{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Title: High Dimensional Images and Low Dimensional Representations\n", "Author: Thomas Breuel\n", "Institution: UniKL" ] }, { "cell_type": "code", "execution_count": 79, "metadata": { "collapsed": false }, "outputs": [], "source": [ "\n", "import cv2\n", "matplotlib.rc(\"image\",cmap=\"gray\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Head Rotation" ] }, { "cell_type": "code", "execution_count": 80, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "251.0\n" ] } ], "source": [ "frames = cv2.VideoCapture(\"headrot.webm\")\n", "print frames.get(cv2.CAP_PROP_FRAME_COUNT)\n", "data = []\n", "for i in range(200):\n", " _,frame = frames.read()\n", " gray = cv2.cvtColor(frame,cv2.COLOR_BGR2GRAY)\n", " data.append(gray.ravel())\n", "data = array(data)\n", "del frames" ] }, { "cell_type": "code", "execution_count": 81, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(200, 10)\n", "[-4958.87141816 1066.76497348 526.50462093 2966.77444885 1029.42127905\n", " -799.54184935 -254.05764835 -456.85720198 -988.66067974 52.12461804]\n" ] } ], "source": [ "from sklearn.decomposition import RandomizedPCA\n", "pca = RandomizedPCA(10)\n", "lo = pca.fit_transform(data)\n", "print lo.shape\n", "print lo[0]" ] }, { "cell_type": "code", "execution_count": 82, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 82, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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uvvllate+nC1btpiOJR5Ip+jFY8yZM5dRo57G6Uzl2mv7MGPGVEJDQ03HEilS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\nXLMAAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mds = manifold.LocallyLinearEmbedding()\n", "vl = mds.fit_transform(lo)\n", "scatter(vl[:,0],vl[:,1])" ] }, { "cell_type": "code", "execution_count": 83, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 83, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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MImQoF6w+3SIX5e3yYeHpo/iECzb/6AOIFEXB4XAk7kkhU1iEd8F4pLJAtWdElmU+9rGP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iEnBWlvMMOFZONB7kk0BDVcCCaEY8KKcJuQKxMM0GBqeTIbW9cHNQuSh4Isy7jd7uPIMvHu7xnv\nMce71OWbb77B4ZDw+z9Co7meqqrvkeX36NNnUYOPDXWLKIQK3cbS4zPeaCrGsqSkhBkzZvDPf/6T\n/v37AzXEnKuuuiplY0020t5gCigNZrAhSuS5YoGSCStyqnUxYYO9NEmSArvzYFUQNYS0GpMgOdTO\n/4UK2yez3jOaMSeiDOPzz1fg803B7/8Bn28QWq2Zli11dOvWrcHHjkZxSKlOI74bSY/PeKMxGkvR\nVizYs5w+fTqPP/54yok3qUSzwQxCKJZpohCqVU4k36mursbv9wcEE8IZy0i8tGBquTKk1ZDaw1ih\nhga/0UAZ0oyUkBRc75nsOU9kqcunn36F19sbWIRG40WW3yQv7/UGH1c8y7FuoiLp8RnvOW+sz7Is\ny7WM5eHDh7nooot49NFHGTJkSIpHmVo0G8wg+Hy+qJV7okWsL6Tf78dms6HVarFarWFl7iA2Jmy4\nkFY8VFjqQ31emhoRj5BmXXMO8c97huo4Ei/IssyOHQeQ5RxgFrLcCviAP/5xfIOO21BjGYxwNbai\n56Sy9jDW+RHGsjE9y6Fy2UePHmXatGnMmzeP0047LcWjTD3S3mAK5pfoYZksaTilJF8kECzeYCZs\nKE3YeBT3hxJ0VuaD4rGoCDRGab5EsHfDzXm88p6hyDLxxJ49e7DbfcBFQBZQiSR926DuJMmQjhNz\nLiI1DQ3dNhVjWV5ezrRp05gzZw6nn356agepEqS9wRRtucxmcyB2rzbUx4QNpQkbz5c1WIUlOB+k\n1KKMNcQsSVKjkeZLpJcmEO+8ZzJIVB9//DF+vxF4HigCDqDRFDN06NCYjpdoYxkM5ZyH6/FZX+hW\nbFYbk7EUGzLl+1dZWcn06dO5++67GTVqVIpHqR6kfR2myB3p9XrKy8uxWq1JyTdEeq7g1mH1acKK\nUpJkGR7loiLq4CLdkTdG2bhEe2mRQJn3FC2Z6lrI4x3SDIehQ0fw888AQ4HuwAYMhvcpLf0l6vOq\njSyjFIr3eDzA8eFyZWSnMRnL4J6hVVVVTJs2jdmzZ3P22WeneJTqQtp7mEKjEpLb2Lm+c8XChE2F\n4QkmDYlFPFQfPiXUYHiihVpKXaLJe4p7kWgv7bfffmP9+u3AH4BM4DvgEN26dWj0xhLCC8ULgyPI\nd43dWFZXV3PRRRdxww03NBvLEEh7g6k0Lsk0mHVBlmWqqqpqtQ6rjwmrBsMTTKYIbt0kjKff78fp\ndB7n8QgPVeSTjUYjR44cISsrC6gJE+Xl5QWMQHZ2Nm63O0AUAo6bn3gh2eHBSFFX3lN0lTAajQk1\nPNXV1YwfPwlZbg30BD4GrMBerrzyuqiO1RiYpcHhcqFxrNVqqaqqqnOjqAaEM5YOh4MZM2Ywc+ZM\nzjvvvBSPUp1I+5CsKDgHsNlsGI3GpHgPIm8avPtWMmHFw1wfE1bt9YqyLHPgwAG2bNnC5s2/Ulxc\nwq5dR9FooKKiCq8XysuPoNNZsNkOYzC0QJJ82O02WrbsRlXVTsBAZmY7XK7d+P0m9PosZLkUr9eE\nTmeifXsjR464qapycMIJbbDbfRw+XEnXrq3xeKCkpIKTTuqI1Wrh11/306FDSwYPPpGVKzdiNOqZ\nOHEUGzb8QllZOSef3JeePXvy/fffI8tyoEh7z549mEwmTjzxRHQ6HUePHsXv95Obm6u6cLJo7yZE\nyxMlG7d27VpmzLiaXbvswGnAdmAksBmz+Qf27FkTaP8UyZgbU0gTalImHo8nMObg0G2i2eXRQpAC\nlWMW1zFjxgwuvvjitFDsiRXNBlNFBlMwYY1GYyC0mkgmbCIhyzJbtmzhpZdeZenS7ykp8eP36/D7\nOyHLleh0o4HPgQkYDMtxu4djsRzF6TyETncWWu0LOBzj6dChPcXFTyFJF9OzZx4bNjyB2XwVHTu6\n2bTpDXJzr6OoyMKaNX8mP/8uOnXqzg8/zCAz82q6dz+FtWsvx2icRs+e49i8+Tr8/i6ccMLllJS8\nRlnZt3TufBc+31GKi+eRlzcVs7knbvcbaDSlaDSjkGUNJtNyjEYTVVVF+P02evfW06pVCz777GdA\nw6mndmf27Ct5+OFn2bp1D126tGPu3NmYzWZeffV/HD5s449/HMDIkSORZZkNGzZQVVVFz549yc3N\njfu8h1oQo8171neOH3/8kUceeYqvvlqN09kOaA2UAmOBQ0jSR9x77yXcccctMY9ZzYhkzCIqJOZc\nMJ1jJcjFA8EGHmo2KpdccgmTJ0/m4osvTrlRVzPUE1tKEVIVkg0+l9vtDjRjTQUTNp7YunUrM2fe\nzrp1e/F62wGt0GgmALvQanOQ5ULM5hyqqo6QnT0Cm+1jcnMv5siRm8nIuBC/X4fH48FkGsXRo0vR\naPoiSZ0pL/8erXYkHk8WlZUr0ekmUlUF1dWb0WjOxulshd2+Da12JE5nd1yug2g0p+J2D0SjMeFy\nGYCLMRq7Y7fb8ftvwmAYjNe7GodjOJJ0Ca1aFbJ9+0bKynoxcOAdyDJs2rQOjeY0evW6Dln2s3z5\nhYCfoqJ3kCQNK1Y8yPLlV6HVXovVeg/r1i3n8stvBSQOHhyOVtuHxYtf5ZZbDrJmzWaWLy9Gqy3A\nZPo7Cxc+RMuWLbnnnvmsXbuZNm3ymTfvZk466SS8Xi9LliyhuPgAPXp0Z8SIEbXCZ0ePHqVVq1aB\nTVddHUcaUu9ZXl7OypUrqays5O23P2P16lVUVmqQ5Xb4fBcDh4FtwNnALuBnTjyxJbfeelO9z0o8\nu6QkC5Ea+HBM5+Aen8kK3YYylm63m8svv5zzzjuv2VhGgLQ3mEqkymBGyoRtDCUYr776Ktdf/whu\ndxEwDmgD7DyW36rG5/MjSW7AgiwfQpb1SJIHr3cvOl02fv9GZLkfWq0fl+tnsrMLsNs/R5JKsVja\n4PcvxmDojdmcj8/3I2bz+eh0Ofj9n2I0nolWm4HPtweTSYNWa8LvL0OS/Gg0emTZjSS5joXO/Mhy\nzX3w+11ANuLW+3xuoAhZltFqdcdIHT0BkCQNLpcJvX4kGk1NJEKr7cv+/d9y4ok1oawWLSaze/dz\naLWDKCj4MwAuV38efXQSGs0faNFiEZKko6LiU+6553H0eg2//HIyVutcdu9exxVX3MP77z/Pgw8+\nyRdfOPH7B6LVvsIVV/zK7NnX8tFHy7jrrsfx+zPJyvLy3HMP0atXLzZv3sxjjz1PWVklQ4f2Yfbs\nWZhMJlasWMGnn64kJyeDiy+eSn5+PsuXL2fVqnXk57dgypQL+Omnn1i0aDF+v8zEiSN5993P+Prr\nVZjNBjweH17vEMrKvsbrHY/JlIfPNwS//2W02tPx+e4FZgGfoNFspEMHPcuWfVCvEQjOpTUlYxkK\ndSk8JVooPpSx9Hg8XHXVVYwdO5bLL79cleuJ2tBsMKktIpDMCLUwgEopvnDknsZQgvHVV19xzTUP\n4fMNoKYOLw+wAT78fh8azY9I0qlI0v9wu0dgNhfjdt9L69adOXLkCtq2HcLRo4uwWFZhtRopLb2H\nFi1Ow+vdiSTNR6vtQ4sWa8nIsGEwdMBqXUZeXil+f0vy8n7Can0Ol6sTGRnryMpaSFVVP0ymn7FY\nFnH48FCsVhsazQscPVqOyVSF2/0sXm8eXm8lOt2H6HSDsdtdSNJvWCy/4vOdgyzr0OuPYjAsR5aH\n4/c70ekOoNNtRJYnU9ORZCt6vR2fz4FWa8bvd+L329DrrYG50WozcTrtmEz9kKSa1y4jYwB7987H\n4YCcnH8jSRJZWSOoqlrK0qVLWb58Hzk5ryFJOny+SSxceC5jxpzOnXc+hU73IhZLZyorv2TWrHt4\n+eUn+dOfbsNmuwK9/iS2bXuZ0tIHOPXUgdx778v4/Zciy3t5550rmDTpTJ5//ht8vklI0i8sWjSV\nsjIvPt+fAYnFi+/EbD6fnJwvOHDgDqqrC2jf/lY8nqHI8mzc7nuRJBOSNBxZXohGcwPwPBrNLkaP\nPoX/+78n621dF+8uKclAPL3hUB6/ILPFWyg+lIH3er1cffXVDB8+nJkzZzaK+VcD0j6HCTVhCSFz\nJkkSZrM54eesqqoK5JJEaLUxMGHDwe/307XrYEpKzEB/wALYAS3gRqPZgcFQTXY2dOnSnoKCLAYM\n6EOLFqZAh3eDwUBOTk7g2vPz8zl06BC5ubl4PB5KS0vJz8/nyJEjuFwuioqKOHjwIB6Ph27durFp\n0yZsNhvdu3dn586dHD58mC5dulBSUsL+/WV0717E0aMVbNiwg44d82nZMpdly1ZjNOo4/fT+LF68\nnIMHjzBkyElkZ1t49dVlyLKfiRNPZ9u2PaxZsxvwMnHiUDZv3sWWLSBJegoLbfTqVcSSJQfw+Yai\n1a7ijDOy+PbbTTgcV2M0dsLh+DfDhrn45pvDWK0L0GpzOXr0BQYP3sCqVRuwWN5Er89Hln1UVl7C\nLbeczhNP/ERGxrNAzWJts53F/fdfypw532OxPHls5mUqKkZx551TmT9/C5mZjx27Hy4qK0+jZcs8\nbLa/YzL1AuDo0ftwOt8kL++r/2/v3KObKtP9/0nShqY37hRoOVMcKEWtgD/AsQ4ol3KTpoVRChRB\nuayKInI5p+A4jnAcZ2BUkAMzgKBcZoaeQltKkdKhiFZlYRnOgOJBBgRBLKVUoPSetEl+f3D2NmmT\nXnPb7ftZi7Vou3fyZid5v/t93uf5Pvj4hGCxWLh27RE6dFhCjx4zAbhw4SH8/dMIDY2goGAhFRUT\n6Np1BHfuTMRi2Y5We4WamrcxmZ5FpztBTc0x+vfvw+9+t5Tx48c1+llp72LZGNb7nq1N1rKXSGUy\nmXjhhRd4+OGHWbJkSauvf05ODkuWLMFkMjF//nxWrFhh8/fz58/z3HPPcfr0ad58802WL/9pXzs8\nPFxeLPj6+nLy5MlWjcXViBWmFe5aYUpfCLVa3agnrFI6d3zzzTcUFVUCPwcqgBqgCLhJUFAZs2aN\nIzFxOlFRUc0qy+jdu7f8/75974VJ/+3f/k3eC/r5z38uTybR0dHyl/++++5z+JhxcT/9f+LECcC9\nSeSXv/yljXvP88/PA376XNy5cwetVktgYCBGo5FvvvkGs9nMwIED6dChA6NGHeO7764SHh7L6NGj\nuXTpEuvWfcCtW6WMGvX/WLBgNrt2pbBx49NYLB2IjAzhzTd/x+HDubz99kJMpjFoNF8xcmQPYmNj\n2bYtk5KS/fj7P0JFRSYDBnRh4MCBmEy7MJlK0Gg6Uln5v2i1NfTo0QM4Jb8ui6UStVqF0ViDRhNs\n9Xt/TCYzGk1n+bWBH/DTZ06tDsBsvgpEoNP9PyoqdqDRDKVr15cpLp6Br+9k/P190Ok2MXz4w8yf\n/ycef/zxJr2frmgp5mqsQ8dNNdhvDc4K3dqz6DOZTCxevJioqCiniKXJZGLRokUcPXqU0NBQhg0b\nhl6vZ+DAgfIxXbt2ZePGjWRmZtY7X6VS8cknnzg9+c1ViBUmP60wrfdTXIWUCStlKVo3eK6bCWuv\nv6K3sm/fPp599h2gD/fuw24DBTz8cA+OHj3sspWxdSKFyWRqUW/P5rSNcgZVVVVUVVXRuXNneYwn\nT57k/Pnz9OjRg5iYGDQaDZcvX+a119Zx9WohgwZFsHr1crp168af//w+mzdnoVKFo1Jd5N13k/nF\nLx7hqafmc+nSQ6hUDwLpJCUNpaamlvffP49W+zK1tT/g6/sWUVF9OXmyJzrdPAyG/0WlWoXJFIhK\nlQyoMRh+g1rti49PHHAZrfYMBkMtoGL8+Md45JHBdOvWTTbjbqrPraM+i96Mo5pFT41FCt3W1NQ0\nGLq1J5Zms5lly5bxs5/9jF//+tdOeS0nTpxg9erV5OTkALBmzRoAVq5cWe/Y1atXExgYaLPC7Nu3\nL6dOnaJr166tHos7ECtM3LeHKWXCBgQEyALZUCasdEerhGSIbt260aGDGqPRhMVSAZShVlfz17/u\ncGkY2fpu3J73pySejq6hu2zjrNHpdPXC/sOHD6/XZ/C+++7jb3/bVO/8pKRnGZIrHHEAACAASURB\nVDFiOCUlJURERBASEgJASspmdu/ew/XrZ3j00alMnvwkJpMJf/8dHD78Bzp2DCQ5eS39+/fnd79b\nx/HjS+nZsyurVn3AnTt3eP/9dCwWC88990d69OjBqVOnCA6OYNy4dXJUwN6NW1N8bqX9emf333Ql\n3iSWUN+kwl6PT+l9sieWycnJ9OrVy2liCVBQUECfPn3kn8PCwsjPz2/Waxo7diwajYakpCSvb0Yt\nBNMNSJl1VVVVBAUF4ePjI+/hSGJpnQkr3YW7I/zjDCwWCw8++CCRkT359lsT0Bmo5dFHBxAWFua2\ncTS3t2dLWqB5Gmk1HBERUe9GJDg4mEWLnrf5nY+PDy++uIAXX7SdiH7/+9/Ue+y6JukDBgxo0pia\n0t9T2oJQklh6+z6rvR6fRqNRtuo7f/48VVVVDBo0iNdee41OnTqxatUqp76W1j7W8ePH6dWrF8XF\nxcTExBAZGenVbcS8f+niRlyxwpQE0GAwEBwcLLcRAuQPuNlslhN+pHCtkkJW0h7rzp1rGD++LwMH\n1vLUU8PYuvUPHgslS3s9/v7+BAUF4efnJ69yysvLKS8v90qru4aQbAb9/Py8Nvmr7nXXarUYDAbM\nZjMmk0lOnPHmnSAliGVdrJswBAQEoNPpOHfuHHPmzKF///7k5eURHR2NwWBw6vOGhoZy7do1+edr\n16416yZZav3WvXt3pkyZIpJ+lISzBVPyhAUICgqyyYTVaDT4+/vbNK61WCxotVqvLRupS9260IiI\nCP7yl3fl8La3YB3K6tChg1yTplarbdqTOSOF31UoJfnLGimyIrlnSasgZ/X3dAVKFEuwb1j/q1/9\nim+++Ybi4mIiIiL44x//SGJiIjNnzmTz5s1Oed6hQ4dy8eJFrly5Qu/evUlNTSUlJcXusXXn1srK\nSkwmE0FBQVRUVHDkyBFef/11p4zLVYikH+7duUv7ARUVFXTs2LHVjyk1pZYSexrzhK2qqpKNyS0W\nS4POK96AEupC62I9Gfr7+6NWq22SKEwmU6t6e7oKbzV+bwjrnqF+fn52/+6s0gln0ZbE0mKxsHbt\nWn788Uc2bdokX9Nbt27x7bff8sgjjzjt+Q8fPiyXlcybN49XXnmFrVu3ApCUlMSNGzcYNmwYpaWl\ncmXAuXPnuHnzJlOnTgXuzcGJiYm88sorThuXKxCCifMFs7a2lrKyMnQ6nVyi0JxMWOtJ3BvvxJXY\nmqspGZqt6e3pKryx1VVjNPfz4Uyf25YiiaXFYlHMdgj8dDNVVyzXr1/P1atX2bp1qyKSBpWCEEx+\nEkyTyURZWVmjLiUNYZ0JK5UoWGfCWif3NKUQum7ZhKdXQEoNDTY3Q1MKH0oTuSdaNimh1VVdWnsz\nZe1z66hRs7Npa2K5adMmzp8/z/bt2xXzuVEKQjD5aUVnNpu5e/cunTt3bvZjSAJYXV0tZ8I25Anb\nkno0T6+AlJhV6ozQsXTDY92yyZW+n0rs3gHOr2d11O3DmdEWJdaGgv0wvcViYevWrZw+fZqdO3cK\nsXQBQjD5STAlN5fmuk5IX7ra2tp6yT2u8oR1tAJyxR6QNIF7czsxe1ivdrRardMm2LrF485cASmx\newe4p57V2fuebU0sP/jgA44fP85f//pXxdzQKg0hmNQXTGsHlsaQSkFUKpVcN+lILF0xgYP9PSBn\nhQ+tTRSUOIG72r1HCh86YwWk1KQTT5g/tHbfU6liKV3rumK5e/dujh07xp49exSzVaJEhGDyk2AC\n3L59u8mCKe15SnVn3uAJW3cPyLorQksaBStxUvHUPqu9FVBTQ+ZKv9aeDNM3d99TqdfakVimpKRw\n6NAhUlNT3WLt2J4RgslPEx3AnTt36NixY6MTXE1NDeXl5eh0Ojlt3pFYSskb7p5UrCcSaQXd1PCh\n2WymsrJSUe4s4D37rFLIXLr2DYXMlWgbB94hlnVpbN8TaDNiCZCamkpGRgZpaWmKyVhXMkIwsRXM\nkpISgoKCGgxlSt6NzsqEdQfWE0lje29S6Fir1cplMUrAW7NK64YPrVf9gOwDqpR6VvCeG5PGqLvq\nl76f/v7+XvUZaQhHYpmenk5KSgoZGRl2a10FzkcIJk0XTEkAJWNjV2TCugtHtZ5wr5uGuzp3OANv\nujFpjLrhQ4vFIvuBekudbWMosTZUWsXDPe9bT9V7NhdH+8NZWVns2LGD/fv34+/v78ERti+899bQ\nQziyx5O+cCaTieDg4CZlwmo0Gq8NsVkbN0s3DJJlmXVNlzeO3Zq6iTLeLJbwk02fZP4uJX9VV1c3\n2K7JW/DWVXxD2At5W9+4SELqbe5ajsQyOzub7du3k5mZKcTSzQjBxNZx355gWmfCBgcHeyQT1pVY\nOw8FBATIAirZ9Xna7cYR1qt4JWWVSp8RnU4nr+L9/Pzk627drqm5vT1dSVsRS6jfKqvuTaOnb1xM\nJpNdsTxy5AibN29m//79BAYGun1c7R0RkuUnizqA0tJSm3CklAmr1Wrr3Z16KhPWmTQUznRnrWdz\nUWpSUlNLMOqaVHjy2ivVSKGlyVSe9rm1vqGy/owcO3aMt956i6ysLKf4XQuajxBMbAWzrKxMXh0q\nIRO2NdgzI2/oWFfVejYXa2NvJSUltfSGypNeq+1NLO09jjuvvSOx/PTTT/n973/PgQMHWuREJnAO\nQjD/D6lPXHl5uU32YmBgoPyz1NPPWzNhm4M0oUgZg82tz3RWrWdzUaLxOzgvq9TetZcmcGfvvSn9\ns63RaJyaeexqn1tH1oLHjx9n9erVHDhwgK5du7bqOQStQxnfADdjMBioqqoiKCgIX19f+YtiTyyl\nnm6BgYGKmVCkPVmpJ2dzv+jSJK3T6QgKCkKn08nXoqysjKqqKpc0CVZCA2V7GAwGOau0tdGHutde\nev+qqqrkay9l37YGa4cnJX22XSWWUP/aS/vm1dXVlJWVUVlZidFobNG1dySW+fn5rFq1iv379ztF\nLHNycoiMjKR///6sXbu23t/Pnz/Po48+ip+fH++8806zzm0PiBXm/2E0GmXzdYvFIpsXNJQJq8Q9\nNFeu0JpT69lclLg/DFBdXe02D15n9fZUqkWfK8WyMVqz7+lILE+dOsWKFSvYv38/PXv2bPUYTSYT\nAwYM4OjRo4SGhjJs2DBSUlIYOHCgfExxcTFXr14lMzOTzp07s3z58iaf2x5Qxm2jGzCbzZSVlQHQ\noUOHBsXSujm0ksRSSqGX+nQ6G5VKJU9W0h24Wq22uQNvyepHarDt7++vGLGURKempobAwEC37PNK\nZUKBgYFyx5yamhpKS0upqKjAYDBgNpsbHXdlZaWcMa2Uz7YnxRLuZZp36NCBgIAAgoOD0Wq18jxR\nXl5OdXW1nPtgjbQfX1csz5w5Q3JyMunp6U4RS4CTJ0/Sr18/wsPD8fX1Zfr06Rw4cMDmmO7duzN0\n6NB637OmnNseUEZ2iouxWCyUlpbafEgay4RVUmE/eMaZxV6tp1Qy0ZTVj1K7pHhDbaharUar1aLV\nam2ynaurqx329vR2sw1HOKsDkLOw3tNvqN5TpVLZlKBJnD17lmXLlpGWlkbv3r2dNq6CggL69Okj\n/xwWFkZ+fr7Lz21LCMHk3gdcassl3Qm2pUxYbxAd6Q5cEk8pdOio1tM64URpe2jeFs5UqVQ24imF\nDaWkL+naV1VVebXZhj28TSzr4qjeU/qMqNVquf6zY8eOnDt3jsWLF5OamkpYWJjTx+KJc9sSypj1\n3YCPjw9ms1m+G9doNDYdAayzBZW20vG2xA1Hqx9pwvb19ZWThqSWaUpACUYK1qsfPz+/eqsfjUaD\nyWTyGrebhlBaeZG0ZaFSqaipqZHHfPLkSZ566imGDBnC9evX2blzJ+Hh4U5//tDQUK5duyb/fO3a\ntSaLcmvObUt4xwzqBUihE2nCNhgM8r5beXm5IsVS2ovyJrGsi7T68ff3l/d+DAaD3G7NaDRiMpk8\nPMrGaU2ZjqdQqVSo1WpMJhNardZpe87uQGliKSGNW6vVytneI0aM4MiRI/j7+xMVFUVcXBxDhw7l\njTfeoLy83GnPPXToUC5evMiVK1cwGo2kpqai1+vtHlv3PW/OuW0ZscLk3of4q6++IiIiwmZfR8pw\nhJ9Wmd7s8ymh1AxeKXwsTYJS+Mo6dOiNRtneHhZ0hL1xS1EV6dobjUYbmz5vsEhUulhK45a4fPky\nL7/8Mrt37yYyMpLa2lo+//xzDh8+7NQuJD4+PmzatInx48djMpmYN28eAwcOZOvWrQAkJSVx48YN\nhg0bRmlpKWq1mg0bNnDu3DkCAwPtntveEGUl3NubXLhwIWfPnuWxxx4jLi4Of39/EhMTSU9Pp1+/\nfjb9DVuTsu9qlNqaS/LOtDcJurpgvDW0lcm7oXE3p7enq7Eet5JaWjka9/fff8/s2bPZsWMHDzzw\ngAdHKGgKQjCtqKmp4dNPP2X9+vV88sknPP3008ycOZNf/OIXNqHYuj6f3mKSLfmUKi2Dtzm1oa6s\n9WwuSnUdkowrWjLuhnp7unrl39bEsqCggFmzZrFt2zYeeughD45Q0FRESNYKX19frly5wqlTpzh4\n8CBqtZq0tDReffVVhgwZQnx8PI899hg+Pj71klY83d1DqYX9TTUjl5ASJ6R6O6lY391dJtrDzYk9\nmloy4eybF+u9P6XdnNgLwxYWFvLMM8+wefNmIZYKQqwwrbh06RKTJ0/mwIEDREREyL83mUzk5+ez\nb98+jh8/Lm/Mjxw50mayrBu6cpd4KrHtEji/NtR65enKsHlzRd5bcOQo4wzsrfyddfOiVLG0WCyy\nwYn13nZRUREzZ85kw4YNDB8+3MOjFDQHIZh1kITOEWazmVOnTpGWlkZeXh4DBgwgPj6eUaNG2XyZ\nrUNXrmqNpVRzbHC9yDsKm7f25kVaySupFhfcvyKue/PS0m0LJYulPeeh4uJipk+fzrp163j00Uc9\nPEpBcxGC2QrMZjNffvkl+/bt4+OPPyY8PJz4+HjGjh2LTqeTj3OFeDanNZc34Yl2Uc7q6+kJtyRn\n4OkVcUt7e7Zmr9WTOBLLW7dukZCQwNq1axkxYoSHRyloCUIwnYTFYuHrr78mLS2N3NxcwsLC0Ov1\njB8/noCAAJvj7PWVbM7krcSaP/AOkW9pX0+lhr09LZZ1aWp/ybYmlnfu3CEhIYE33niDUaNGeXiU\ngpYiBNMFWCwW/vWvf5GWlsbf//53unXrRlxcHBMmTCA4ONjmOMmmrG5fSUeTslJr/rzRp7QpfT2V\n2kAZvD987Ki3p0ajkf2alSiWdeufS0pKmD59Oq+99hoxMTEeHqWgNQjBdDEWi4VLly6Rnp7OoUOH\n6NixI3FxcUyaNIlOnTrZHNfY5K3UMgZHE4k34ajWU2oa7s1uSfbwdrGsi5Q0JN2cAGi1WtmH1Rs/\nM9Y4+oyXlpYyffp0VqxYwcSJEz08SkFrEYLpRiwWC1evXiU9PZ2DBw/i7+9PbGwskydPpkuXLjaN\nqeuKp1qtpra2Fp1Op6gyBiWuiKXrL4WP6678vf01SHutSgsfW2fxajQap/T2dAdS9ESlUtmIZXl5\nOTNmzGDJkiXExsZ6eJQCZyAE00NYLBYKCgrIyMggKysLtVpNbGwssbGxdO/e3UY8y8vL5YlbClsp\nYfK2XhFrtVqvHqs1dcPH1kkr7qz1bAltQSzr3hDay3huanNmV+NILCsqKpg5cyYvvPACU6ZM8egY\nBc5DCKYXYLFYKCoqYv/+/WRmZlJbW8vkyZOJjY3lgw8+4Ouvv+Zvf/sbarXaa1xuGkOphf2NhY/d\nVevZEpSamNSc+lBHGeeNJW25Akf78lVVVcycOZP58+fz9NNPu3VMAtciBNPLsFgs/Pjjj6Snp7Nm\nzRrUajVz587lqaeeok+fPjYrT28VT6W6DjXXtN5VtZ4tobq6WpGJSa0xU3CUNCeJpyu/A47Esrq6\nmlmzZjFr1ixmzpzpsucXeAYhmF5IeXk5CQkJmM1mtmzZwscff0xGRgYlJSVMmDCBuLg4wsPDbSYE\n6z1