyRlOELFHwy4Pbt2xEeHg6FQuHSLVxYWIjc3FyYzWYYDAZcvHgRFy9exMTEhNvzcBzndfAa/z6dTofXX3/do/MEggU19TAYDPjggw+cLK3VasXw8HCIesXwl6GhIVH498DAABobG6FUKhEXFxe00nxJSUkoKCiY1U0dHR2NnJwcUErR2toqrIs1NjZi8eLFbpPnfIVSikePHnksiOwvC9JQMBYG/f394DgOT548cZqz869zcnKCWsNz6dKlGBkZEZK8pIiLi0NYWJgop8hsNrsdLSiVSiQnJ2NgwFmonk/Vl8Jiscx5oeMFZSgYCwej0Yjbt2/PmnKvUCjmJKLzwYMHwujCFRqNxmtlqtjYWGzZskUQrjGZTKCUQqFQIDExUfJ4fLlDvpKZTqdDVFRUQEoLzIbPaxSEkHxCyF2Hf+OEkD8lhHyPEPLEod2zCjABYD4HUjE8h+M4nDhxwq0ux5o1a3zyNnhDsL9TSqUSL774Il588UVERUWBEILs7GyUlpZK7t/T0yMYCQD49re/LYgnBxN/VLibAKwFAEKIHMATAEcB/C8A/0wp/cdAdNBT7ty5g3/4h3+Yy1MygoDBYJhVpXyu4Q3W4OAgRkZGgqpn+fzzz88qrnvv3j08fvw4aOefjUCN23YCaKWUdoYqMGlmIpcjcXFxXqX6MkJDf38/ampqPMqrKSkpmZMasbzBcpWZG0hcqY6fPXsWVqtVmJqEgkAZik8A+LXD69cIIZ8FUAPg/1BKR6XfFjzWrVsnaFmGh4fPu8Sjuro6mEwmpKWlIScnJ9TdCTldXV1obW11KzLEo1arg7o+wRfl8cV96S/9/f2iRLK5TEp0hd+fNCEkHMBLAP5iuunfAbwBe6XzNwD8GMAXJN4XtCLFeXl5WLRoUcBEb1taWkSWXKVSYdGiRX4dk6+zaTKZYLFYIJPJntqiOf6i1WrR3t7udiVfJpMJyt+82lawoJR6XNFNp9NhYmLC7+8Ej16v9/jc7e3tTkWjgkEgTHIFgDuU0n4A4P8HAELIuwCqpN4UrCLFhBC3tTM9heM4jI6O4u7duyJDER0dDY1G43VtTSm0Wi1aW1uRkJCAuLg4xMXFPVN5JaOjo2hoaHCqOToThUKBhISEoC9eOhIfH4/R0VHh3lssFuh0OsTGxgr76PV6dHZ2oq+vLyDfCb1e79GoilKK0dFRJ12SYBGIM3wSDtOO6QrmPIcABH9JNghQSjE5OYkLFy44zQsnJib81rlQKBQghKC7uxu3bt2C0WjE+fPnQ6bXGSouX748q5GQy+WCkSgrK5uzfslkMuzcuRORkZGC4R4eHsaVK1dgsViEf/fv3xcKPVdXV/sdANXY2OjRgiWlFJcvX8aRI0dQXFzs1zk9wa8RBSFEDWA3gC85NP+IELIW9qlHx4xtTw19fX0uw77j4uIks1C9Yffu3bh+/Tqam5uh0+lQVVUlqrbFsLN582a/qpn7S0VFBS5duiQERZlMJpdBfVarFR988AEOHTrk8/pJUVER4uLicOfOnVn3k8lkOHjw4JwVNfbLUFBKDQASZrR9xq8ezQEXLlzA2NgYsrKynMrlAXbx2sbGRsn3LlmyBGvWONVm9olNmzYhNjYWsbGxqK6uFrQRd+3aFZBpzdMKIQT79++HXC73WXovkJSUlIBSiv7+fly7dg2UUlRWVmLnzp3QaDRYvHgxsrKyUF1dHZDz5ebmIjs7G1ar1SmzNFQsmKSwFStW4Fvf+hYopTh//rxQJXomFy9ehE6ng9VqhVarFaqVO2Kz2VxOAXi9ykAgl8sRFhaGuLg4bNu2DVarFRaLZd7EEMwF27ZtE835VSoVdu7cCaVSKUzPQg0//ZHL5TCbzTh//rzIGyKTyRAfH4+dO3di586dfn0/6uvr0dzcLJSWnC8smBButVotSJeNjo46/dBtNhvu37+P4eFh4Yc4NTXlpGzV0tKC/v5+uGJoaAhNTU0BU4xOSkpCYWEhGhoasHbtWsjlcjQ1NWHp0qVCYZiFTGxsrDBMj4mJwbJly+b1aEoulyM7OxvZ2dkir5pcLnepZOUpDQ0N6Orqglwux+joqKjoUqhZMIZiJr29vcjIyEBERATMZjN6e3vR0tLi9n3d3d2z3iB+NMJXdMrMzPTrqRcTE4PFixdDr9cLq9darRZJSUnPhKEA7KLAKpUK8fHx8yKmxGq1CtmqGRkZwn1RqVTIyckR9TGQuicmkwkcx0Gv12NsbCxgxw0EC9ZQ1NXVISIiQsjOu337dsCOrdfrcePGDQD2sNuoqCi/XFQajQabNm3C2bNnBZ0Fs9kMk8k0Z4tVocSVjH8o4CUJ+Pu7Y8cOxMbGQi6XIzY21inCV2rq6glmsxkWiwWEECEYcN26dUKR4plERETAYrGETBJvwaxRzIR/yre1tQk3XWofx9GAL9Fv586dm1WY11MUCgUqKiqEYfijR49QV1f3TK1XzAd6e3tx9epVwfBfuHABg4ODAb8Pra2tOHXqlCjBC/hD8Sn+eymTySCTyVBcXBzS0daCHVFUVFTg3r17ePLkict9srKyhEpcgL2qmKe1FnheeumloKX4arVafPjhh6ioqAjK8RnOLFq0CJmZmeA4DkeOHAFgV9RypZkZaDZt2oSNGzdCp9OhuroaBw8eBGA3IJ2dnUE/vysW7IjCEwKxoh7oVfmKigqRF2ByctJrLcbZMBgMOHHiBBupzALv2eLTv31dK3r48CGqqqpw8eJFl/uYzWZUVVWhqqpKmHYSQhATE4OKigoQQnDmzBlUVVWho6PDp34EggU7orh161bQdBU1Go0QSuzOFfbgwQPExMR4nM+iUqmwfv16NDQ0oLe3V4gQvXLlCjZt2uRT/kpdXZ3wWVitVhgMBsH1VlhY6Pdq/UKFr2y2Zs0ar3NL6urq0NPTA6PRKPkdycrKgkwmw4MHDwTdjdu3b2PlypVISkqCTCYT1qf4SvWhZMEaCk+kwnQ6Hdra2pCbm4vGxka3NyMjIwPR0dFQq9VITU31qB8jIyNe+9UTEhKEBa6pqSm0trYCAJqbm0URfwqFwqnC9ejoqFNRmSdPnjiJwPT19SEvLy/oykgLAVeGtLW1FRMTE5ILziMjI0LOxtTUFBobG7F8+XJhu1ReyNDQkHCfTCaTIPc3H0Z/C9ZQeIJOp0NDQwPUarVHKkFZWVmS+oyjo6OSRsYfYVWNRoPo6Gj09/djYGAACQkJGBgYQGxsrPB0Cw8PF01TALsCUnNzs9Px9Ho9bDYbYmJihLbly5cHvfDyXGCz2TAyMuKzPsXQ0JAonsNTmpubodfr3Z53amoK9fX1IkMhRXx8PJRKJYxGI3p7e+dEucpTFpyhMJvNXg3PDQYDrly54tG+FotFcrHz9u3bkn7vPXv2+KwjsHTpUqhUKoyPj6O0tFRYaN2yZQuSk5Mhk8lAKcXp06dF12u1Wp2CzcLCwtDe3g6TySSUVgTsX2C+Clag4TgOFoslYKn+szE5OYnLly/jxRdf9Ol8t27dwnPPPScyosHA8bsjZZTWrl0LjUaDjo4O3L9/P6h98ZYFZSgMBgOOHz+Ow4cPB+XLX1NT49X+fHGXlJQUv84rk8nw0ksv4fjx44KrNzk5GZs3b8bx48fx8ssvC9fb2dnplFBUXl6OVatWOR33zJkzKCkpEQo4B5KRkRF89NFHOHDgQMCPLQXHcaisrMRLL73ktbHYuzfwsq4zpwt8/3gKCgqcFklnukrnE2Q+zH+Kioqotz9CKYaGhvDqq6/i+PHj4DgOW7dudaoKHQoIIUhLS8Nzzz3n1fv4YkZnzpwBANH0ZnBwEHfu3MGePXtETycpSUC5XC7pndm7dy/UanVQ8il46bi50EoYHx/HuXPncODAAZ/yLCorK1FWVuY0jQPsmplFRUUYHh7G6OgoNmzYIHih+M+ZEIKEhASUlpYKxsCdXAAfw+PNiPP+/fswGo2iAsU/+9nPArYYTQippZQWSW1bUCMKwD6k27lzJyilQph1qKGU+jQF6e/vR11dnfDa0SAkJSWhrKzMaQhLCHE71yaEYPfu3U5Gwmw2CxmQJSUlfskHEkJgtVpx9uxZ7Nq1K6hZoBqNZtZzUEpx7tw5lJSUoLm52Wmxd2pqCteuXZN8v9FoRE1NjZAoePHiRScjwIvInD171mM9EXcanOPj47h16xZ27doltC1btgy9vb24fPnynGpzAAvMUExNTeH27dsoKipy+ZSsra3FihUrAmZEamtrkZ+fP2s1KV/hC708ePDA6ZoUCgWioqLcHmP9+vVOPwDeTy8FH2V679495OfnIyEhAQaDAfX19W7PtXr1amHYPzExgUePHmF8fBy1tbVC35OSkgIaYTg0NOS2oC+lFGfPnkVDQ4OwYOjI+vXr0djYKFy7SqVymqo9efIEPT09Ll3uNpttVnc8IQRFRUWoq6vzyNWpVCqxZMkSUepBVlYWkpKSwHGc8D2fKxaUofCEQA2zOY5DZ2cnOjo6BB1HV8TFxXnsTpXCMaTXW/gnV0JCAqKjo2fdVy6XIzc3V9Q2MTGBrq4udHZ2evUD54OWZh4v0Oj1eqdApLS0NJHLkhCCJUuWgOM4pKSkOLklHWuHTkxMwGQyOV1reHg4OI5zGo0AdmlERw9XZ2enaASpUCiQlZWFnJwcjI2NCZJ6syUfKpVKLFq0yMnNr9FoEBYW5lY6MNAsGENhNBoxNDQkWtWXYv369R4fkxCC6OhoSY+GzWbD48ePERUVJTyxFQqF03B9cnIS6enpTvEOnhAWFobExEQncR2TyeTkfYmMjMTU1JRQYJeHn7rk5+cjOzsbMpnM5UhEoVAIT6mJiQlwHIeuri48evQIcrlcuAaNRgO5XA6LxSLSdzSZTIIOiOOx5gp+lFRQUOA0b3fXFz48u6urS3L0lJ6eDplMJmkokpOTRVqe3d3dIkOhUqmEe8iLHj169MhtGrlCoZD8PiuVSknBpWCyYAzFo0eP8MMf/tCn98rlcsm5pUqlwu7du0WFj/n1hrCwMDz//POi/dPT00ULTQBECUbekpKSguLiYmExE7AvaD5+/NhJgWv37t1obGyEXC4XvrSOaxVNTU1oampCZGQk9uzZI1y3K27evCkMxfn9zp8/DwDYvn074uPjMTg46DLhLjExcU7m0TKZTFDCmnk/GIFjwRgKX4mOjsauXbuEBKCZEEJEWpaPHz/G3bt3PT6+P5WltFqt0w/x+vXrkk81vn4lAHR0dEChUEhqcE5OTgrX+uKLL7oMuHJcRHNFeno6Dh8+7Ha/YJKVlRXwcg8MZxaEofj9738/L7QFtVot9Hq938K7gN0VxoducxwnXJ/FYkF+fr5bhS3HNY3Lly9jdHQU6enpoqHsmTNnsGXLFuh0OjQ2NiI8PPyZz1TNzMz0Kq6kqKhIMFRWqxUnTpwQFitXr16N8PBwl/qrgH0awY/wAHtpTE9reswlC8JQmEwmtwVtA0VmZiZkMpmkSjLHcQGpLFVbW4ve3l4hgevmzZuYmppCcXExwsPDERER4VVQ0erVq4UoSaPRiFu3bqGsrAxTU1O4d+8eMjIyUFxcPCcxD/MdXv9hJu3t7ZIy+ryWJmCflvL3f8OGDUhLS4NMJpP0MOXk5AjJX473cuXKlcjLy4NerxcC/EpKSqBQKNDS0hIyI+LWUBBC/gvAiwAGKKUrp9viAfwWQA7skvwf58sGEkL+AsAXAdgA/G9K6emg9HwOsFgsePDgAVauXCk8oSMiIoKu6ajT6WA0GqHT6dDd3Y3U1FSkpqYiJSUFCoUCycnJHkd7Pnr0SBRINDU1JfLAjI2NIT09fU7qeGq1WoyOjkKlUvm0uBtKDAaD06J2fn6+SzdzbGysMK2TMupqtVrSRR8VFSX84120KSkpc1YRzBWejCh+DuBfAfy3Q9u3AZynlP6AEPLt6dffIoQUwF6HtBBAOoBzhJBllNKgVbVpbm52EsPlh46jo6Mu1bgd4SMn+/v7RavVVqsVTU1NKCwsnDM16L6+PuGpZLFYMDU1JfrCyGQyr+bljkLDJpMJo6OjwrSFP54n8RiBgE92slgsQtwJ34f5TlRUlNOUZNmyZUGTKlSpVEISWV9fn5CAFircGgpK6WVCSM6M5gMAtk///QsA1QC+Nd3+G0qpGUA7IaQFwCYAvgkLekBVVZUogYYQgnXr1kGtVqO2thb9/f2w2WyzKlfJZDKUlJSgsrLSa4WrQGIwGHD9+nVhjpuUlCQ86SMiIrB582av8xgcNR57e3tRU1MDk8mEiIgIbNq0aU41OflEt7t37wp6GIHQHJ0LvF005eMy5HK5X4lxM78TocLXu5NCKe0FgOn/k6fbMwB0O+ynnW5zghDyKiGkhhBSMzg46GM3gD/7sz/D7t27hdeUUpw8eRIGgwFFRUXYt28fnnvuOZcl5R3bvBk1uNrX1y+82WzGiRMnhLoejuG9vNqSv5mYaWlp2LFjB2QyGfbt2xcS4d5FixZh27Ztwud35swZDA8Pz3k/goHjaPTq1as4ceIE7ty54zJUm7/PrsK5LRaLaHE0lATajEv9eiQ/JUrpO5TSIkppUTDmx6dOnUJPTw8Auy7Eyy+/jJdfflkUO5CdnS0yMlKyZ5RSHDlyRDQ/jI+Px/79+53OmZWV5ZMvf3R0VPBqVFZW4v333xfK3ms0moCWGoyMjMThw4dDWlgnOjpalFV66dIlNDU1haw/gcDxHjqi1WpFcTA8DQ0NeP/990X/JiYmhO06nQ7Hjh0Lap+9wVevRz8hJI1S2jtdlHhgul0LwLH2eyaAHn866CszrTT/w3B0Rc2sROXqxyNl7cPDw53Sk32tbOXYV961qlQqkZaWhvXr1wf8Rz0fqm+FhYUJn9+NGzfQ2NgIvV4/5xGHvnLq1CnR94LjOJcjB6mEQHdJYe62zzW+GopKAJ8D8IPp/485tL9HCPkn2BczlwK45W8nA4m7jMiVK1fi8ePHIvXuLVu2OA37Hesx+ENfX5/oaVpfX4/CwkKEhYVBLpfPmwzYYMB/fjKZDFNTU8IIcD4bC4vFgtu3b0suLMrlcpGqO4+vBYvnE564R38N+8JlIiFEC+BvYDcQvyOEfBFAF4CPAQCltJ4Q8jsAjwBYAXw1mB4Pd/T29kKpVHqlopyUlASr1Sq4tmQymd/VwGZDr9ejq6tLKPqiUqkgk8mQnJw8L7Q0gk1bW5tIJ7Krq0tIXsvJyZlXmp4GgwEdHR2SJSD4KmJSUokzefLkyVO3LuOJ1+OTLjZJhh9SSv8ewN/70ylvSUpKQnp6uvBE4mlvbxcSq7whLS0tKKpPM9Hr9RgeHkZvby/u3bsHADh48CDCwsKQkZEh1FJdyGi1WpGnyWq1CiHyarUaERERUKlU82JkNT4+LpkwplKpkJqaKqkiJkVbW5tkGP58Zn77pDxkz549+MxnPhPqbniF1WpFXV0dzp49K0TghYWFCcIz891dGChcKUsBwLVr13D+/Hk0NTWFfOWf4zjJxEG+aLFUlqfNZoPFYnH6J7Vm4cv6lsVi8Wp/f3j6J09PKWfPnsW5c+fQ3W33JisUCqEq1LZt21itDQdaWlqg0+lQXl4esj40NDTg0aNHTu0bN27EokWLJN5hz9fxpDA2ABw4cMCrhwPHcfjggw/w05/+dE6+Kwv+sdXS0oLLly+Huhsijh075jLKbv/+/UEPEZ9vlJWVIS8vb9Z9hoeHceLEiTnqkTMrVqxAcXGxR/seP34cR48eFVzcwSAsLAxjY2PIyJAMUwo4C35E4WrIGErKyspw7do1rFy5Ugin5oedvrpYn2bkcjmWL18OtVrtUqaeUgqj0Yhz586hvLw8qBqcUvALzKWlpU7lHbq7u0WeK7PZ7LFrMzw8HGVlZT5NNaOioubsu7LgDcV8JC4uDitXrpScYz4raxMzGR0dhbsIXV7E9u7duygoKJjz4kVhYWFO6ynt7e2w2WySalWZmZluk+0UCsVTMYJkhiJEPAseDW+wWq2wWCyQy+VIS0ubNZ26ra0NkZGRyMzMDIqosTc4JiTyrnSenJwcr2u6DA8PY3JyUhQJnJmZiYGBASFZUKVSScZrBJMFYyiUSiWSk5MxMDAw6356vR5qtfqZfXLPV7KysqBUKvHo0SNs2bIF77//vsvhu16vx71790ApRW5u7pzlrNhsNpep3jKZDNHR0U5SiN6i1WrR2dkpchkvX74cer1eMBQxMTF47bXX/DqPtyyYX8vKlSvxve99T3Ibr3PJcRzOnDmDsbExIUTW15J/jMCTkpIieDZcCcgAwLlz5zAxMYGHDx/iwYMHc9I3SikGBgacqnkRQiCTyRAXFyfKG/IW/nu4Zs0aFBYWiradO3duzlW3Z7JgRhSzMTw8jPfff194fe7cORQVFUEmk6GxsVGU/8EIPYQQQYvzo48+cgqkO3DgwJwv+D569EjSPbpp06aAaHZ+8MEH2L1795xpg3jLM2EopOCj/2w2G06ePBmU+pMM/ykqKgKlVKhlCvzBQ7R69Wq3NVX85cyZMzCbzZIBXzt27HAZLOYte/fuxbVr1zA5OQmr1YqYmBhBxfzUqVPC+Tds2ICvfOUrATmnNzyzhsLxxvMVzbds2TKvcgsYf5CRS0pKQmlpqWhbTExM0O4Xx3H46KOPhPomMykpKUFsbGzA3LQqlQpms1lQZJucnBSqhDm698PCwtwWcgoGC8pQqNVqHD58GEePHvUqRZdSir6+PjQ2NmLJkiXzIq+AISYsLMyvamu+MDMfQ6PRYNGiRSCEIDU11e/pz+TkpJAMCIhDsq1Wq9P5V69ejS1btvh1Tl9ZcIbi4x//uKhgjzcMDQ1h0aJFzFAwANgrgDkSHx+PlStXBuTYk5OT0Gq1ePjwocfvWb9+vcfRoYFmQRkK4A8FeMfGxrzyaCiVShQXF/stN8dYGMhkMmzbti1ox+/s7HRZ+NlqtcJqtYIQInwfNRoNwsPDg9YfdywY9ygPIQRvv/22V4kycrkcL730EjMSjHlBZ2cnjh8/jpMnTwpt3/nOdzyq3hYsFtyIwls0Gg1zjzL8ZnR0FBcvXpTcptFoRFqqH330EXp7e10ea/HixaLI3XfffTckC5iOLFhD8d3vfhfvvvuu24Cc2QJ7GAxP6OrqwsOHD10mH05MTOD06T/UwTIYDLOuofGaJDy8TkkoWbCGIjU1FS+//DKio6MF//tMEhMT3dbwZDDcMTU1NWsVL47jhMrw3qBQKPDlL395XkyJF/SjtKCgAEuWLJHclpiYiNzc3JDqUvb396OtrU1Sg3GhMjExgba2NnR0dIjaR0ZGnCq+PS1ERUVh8eLFwj9PR6hGoxGdnZ0utysUCpSVlc15Sr1kX0LdgWATHR2N1NRUwSfN14pctmzZnIl+uKKtrQ1arRbx8fFe98VqtQpPMVf1L+cbRqNRMI5yuRw5OTnCNq1Wi+HhYURERIR8Pu4tKSkpoizRsbExWK1WGI3GWYtWT05Oor29XTKTODw8PCCh4YHC1yLF/wBgP4ApAK0A/helVDdderABAK/icYNS+uVgdNxTysrKkJKSgr/+67+GXC7Hzp07Q2qhbTYb5HK5aD5LKRXaPWV4eFhQ7npaPDYNDQ0A4LJI0tDQEK5cuYJ9+/bNZbcCzo4dOwAA9+7dQ2trq2ib431PTEzE9u3bJY+RkZGBv/u7vwtaH73FkzHSzwG8MKPtLICVlNLVAJoB/IXDtlZK6drpfyE1Eo6Eh4fj8OHDITUSJpMJR48eFbJYec2F0dFRVFZW+nzcyspKUZWp+cr69euxfv36UHdjzlizZg0OHz4s+udpSnyoFy9n4lORYkqpY420GwD+nwD3a8HR39+Pa9eugVKK48ePO6lbWa1WHDt2DPv27VsQBWN8ITU1NWQhynPFCy+8AI7j0NzcjMbGRsl9ysvL8fnPf35uO+aGQHwjvwDgtw6vcwkhdQDGAfwVpfSK9NvmjqysLHzzm9/EO++8I7Tl5+fP6UImpVRIRHOct2ZmZiIlJQW1tbWS81mj0YgbN24Ir9esWYP4+HjEx8eLVKn5sPOenh709PSgqKho1r5UV1fPGol669YtTE5OIj093SfPkE6nw8OHD1FSUuJ237q6Ojx58gRxcXELPimPv74lS5Y41Y65efMm9u7di23bts25zJ87/DIUhJC/hL0i2P833dQLIItSOkwI2QDgA0JIIaXUyTdECHkVwKsAgr5oExERgby8PAwNDQltcy1FFxUVhRUrVgjzdB6VSoX09HSYTCbU19fjwYMHoumRxWIR9bupqQmRkZHQaDSSKdZGoxG9vb0ikdq8vDxR/gqlFMPDw7OGuI+OjiI6OtppobS+vh65ubku82E6OjowPj4OmUzmcRKXTqeD0WiEXC4X9Ts/P/+pWHvxBbVaDY7j0N3djRUrVuDhw4ewWq1IT0/3Wj5vLvDZUBBCPgf7IudOOh09Qik1AzBP/11LCGkFsAxAzcz3U0rfAfAOABQVFQW9GqtCoUBRURHu3LkDjuOg0+mg0+kCpifgjsjISOTl5TkZCsBuLPLz8zE6OgqDwYCBgQFh9KFQKERV0Ph1jeTkZElDwRsRXhU6LS3NKRCIEIL09PRZ3XjJycmS4rB6vd5lYFF/fz9aW1sxMjKCxMREj+pw9PX1CSMpvV4vUrPWaDRIT0+fM6m7YGG1WiUlGnU6HZqamhATE4PGxkYUFhYiISEhBD10j0+GghDyAoBvAdhGKTU4tCcBGKGU2gghi2EvUhy84gZeoFKp8Od//uf40z/9UwwMDKC1tRU2m02ywtNsWK1WTE1NgRDi9fCQEAK1Wg2DweC0TS6X47nnngMAnD9/HiMjI0K/t27dilOnTsFoNLrNik1NTUVERASuXr0KANi8ebPTcJ4Q4jYLcd26dZLtrjQhDQYDbt++DaPRCIVC4fGP++bNmy5diLW1tVAqlQF3Y/tzD72FV+h2FfQHQNj2x3/8x/O23qxbr8d0keLrAPIJIdrpwsT/CiAKwFlCyF1CyM+mdy8DcJ8Qcg/A7wF8mVI6EqS++8Rbb70laAp4A6+x2draihMnTuDDDz/0+txKpRL79u3zOmRcJpNh3759Hv/4YmJisG/fPuzbt2/WOT9/Td4y8z0cx+HkyZMwGo0ghCAvLw9bt2716P1zubovdQ99/Qw8paenB9XV1aI+SDHf0wh8LVL8ny72fR/A+1Lb5hPf//73UVtbi/b2do/f8+GHH84aphtIduzYgbq6OpjNZpEXYN++fbhy5UrAIhj5H/eKFSucBF1no7q6WljkNBgMOHnypPAD2Lp166xPxY6ODjx+/FgQot2/fz+qq6tF6zDBYuY9tFqtgpbqrl275mQaeuLECWzYsEG0kEkIwS9+8Yt5vR7zTPrhZDIZ1qxZg4mJCfzyl78EIQQVFRWS+1JKhS8Y/2OIjY0Vpgm+UFFRgYsXL0pOQQD7F4f/4To+cQkhwuvh4WGcO3fOr9Rj/mna3NzsFEpcVlbmsmYGpRSNjY1obW0Fx3FOI4TZRgkzn+CEEGzduhX19fXQ6/VYuXKloHRdXl4ekOI4UvfQcRsAXLlyBWvWrAn4wnpaWhq2b98ujCp27Ngh0pXQaDT44Q9/OK+NBPCMGgrAHoC1evVqfPzjH8fPf/5zXLt2DQBQWFjotNI/M9tPJpNJrvoPDQ2hu7vb5fyeR61Wo6ioCFar1eWP0dUXp6CgAAqFAlqtFkajcdbzuKOoqAg2mw1arVYkyQbArejP1NSUsLZACMGWLVtACJlVB6SlpQUGgwFr1qwRtatUKixduhQDAwMipeuIiAi/AuRGR0eFxWNXtV55TCZTUKqDKxQK0TqI4/cmOzsbn/rUp9xWE5sPPLOGArCH0BYXF6Ovrw+nTp0CACxdulTYbrVa0dra6vQUMplMotX5nJwc6HQ6dHR0oL+/HxqNRnQcKXx1gSUkJCAmJgZarRZWqxVNTU1YtmyZT3N93n2pUCjAcdys1bkcycrKAsdxsFgsSE9PByFEVCFLis7OTnR2diImJkby2qOjo6HX64WcnLy8PL8Dz0wmk1cJdwMDA4iMjAyoNufExIRTAhxgv77y8nK3D5X5wjNtKAD7wt9nPvMZISbf0fpbLBbJorkGg0HUrlQq0dPTI3wp79+/79ZQ+MrExIQwZbFarcK5/FkUTElJQXh4OCYnJyVraM4kLy9PKHs3c3TgiqamJthsNkRGRrrdlxCCtWvXznkYs1arnTX+w2KxiNLF3alwT05Ooru72ykCMyMjAzt37sTOnTsD0/E54Jk3FID9icon4Fy9ehUDAwNeVUDnZdXngrt374rUmQOloxgXF4fS0lJBfm22Hymv5+jpE99isYBSiuXLlyM3N9flfjKZDAqFYt5Vn+cZHh4WVTLftWsXYmJiJD0WVqsVDQ0NTgvmarUaX/ziFwMm0jtXzG+fTAgoKSnBsmXLQt0Nj1CpVDhw4EDAXGtKpRKHDh3CoUOHZq1YdfnyZSiVSo8L5R4/ftwj4ZbU1NSnSpbw3LlzLqc2ly5dkvSqvfXWW0+dkQDYiEKSgoICxMbGOtWZ9ASNRuNXDcrZOHXqFCYnJ7F8+XKsWLEiKOdwR1VVFUwmU9C0PNRqNQ4ePBjUaceSJUuQkZEhpOl7QkNDg2RU7e3bt1FTU4PY2FghEvX48eOiIsOpqan40Y9+BABPbZQpMxQS8PPU0tJSVFVVef3+QGZ/GgwGwSMzOTmJtWvXIjMzc84zTG02Gy5evAiTyRTUACVA+vPT6XSoqflDJsCWLVtceowAu4fl8ePHorbnnnsOERERGBgYwJ07dyTf19fXh2vXrjlFrnIcJzkl4ttGR0dx7tw5AIDZbBY+o9WrV+Pzn//8U2sgeJihcAGfY/HKK68AAH7961+7dbHFx8cHdNoyOjqK5uZm0QKjRqPx6kt379492Gw2ZGRk+J1sxPcjPz/fq2OtW7cO9fX16OjogEwm8ykhz2q1ij4Hd+sY8fHxSE1NRUtLi9CH5ORkKBQKDA0NubyXU1NTGBsbE7U9fvx4VtVsvj8zF4KLi4uxc+dOtx6hpwFmKGZBqVQK04ienh6MjY2hp6cHWq1WcmU8MTERixYtCtj59Xq9U3yDp1BK0d3dLeS0WK1WyOVyJCYm+nQ8QogQjLR48eJZn+Yzyc3NxePHjzE0NISoqCivDcXExIRTNGpvby/GxsYQGRkpmUgVHx8Ps9ksGAp/0td7eno88gY5snbtWuzYsQOrVq3y+bzzCWYoPORzn/scAPsi1YULF7Blyxa3Iwx/USgUwg+SP5fRaITZbHYbyWez2XDz5k3hdWdnJ8xmM9avX++Ri3ImMpnMZUKYJ6jVakxOTsJiscBgMHhVtrGnpwdNTU2iz4Ivw5CRkYE1a9a4vaZbt25h7969bqdsjp+5J6hUKlBKndYkPv3pT88rzUt/YV4PL9m2bRtef/117Nq1S6gJ4u3CG8dxkv9mkpaWhoqKCpEnoKamRnhKektfXx8uXbrk03v9paSkBFlZWXjy5AmuXLni8ppdERcXh4qKClRUVIhcwk+ePBEyZQNBenq6U9X02Vi9ejVWrFghuIsVCgV+9KMfLSgjAbARhc+EhYXh5ZdfBmB3k3kzNOV1Mx1RKBQ4dOhQQPs439iwYQPi4+NRU1MjJGP5Igx84MABnDlzxmktIRTcunULgN2T8uabbwKYf3qXgYCNKAJAWVkZ9u/fj5SUFJdl5QJJc3Mzrl+/7nL72NiYEJI+3zl9+jSGh4dn3ScvL8/JC7Ft2za3T+2UlJSguap5XnnlFbzzzjv4y7/8S7cJcU8zbEQRAPih8OrVqxEfHy8k+dy4cUNSlKWkpEQQeQHsngxv1KnT09Nn9a5wHAeTyeTNJcwZqamp2LBhA2prawHYXYl3795Ffn6+S++AXC53CpWur6/H4ODgrOeSyWSIjo5GWVkZgD/EMGRkZCA6OhpWq1VwPfMMDAygpqZG0By9fv06dDqd5PH/5E/+BGvXrp0zlbRQwgxFAImNjRV9aZYvXy5oXjp+qVNSUkRf/PDwcI/djVlZWcjJyXGZfj06OupSZyM6OlpSPm8uiYiIQEZGBiYnJ4UciJGREa+1PoaGhjzKnpXJZE6frVqthlqtlswWNZlMons1NDQkMvYqlQovvvgiAHv2rTcLn08zzFAEEV69urOzEzKZDDabTVKgZWpqCoODgx6lG2dnZ7s0KuPj4+jo6BAVnUlMTBRCvJOSkoKWrOYNSqUSBQUFLuXqvcVqtaK/v1/0uej1ekxOTvrkEuY4zul4gH3kt2rVKnz84x8PSL+fJpihmAOys7ORnZ0Ns9mMM2fOOG3X6/W4evWqSDyH9/vzCVXuMJvNePjwoSj3QKVSoaSkJGAS+Px0Jjw8fF5JtxkMBly9elVUYezx48doaWlBRESEMALw5Xj8Z69SqbBmzRp8/etfD2jfnxaYoZhDlEol9u/fD8DuKXEcbttsNlG4+Lp16xAeHi6KhZiNCxcuiOI6FAqFcK5AYLVacfz4cQB25SlfA7eCBcdxQv8CeTx+gfLAgQOCl+tZhBmKEPHjH/941u386jlfOOhzn/scKKX46KOPsGLFChQUFLh8b2xsbEC1DsbGxoQ8BsAedLZ69ep5MY1xh9FoxJEjR3Do0CEnjwTv4j527JhQHmEm//Zv/4bY2Nh5NYIKBcxQhAhvkroUCoXIsKhUKuj1ekEH48yZM4KYTWZmJlavXu31F3tkZMTl6IVSKor72Lhxo195I3q9XqTrsGnTJsmQ+EuXLsFgMGDx4sU+VSvj4XU9pVyXMpkMu3btwrVr10Sp8HzgVHx8/DNvJADfq5l/D8ArAPjl4e9QSk9Ob/sLAF8EYAPwvymlp4PQ72eOma5DjUYjhFSnpaXhl7/8JUZHR6FUKr0O0e7p6UFLS4tHIekbNmxASkqKX2KwNptNONf69euRmprqdLxbt25hZGQEVqsVHR0dsNlsolHUqlWr0NjY6JF6N6UUt2/fxtq1ayX73dTUJHInx8XF4TOf+cyCSOYKFJ481n4Oex2P/57R/s+U0n90bCCEFAD4BIBCAOkAzhFCllFK56dk0VOMSqUSAo6ysrKEpDVeJ9IbvYixsTG3JQAIIcjNzUV2drZfgrcTExMibc7MzEzRj9dqtaKzsxNdXV3CQuL4+Dj6+/tFhiItLQ09PT0ey/zzfe7v73dyxXZ2dgojptTUVJSUlHhUM/VZwqdq5rNwAMBvpksLthNCWgBsgr2AECOI8C67Gzdu4Ny5c0I8R1dXFyIjI/36cQP2IfqGDRv87SaGhoZEStvj4+OIi4sTpmJTU1OSWhFWqxVjY2NOCumeQAjB+vXrhZKFroxiQkICtm7d+ky6P93hz+TrNULIfULIfxFC+OifDADdDvtop9ucIIS8SgipIYTUuIuwY3jOli1b8Fd/9VfYvXs3du/eLVQlVygUPhsLb/Qx3SGTyUT9qK6u9ihPRqfTiSpu2Ww2r5LKbDYbrl696tJIhIeH42Mf+xg++UmpelcMX+/+vwN4AwCd/v/HAL4AQCrQXTIIYK6LFD+rvP3228LfWq121hwRV8TExAQsZyI7OxuxsbGS8STecP78eY+Twiil+OCDD2bd54033phV+PdZxydDQSkVzDIh5F0AfACAFoCjcksmgB6fe8cIKBkZGTh48KCo7fr165JakPORqakpHDt2zOsAKleo1Wr867/+q/A3wzW+VjNPo5Ty2mCHADyc/rsSwHuEkH+CfTFzKYBbfveSERAIIU5RmmvXrkVubq5kecP3338fd+/ehV6vx6VLl7Bt2za353jw4AHUajWWLFkCi8UiaEVs2rTJpTemrq4Oy5cv90jDYWpqCpcuXRJ5aPR6vZDuXVpaOmsk6oMHD1BeXo6vf/3rkMlkz0yuhr944h79NYDtABIJIVoAfwNgOyFkLezTig4AXwIASmk9IeR3AB4BsAL4KvN4zG+io6MRHR0tua2iokKQlpfJZFi6dCnq6+tn1ascHx8HpRSTk5Nobm4WvBKPHj3CkiVLEB8fD5VKhZUrV+LhQ/vzZWxszKvyiDPT0jmOE9oc1y0yMjIEZWyenp4e5Ofn+xWX8SwS0Grm0/v/PYC/96dTjPnBunXrnErejY2NwWq1oru7GzqdTrLWKK/16ajE1dHRAYVCIUqtn3lcg8GArKwsbNy40at+Go1GocLbpk2bhIXXJUuW4KWXXvLqWAxpWGQmwyv4oj9HjhzBwMCAk5hwXFwc+vv7odVqQQgRCd/qdDqRtoNjvsjk5CSMRiPKy8udRgGM0EOCXaPBE4qKiqhjzQbG009jYyN+/OMf49133w11VxgeQgippZQWSW1jQeyMoLB8+XKRa5bxdMMMBSNosGSqhQO7kwwGwy3MUDAYDLcwQ8FgMNzCDAWDwXALMxQMBsMtzFAwGAy3MEPBYDDcwgwFg8FwCzMUDAbDLcxQMBgMtzBDwWAw3MIMBYPBcAszFAwGwy3MUDAYDLcwQ8FgMNzCDAWDwXCLW0MxXQlsgBDy0KHtt4SQu9P/Ogghd6fbcwghRodtPwti3xkMxhzhU5FiSun/y/9NCPkxAMeSTa2U0rUB6h+DwZgH+FWkmBBCAHwcwI4A94vBYMwj/F2jKAXQTyl97NCWSwipI4RcIoSU+nl8BoMxD/C3rscnAfza4XUvgCxK6TAhZAOADwghhZTS8ZlvJIS8CuBVAB6VkmMwGKHD5xEFIUQB4DCA3/JtlFIzpXR4+u9aAK0Alkm9n1L6DqW0iFJalJSU5Gs3GAzGHODP1GMXgEZKqZZvIIQkEULk038vhr1IcZt/XWQwGKHGE/forwFcB5BPCNESQr44vekTEE87AKAMwH1CyD0AvwfwZUrpSCA7zGAw5h5fixSDUvp5ibb3Abzvf7cYDMZ8gkVmMhgMtzBDwWAw3MIMBYPBcAszFAwGwy3MUDAYDLcwQ8FgMNxCKKWh7gMIIYMAJgEMhbovc0Qino1rfVauE1gY15pNKZUMk54XhgIACCE1lNKiUPdjLnhWrvVZuU5g4V8rm3owGAy3MEPBYDDcMp8MxTuh7sAc8qxc67NyncACv9Z5s0bBYDDmL/NpRMFgMOYpITcUhJAXCCFNhJAWQsi3Q92fQDOtUv5gWpW8ZrotnhBylhDyePr/uFD30xdcKLS7vDZCyF9M3+cmQsie0PTaN1xc6/cIIU8cVOf3Omx7aq9VipAaimmRm38DUAGgAMAnCSEFoexTkCinlK51cJ99G8B5SulSAOenXz+N/BzACzPaJK9t+r5+AkDh9Hv+Ly9y9JTwczhfKwD88/S9XUspPQksiGt1ItQjik0AWiilbZTSKQC/AXAgxH2aCw4A+MX0378AcDB0XfEdSullADOFiVxd2wEAv5mWS2wH0AL7/X8qcHGtrniqr1WKUBuKDADdDq+1020LCQrgDCGkdlpQGABSKKW9ADD9f3LIehd4XF3bQr3XrxFC7k9PTfhp1oK71lAbCiLRttDcMM9RStfDPr36KiGkLNQdChEL8V7/O4AlANbCrkD/4+n2BXetoTYUWgCLHF5nAugJUV+CAqW0Z/r/AQBHYR+C9hNC0gBg+v+B0PUw4Li6tgV3ryml/ZRSG6WUA/Au/jC9WHDXGmpDcRvAUkJILiEkHPYFoMoQ9ylgEEIiCSFR/N8AngfwEPZr/Nz0bp8DcCw0PQwKrq6tEsAnCCFKQkgu7Artt0LQv4DBG8RpDsF+b4EFeK3+FgDyC0qplRDyGoDTAOQA/otSWh/KPgWYFABH7ZUXoQDwHqX0Q0LIbQC/m1Y07wLwsRD20WemFdq3A0gkhGgB/A2AH0Di2iil9YSQ3wF4BMAK4KuUUltIOu4DLq51OyFkLezTig4AXwKe/muVgkVmMhgMt4R66sFgMJ4CmKFgMBhuYYaCwWC4hRkKBoPhFmYoGAyGW5ihYDAYbmGGgsFguIUZCgaD4Zb/H/aAWqSaUGdVAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy.matlib\n", "\n", "max_row = np.arange(np.shape(np_array)[0]).reshape(-1,1)\n", "max_col = np.arange(np.shape(np_array)[1]).reshape(-1,1).T\n", "\n", "row_ind = np.tile(max_row, [1,np.shape(np_array)[1]])\n", "col_ind = np.tile(max_col, [np.shape(np_array)[0],1])\n", "\n", "list_rind = np.reshape(row_ind,np.shape(np_array)[0]*np.shape(np_array)[1])\n", "list_cind = np.reshape(col_ind,np.shape(np_array)[0]*np.shape(np_array)[1])\n", "\n", "\n", "list_rind = np.delete(list_rind,np.argwhere(pixel_list<5))\n", "list_cind = np.delete(list_cind,np.argwhere(pixel_list<5))\n", "\n", "segmented_image = 3*np.ones(np.shape(np_array))\n", "\n", "for i in np.arange(len(list_rind)):\n", " \n", " segmented_image[list_rind[i], list_cind[i]] = np.argmax(gamma[i,:])\n", " \n", "plt.imshow(segmented_image, cmap='gray')\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": 130, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "4.565117792090513e-93\n" ] } ], "source": [ "print(np.max(gamma[:,2]))\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise 2. Image compression \n", "\n", "\n", "#### 2.1. plotting the eigenvalues\n", "\n", "Consider the simple image given below. We would like to compress this image by means of principal component factorization. For this purpose, we will see the columns as our feature vectors. Build the covariance matrix associated to the columns of the image (don't forget to center them first) and plot the eigenvalues associated to this covariance matrix. What do you notice? " ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from PIL import Image\n", "from matplotlib import pyplot as plt\n", "\n", "img = Image.open('shapes.png')\n", "data1 = np.array(img)\n", "\n", "plt.imshow(data1)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYEAAAD8CAYAAACRkhiPAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8vihELAAAACXBIWXMAAAsTAAALEwEAmpwYAAAcNElEQVR4nO3de5ScdZ3n8fenqro7SedGSIdL7kgIZsQBpjfDiKPogAbNMS7j0aDOesmYg8qss86eAVbP6uycOeic2dnRJSNEjRFHw+agMhGj6LpCREHTUS7BEOhENE2AzgXItdO37/5RT4ei7Uo6qXs/n9c5daqeX12eb/+S6k//nt9zUURgZmbplKl1AWZmVjsOATOzFHMImJmlmEPAzCzFHAJmZinmEDAzSzGHgJlZijkEzMxSLFfLlUuaA9wC7AWeiIjP1LIeM7O0KXsISFoDLAW6I+JVBe1LgM8BWeBLyS/8C4DvRsRtkm4/2WdPnz495s2bV+6SzczGtC1btuyNiLaRnlO5Txsh6XXAIeD2oRCQlAWeAK4CuoDNwLXAc8CdQABfi4ivnOiz29vbo6Ojo6z1mpmNdZK2RET7SM+VfU4gIjYB+4c1LwY6I2JnRPQCdwDLgA8An4qINwJvHenzJK2U1CGpY8+ePeUu18ws1ao1MTwT2FWw3JW0fR/4z5JuBZ4a6Y0RsToi2iOiva1txNGMmZmdpmpNDGuEtoiIrcA7qlSDmZkNU62RQBcwu2B5FrC7Sus2M7MiqhUCm4EFkuZLagaWAxuqtG4zMyui7CEgaR3wALBQUpekFRHRD1wP3ANsA9ZHxGPlXreZmZ2ass8JRMS1Rdo3AhvLvT4zMzt9qThtxHMHevine7bzu31Hal2KmVldSUUI9PYPcsuPO/m/256rdSlmZnUlFSEwe9oEzmtr5b4nfLCZmVmhVIQAwBUXzODBnfs42NNX61LMzOpGakLgmktncqx/kM9+/3H6BwZrXY6ZWV1ITQi8auYU/uKyufzbg7/jk3dtrXU5ZmZ1ITUhAPA/lv0B7/uTuazv2MUjXS/Uuhwzs5pLVQhI4mNXXkDbpBbe88Wfc/+Te2tdkplZTaUqBACmtTbz7Y9czrlTx/Of1vycz37/cQ4f6691WWZmNZG6EAA4d+p4vvmR1/DO9tl84d4dXPL3P+Sj3/ilDyYzs9Qp+5XFKqkSVxbb8tvn+c7Du1nfsYujfQP82YUz+PNLZ7Hw7EnMO7OVTGaks2CbmTWOE11ZLPUhMOTZF3v4+s9/y7pf7GLvoWMATJ/YzOsvmMGlc6dy8eypLDxrErlsKgdPZtbAHAKnoLd/kEeffoEd3Yf5Sedeftq5l/2HewFoyWU4r20iF549iUXnTOaV50xm0bmTmdbaXNGazMxK4RAoQUSwa/9RfrXrebY+/SJPdh9i+7MHeebFnuOvmTGphXOnjufsyeM4e0r+ds6UcbRNamHGpHHMmNzCpJYckjctmVn1nSgEqnV5yYYliTlnTmDOmRNYdvHM4+37D/ey7ZkD/Hr3AbY/d5BnX+yhc88hftq5l4Mj7G3UnM1wRmsTk8c1cfaUcSw8axLTJ7VwxoQmpk5oZlprM2dMaOKMCc2cMaHZcxFmVhUOgdM0rbWZy8+fzuXnT/+95w4d6+fZF4/SfeAYew4do/vAMfYd7uX5w70c6Onjd/uP8LUHf8ux/pFPX5HNiDMmNDFpXBOTxuWYnNy/9LhgefzLXzN077kLMxsNh0AFTGzJcf6MSZw/Y1LR10QER3oHeP5ILy8c6WP/4V6eP5IPir2Hetl3uJeDPX0c7OnnYE8fzx3o4UCyfKR34KQ1jG/KviwkJo1rYvLL7nNMbMkxvjnLuKaXbuObsoxryiT3Q7cMLbksTVl5k5bZGFPTEJB0HvAJYEpEvKOWtVSbJFpbcrS25Jh1xqm9t39gkEPH+jlwtP94MBzs6eNAcn98+Wg/B4/ll1882kfX/iPHX1NsFHIiGUFLLh8K45qytOReum9pyvKKtlbee9lcFp0z2WFh1iDKHgKS1gBLge6IeFVB+xLgc0AW+FJEfCYidgIrJN1Z7jrGslw2w9QJzUydcPp7JfX254Okp2+Ao30D9CS3o72Dv9d2rH8weTzIsf6R73v6BrjrV7tZ94tdTB6XD7cJzVn+4NwpLLv4XP7slWeVsQfMrFwqMRJYC9wC3D7UICkLrAKuArqAzZI2RMSvK7B+G4XmXIZpufLu2vrikT42PLKbJ549yNG+AQ729HHfE3v42Y69dHzyqrKuy8zKoxIXmt8kad6w5sVAZ/KXP5LuAJYBJw0BSSuBlQBz5swpb7FWVlMmNPEXl819Wdvffecx7uzoqlFFZnYy1dqFZCawq2C5C5gp6UxJtwKXSLpppDdGxOqIaI+I9ra2tmrUamWUy4j+wcY5FsUsbao1MTzSLGFExD7guirVYDWQzWQYcAiY1a1qjQS6gNkFy7OA3VVat9VQfiTgy3ma1atqhcBmYIGk+ZKageXAhiqt22oolxWDAYMeDZjVpbKHgKR1wAPAQkldklZERD9wPXAPsA1YHxGPlXvdVn9yyekvBhroHFVmaVKJvYOuLdK+EdhY7vVZfctm8n9nDAwGTdkaF2Nmv8cnmLGKGhoJ9A14XsCsHjkErKKyQ5uDPCdgVpccAlZRuWw+BHysgFl9cghYRXkkYFbfHAJWUU3JxLBHAmb1ySFgFXV8JDDgEDCrRw4Bq6iX5gS8d5BZPXIIWEUNjQS8OcisPjkErKKGjhPo9+Ygs7rkELCKKjxi2Mzqj0PAKur4SMBzAmZ1ySFgFTU0MeyRgFl9cghYRXli2Ky+OQSsonKeEzCraw4BqyiPBMzqm0PAKuqlXUQ9MWxWjxwCVlEeCZjVt7JfWexUSMoAfw9MBjoi4qu1rMfKz3sHmdW30x4JSFojqVvS1mHtSyRtl9Qp6caTfMwyYCbQB3Sdbi1Wv3I+i6hZXStlJLAWuAW4fahBUhZYBVxF/pf6ZkkbgCxw87D3fxBYCDwQEbdJuhP4UQn1WB06fqF5HyxmVpdOOwQiYpOkecOaFwOdEbETQNIdwLKIuBlYOvwzJHUBvcniwOnWYvUr63MHmdW1ck8MzwR2FSx3JW3FfAt4s6T/DWwa6QWSVkrqkNSxZ8+e8lVqVeE5AbP6Vu6JYY3QVvTbHxFHgBUn+sCIWA2sBmhvb/dvkgYzNBLocwiY1aVyjwS6gNkFy7OA3WVehzWQ40cM+zgBs7pU7hDYDCyQNF9SM7Ac2FDmdVgD8XECZvWtlF1E1wEPAAsldUlaERH9wPXAPcA2YH1EPFaeUq0RNXlOwKyulbJ30LVF2jcCG0+7IhtTPBIwq28+bYRVlM8ialbfHAJWUclAwCMBszrlELCKkkQuI59F1KxOOQSs4rIZeXOQWZ1yCFjF5TLy5iCzOuUQsIrLZTMeCZjVKYeAVVx+JOA5AbN65BCwivOcgFn9cghYxeX3DnIImNUjh4BVXDbrkYBZvXIIWMXlMhmfStqsTjkErOLycwKeGDarRw4Bq7imbIbefoeAWT1yCFjFTR6X48DR/lqXYWYjcAhYxU0Z38SLR/tqXYaZjcAhYBU3dYJDwKxeOQSs4qaMb+KFo721LsPMRlC1EJB0nqQvS7qzoO2Vkm6VdKekD1erFquuqROa6ekbpKdvoNalmNkwowoBSWskdUvaOqx9iaTtkjol3Xiiz4iInRGxYljbtoi4Dngn0H6qxVtjmDy+CYAD3iRkVndGOxJYCywpbJCUBVYBVwOLgGslLZJ0kaS7h91mFPtgSW8D7gd+dFo/gdW9qUkIeF7ArP6M6kLzEbFJ0rxhzYuBzojYCSDpDmBZRNwMLB1tARGxAdgg6bvAN0b7PmscUxwCZnWrlDmBmcCuguWupG1Eks6UdCtwiaSbkrYrJH1e0m3AxiLvWympQ1LHnj17SijXamXqhHwIvHDEIWBWb0Y1EihCI7QVPUFMROwDrhvWdi9w74lWEhGrgdUA7e3tPgFNA/JIwKx+lRICXcDsguVZwO7SyrGx6IzWZjKCL93/G57sPsTrL2gjlxXTJ7Ywf3prrcszS7VSQmAzsEDSfOBpYDnw7rJUZWPK5HFN3HzNRdx2305Wb9rBrfftOP7cvDMn0NqS42/edAFvvPCsGlZplk6KOPkWFknrgCuA6cBzwKci4suS3gL8C5AF1kTEP1Su1PzmoI6Ojkquwips9wtH+c3ew0TAI0+/wK93H+DxZw/S2X2IS+ZM5T1/PJd3/NGsWpdpNqZI2hIRI+6GP6oQqBcOgbHpSG8///rjHdz10NN0PX+UllyG5lyG+dNbmXtmK+/7k7n84eypNGV9gLvZ6XAIWEPo7R/kaw/+lu4DPfT0DfD4swd5pOtFjvYNcN70Vv7yT89j4dmT+KO5Z9S6VLOGcqIQKGVOwKysmnMZVrx2/svaug/0sPHRZ7jlx538t28/igTXvf4V/OVr53PmxJYaVWo2djgErK7NmDyO918+n/deNpen9h3h4+sf4gv37qApIz7+poW1Ls+s4XkjqzWEXDbD+TMm8u2PXA7ACz7mwKwsHALWULIZMXPqeA4d85XKzMrBIWANZ2JLjsMOAbOycAhYw5k4LueRgFmZOASs4bS25Dh0zBeoMSsHh4A1nIktWW8OMisTh4A1nIktOQ71OATMysEhYA2n1RPDZmXjELCGM7Elx6HefhrplCdm9cohYA2ntSVHBBzp9eSwWakcAtZwJrbkz3biTUJmpXMIWMMZCgEfK2BWOoeANZxWh4BZ2TgErOF4JGBWPg4Bazjjm7MA9PR5YtisVFW7noCktwNvBWYAqyLiB5JagX8FeoF7I+Lr1arHGldTVgD09nsXUbNSjWokIGmNpG5JW4e1L5G0XVKnpBtP9BkRcVdEfAh4P/CupPka4M6k/W2nXr6lUUsu/9+2d2CwxpWYNb7RjgTWArcAtw81SMoCq4CrgC5gs6QNQBa4edj7PxgR3cnjTybvA5gFPJo89tjeRmXogvN9/Q4Bs1KNKgQiYpOkecOaFwOdEbETQNIdwLKIuBlYOvwzJAn4DPC9iPhl0txFPggeosioRNJKYCXAnDlzRlOujXHNyUigzyMBs5KVMjE8E9hVsNyVtBXzV8CVwDskXZe0fQv4c0lfAL4z0psiYnVEtEdEe1tbWwnl2lgxNBLw5iCz0pUyMawR2orO1EXE54HPD2s7DHyghBoshY6HgDcHmZWslJFAFzC7YHkWsLu0csxOruX45iDvHWRWqlJCYDOwQNJ8Sc3AcmBDecoyK84jAbPyGe0uouuAB4CFkrokrYiIfuB64B5gG7A+Ih6rXKlmedmMyMgTw2blMNq9g64t0r4R2FjWisxGoTmXcQiYlYFPG2ENqSmb4Zg3B5mVzCFgDanFIwGzsnAIWENqymY8MWxWBg4Ba0hNWY8EzMrBIWANKT8x7OMEzErlELCG5Ilhs/JwCFhDas7Km4PMysAhYA3JxwmYlYdDwBqS9w4yKw+HgDUkjwTMysMhYA3JE8Nm5eEQsIbU7OMEzMrCIWANyccJmJWHQ8AaUlNWnhg2KwOHgDUkTwyblYdDwBpSUzbjC82blYFDwBpSs48TMCuLUV1ZrBwkvR14KzADWBURP5D0p8B7kjoWRcRrqlWPNTZvDjIrj9FeY3iNpG5JW4e1L5G0XVKnpBtP9BkRcVdEfAh4P/CupO0nEXEdcDfw1dP6CSyVmrIZBgMGBr2HkFkpRrs5aC2wpLBBUhZYBVwNLAKulbRI0kWS7h52m1Hw1k8m7yv0bmDdaf0ElkrjmvL/dfcf7q1xJWaNbVQhEBGbgP3DmhcDnRGxMyJ6gTuAZRHxaEQsHXbrVt5nge9FxC+HPkTSHODFiDgw0rolrZTUIaljz549p/VD2tjzugvaAFj1407PDZiVoJSJ4ZnAroLlrqStmL8CrgTeIem6gvYVwFeKvSkiVkdEe0S0t7W1lVCujSUXnj2Zi2dPZe3PnuLKf76PnXsO1boks4ZUysSwRmgruoE2Ij4PfH6E9k+VUIOl2Kr3XMr9T+7hH767jQ+u3czHrlzAWZPGsXj+NHJZ7/hmNhqlhEAXMLtgeRawu7RyzEZv5tTxvOs/zCECbvr2o/yX//MwAJedN41rLp3Fla88i2mtzTWu0qy+lRICm4EFkuYDTwPLyU/wmlXV8sVzuPqic9hzsIdv/vJpbrtvBw/u3M/86a2s+9BlnD1lXK1LNKtbo91FdB3wALBQUpekFRHRD1wP3ANsA9ZHxGOVK9WsuCnjmzh/xiRuWHIhj3z6zfyvd/0hv9l7mMtu/hH3PeEdCsyKUUTj7Gfd3t4eHR0dtS7DGsTPduzlb9Y/TEZi09++gWxmpGkss7FP0paIaB/pOc+e2Zj1mldM55NvXcTTLxzlwZ37al2OWV1yCNiY9sYLZ9DanOU9X/o5N39vG995eLcPMDMrULVzB5nVwvjmLDdcfSH//tBubrtv5/H2P10wnXe2z2bpq89B8mYiSy/PCVhqHOjp45FdL3Lv9m6+8rOnGBgM3nLR2bx78VwuO8/HFtjYdaI5AYeApVJP3wBfvv83/NMPthMBn7nmIpYvnlPrsswqwhPDZsOMa8ry0Tecz09veCOtzVk2PLybRvqDyKxcHAKWaudOHc8HXzufn+3Yx9Wf+wkP7NjHoE9PbSniELDU+8Dl8/nwFa/g8WcPcu0XH+Q7j/jsJ5YeDgFLvWmtzdyw5ELu+ujlABw42lfjisyqxyFglpg7bQIA/d4cZCniEDBLZLP54wV8yUpLE4eAWSIrh4Clj0PALDF0grkB7ypqKeIQMEscD4EBh4Clh0PALHF8c5BHApYiDgGzRCYjJM8JWLo4BMwK5DJyCFiqVC0EJL1S0q2S7pT04YL2VklbJC2tVi1mxWTkELB0Ge01htdI6pa0dVj7EknbJXVKuvFEnxER2yLiOuCdQOHZ7G4A1p9q4WaV4JGApc1oRwJrgSWFDZKywCrgamARcK2kRZIuknT3sNuM5D1vA+4HfpQsXwn8GniuLD+NWYkyGfmIYUuVUV1ZLCI2SZo3rHkx0BkROwEk3QEsi4ibgRE37UTEBmCDpO8C3wDeALSSD5GjkjZGxGDheyStBFYCzJnj871bZeUyYtB7B1mKlHJ5yZnAroLlLuCPi71Y0hXANUALsBEgIj6RPPd+YO/wAEhesxpYDfmLypRQr9lJZT0SsJQpJQRGujBr0W9PRNwL3FvkubUl1GFWNtmMfD0BS5VS9g7qAmYXLM8CfCJ2a2hZeSRg6VJKCGwGFkiaL6kZWA5sKE9ZZrWRzXrvIEuX0e4iug54AFgoqUvSiojoB64H7gG2Aesj4rHKlWpWeVkfJ2ApM9q9g64t0r6RZJLXbCzI+jgBSxmfNsKsQC6TcQhYqjgEzAr4YDFLG4eAWQEfLGZp4xAwK+CRgKWNQ8CsQM4Hi1nKOATMCuQPFvu9s5eYjVkOAbMC+dNG1LoKs+pxCJgVyJ9Azilg6eEQMCuQzYgBTwlYijgEzArkjxj2SMDSwyFgViAfArWuwqx6HAJmBfInkHMKWHo4BMwK+FTSljYOAbMCPpW0pY1DwKxALiMGfO4gSxGHgFmBTEYMeB9RSxGHgFkBjwQsbaoaApJaJW2RtDRZPk/SlyXdWc06zIrJ+MpiljKjvcbwGkndkrYOa18iabukTkk3juKjbgDWDy1ExM6IWHFqJZtVTs4hYCkzqmsMA2uBW4DbhxokZYFVwFVAF7BZ0gYgC9w87P0fBF4N/BoYV1rJZpWTka8nYOky2gvNb5I0b1jzYqAzInYCSLoDWBYRNwNLh3+GpDcArcAi4KikjRFx0qNyJK0EVgLMmTNnNOWanTZfT8DSppQ5gZnAroLlrqRtRBHxiYj4a+AbwBcjYlDSmZJuBS6RdFOR962OiPaIaG9rayuhXLOTy/rKYpYyo90cNBKN0HbSb09ErC14vA+4roQazMoq6zkBS5lSRgJdwOyC5VnA7tLKMast7yJqaVNKCGwGFkiaL6kZWA5sKE9ZZrWRyYgIPC9gqTHaXUTXAQ8ACyV1SVoREf3A9cA9wDZgfUQ8VrlSzSovl8lv5fRowNJitHsHXVukfSOwsawVmdVQZigEBoOmbI2LMasCnzbCrECuIATM0sAhYFYgo3wIeDdRSwuHgFmBoZGAJ4YtLRwCZgWyGY8ELF0cAmYFspn8V2LQewdZSjgEzApkk2+ERwKWFg4BswLHRwIOAUsJh4BZAY8ELG0cAmYFhkYCA4MnPcu52ZjgEDArkOwchOeFLS0cAmZmKeYQMDNLMYeAmVmKOQTMzFLMIWBmlmIOATOzFHMImJmlmEPAzCzFHAJmI/CxYpYWigY6NFLSHuC3JXzEdGBvmcopJ9d1alzXqXFdp65eazvduuZGRNtITzRUCJRKUkdEtNe6juFc16lxXafGdZ26eq2tEnV5c5CZWYo5BMzMUixtIbC61gUU4bpOjes6Na7r1NVrbWWvK1VzAmZm9nJpGwmYmVkBh4CZWYqlIgQkLZG0XVKnpBtrXMtTkh6V9JCkjqRtmqQfSnoyuT+jCnWskdQtaWtBW9E6JN2U9N92SW+uQW2flvR00m8PSXpLNWuTNFvSjyVtk/SYpI8l7TXtsxPUVdP+StYzTtIvJD2c1PZ3SXut+6xYXTXvs2RdWUm/knR3slzZ/oqIMX0DssAO4DygGXgYWFTDep4Cpg9r+0fgxuTxjcBnq1DH64BLga0nqwNYlPRbCzA/6c9slWv7NPBfR3htVWoDzgEuTR5PAp5I1l3TPjtBXTXtr2RdAiYmj5uAnwOX1UGfFaur5n2WrO/jwDeAu5PlivZXGkYCi4HOiNgZEb3AHcCyGtc03DLgq8njrwJvr/QKI2ITsH+UdSwD7oiIYxHxG6CTfL9Ws7ZiqlJbRDwTEb9MHh8EtgEzqXGfnaCuYqr2bxl5h5LFpuQW1L7PitVVTNX6TNIs4K3Al4atv2L9lYYQmAnsKlju4sRfkkoL4AeStkhambSdFRHPQP5LDcyoUW3F6qiXPrxe0iPJ5qKhIXHVa5M0D7iE/F+QddNnw+qCOuivZNPGQ0A38MOIqIs+K1IX1L7P/gX4W2CwoK2i/ZWGENAIbbXcL/byiLgUuBr4qKTX1bCW0aqHPvwC8ArgYuAZ4H8m7VWtTdJE4JvAX0fEgRO9dIS2atZVF/0VEQMRcTEwC1gs6VUneHnVaitSV037TNJSoDsitoz2LSO0nXJdaQiBLmB2wfIsYHeNaiEidif33cC3yQ/fnpN0DkBy312j8orVUfM+jIjnki/uIPBFXhr2Vq02SU3kf9F+PSK+lTTXvM9Gqqse+qtQRLwA3AssoQ76bKS66qDPLgfeJukp8put3yjp36hwf6UhBDYDCyTNl9QMLAc21KIQSa2SJg09Bt4EbE3qeV/ysvcB/16L+k5QxwZguaQWSfOBBcAvqlnY0Jcg8R/J91vVapMk4MvAtoj454KnatpnxeqqdX8lNbRJmpo8Hg9cCTxO7ftsxLpq3WcRcVNEzIqIeeR/T/2/iHgvle6vSs1w19MNeAv5vSZ2AJ+oYR3nkZ/Nfxh4bKgW4EzgR8CTyf20KtSyjvyQt4/8XxQrTlQH8Imk/7YDV9egtq8BjwKPJP/5z6lmbcBryQ+1HwEeSm5vqXWfnaCumvZXsp5XA79KatgK/PeT/X+vUp8Vq6vmfVawvit4ae+givaXTxthZpZiadgcZGZmRTgEzMxSzCFgZpZiDgEzsxRzCJiZpZhDwMwsxRwCZmYp9v8BUDMYBLz5EhgAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "mean_col = np.mean(img, axis=1)\n", "\n", "centered_image = img - np.matmul(mean_col.reshape(-1,1), np.ones((1, np.shape(img)[1])))\n", "\n", "\n", "covariance = (1/np.shape(img)[1]) * np.matmul(centered_image, centered_image.T)\n", "\n", "w, v = np.linalg.eig(covariance)\n", "\n", "# sort the eigenvalues in decreasing order\n", "\n", "wsorted_indices = np.argsort(w)[::-1]\n", "\n", "\n", "w_sorted = w[wsorted_indices]\n", "v_sorted = v[:,wsorted_indices]\n", "\n", "plt.semilogy(np.real(w_sorted))\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 2.2. projection onto the principal vectors\n", "\n", "Given your result from the previous question, compress the image by computing its principal component factorization for increasing numbers of components. Compare the reconstructions." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "subspace = np.real(v_sorted[:,:8])\n", "\n", "reconstructed_image = np.matmul(subspace, np.matmul(subspace.T, img))\n", "\n", "plt.imshow(reconstructed_image)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Exercise 3: Face recognition\n", "\n", "In this exercise, we consider the 'Labeled Faces in the Wild' dataset from UM Amherst. We would like to train a Maximum margin classifier on this dataset (scikit learn 'svm') with a Gaussian kernel. In its original form, the dimensionality of the data is too high (if we used the raw images as our feature vectors, each vector would encode 75$\\times$56 features). Although it can sometimes be a blessing, high dimensionality can also be a curse. Working in a high dimensional space means that the feature vectors will be very distant from each other which could result in a meaningless classifier. To avoid this, we will start by computing a principal component decomposition of our set of images. The SVM classifier will then be applied on the PCA representation of the training images. " ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "\n", "from sklearn.datasets import fetch_lfw_people\n", "from sklearn.model_selection import train_test_split\n", "\n", "import matplotlib.pyplot as plt\n", "\n", "lfw_people = fetch_lfw_people(min_faces_per_person=70, resize=.6)\n", "\n", "n_samples, h, w = lfw_people.images.shape\n", "\n", "images = lfw_people.data\n", "targets = lfw_people.target\n", "\n", "training_images, test_images, train_targets, test_targets = \\\n", "train_test_split(images,targets, test_size = .10, random_state=10)\n", "\n", "plt.imshow(training_images[0,:].reshape(h,w), cmap='gray')\n", "plt.axis('off')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Question 3.1. PCA decomposition\n", "\n", "- Extract the first 50, 100, 200 and 300 principal components from the image dataset and display the corresponding reconstruction for one of the faces. \n", "\n", "\n", "- Display the plot of the reconstruction error (deviation between the true image and its PCA reconstruction for K=1 to h*w)\n", "\n", "\n", "- Finally, plot each of the principal images for K=1,...10" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from sklearn.decomposition import PCA\n", "\n", "# put your code here \n", "\n", "import numpy as np\n", "from sklearn.decomposition import PCA\n", "\n", "\n", "pca = PCA(n_components=300, whiten=True)\n", "latent_rep = pca.fit_transform(training_images)\n", "\n", "reconstructed_image0 = pca.inverse_transform(latent_rep[2,:])\n", "\n", "plt.subplot(1, 2, 1)\n", "plt.imshow(reconstructed_image0.reshape(h, w))\n", "\n", "plt.subplot(1, 2, 2)\n", "plt.imshow(training_images[2,:].reshape(h, w))\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Question 3.2. \n", "\n", "Now that we have a PCA decomposition, we can learn our Max Margin classifier. We will do this with the svc model of scikit learn. finding the optimal parameters is a little tricky because of the dimension. One approach is to carry out cross validation over a parameter grid. To spare the search for the parameter values, this step is implemented below. \n", "\n", "- Complete the code below with the training of the Max Margin classifier (remember to split your dataset between a training and validation part).\n", "\n", "\n", "- Once you have trained the SVC, apply it on the test set and display the predictions vs actual targets. " ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "GridSearchCV(estimator=SVC(class_weight='balanced'),\n", " param_grid={'C': [1000.0, 5000.0, 10000.0, 50000.0, 100000.0],\n", " 'gamma': [0.0001, 0.0005, 0.001, 0.005, 0.01, 0.1]})" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sklearn.svm import SVC\n", "from sklearn.model_selection import GridSearchCV\n", "\n", "param_grid = {'C': [1e3, 5e3, 1e4, 5e4, 1e5],\n", " 'gamma': [0.0001, 0.0005, 0.001, 0.005, 0.01, 0.1], }\n", "\n", "clf = GridSearchCV(SVC(kernel='rbf', class_weight='balanced'), param_grid)\n", "\n", "\n", "clf.fit(latent_rep, train_targets)\n" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "\n", "latent_rep_test = pca.transform(test_images)\n", "\n", "predicted_targets = clf.predict(latent_rep_test)\n", "\n", "plt.plot(test_targets[::4], '-r', alpha=0.4)\n", "plt.plot(predicted_targets[::4], '-b', alpha=0.4)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.8294573643410853" ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sklearn.metrics import accuracy_score\n", "\n", "accuracy_score(test_targets, predicted_targets)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### II. Independent component analysis: The coktail party " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this exercise, we will use another approach to dimensionality reduction, known as independent component analysis (ICA). ICA is particularly useful in speech or more generally, source separation. In the classical version of this problem, known as \"The coktail party problem\", one is interested in recovering two distinct signals from their mixing. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\"Drawing\"\n", "\n", "image credit: [The conversation](https://en.wikipedia.org/wiki/The_Conversation) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__Exercise II.4.a.__ Using the FastICA transform from scikit-learn, recover the two speeches from the mixed1.wav and mixed1.wav files which are given on github. \n", "\n", "(Hint: start by storing the two signals 'samples1' and 'samples1' into a single matrix, then pass this matrix as an input to the FastICA method of Scikit-learn) " ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Automatically created module for IPython interactive environment\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "print(__doc__)\n", "\n", "import os\n", "import wave\n", "import pylab\n", "import matplotlib\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from scipy import signal\n", "from scipy.io import wavfile\n", "\n", "from sklearn.decomposition import FastICA, PCA\n", "\n", "###############################################################################\n", "\n", "\n", "# read data from wav files\n", "sample_rate1, samples1 = wavfile.read('mixed1.wav')\n", "sample_rate2, samples2 = wavfile.read('mixed2.wav')\n", "\n", "fig, axs = plt.subplots(2)\n", "axs[0].plot(samples1)\n", "axs[1].plot(samples2)\n", "plt.show()\n", "\n", "# add your code here\n", "\n", "observations = np.vstack((samples1, samples2))\n", "from sklearn.decomposition import FastICA\n", "ICAtransform = FastICA(n_components=2)\n", "\n", "S = ICAtransform.fit_transform(observations.T)\n", "A = ICAtransform.mixing_ " ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(156239, 2)\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "print(np.shape(S))\n", "\n", "fig, axs = plt.subplots(2)\n", "axs[0].plot(S[:,0])\n", "axs[1].plot(S[:,1])\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "__Exercise II.4.b.__ Once you have recovered the original signals, plot them as time series. Then use the lines below to store them in new .wav file. Then play them and compare them with their mixings." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# write data to wav files\n", "\n", "scaled1 = np.int16(S[:,0]/np.max(np.abs(S[:,0])) * 32767)\n", "wavfile.write('recovered-1DemoJune28.wav', sample_rate1, scaled1)\n", "\n", "scaled2 = np.int16(S[:,1]/np.max(np.abs(S[:,1])) * 32767)\n", "wavfile.write('recovered-2DemoJune28.wav', sample_rate2, scaled2)\n" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 4 }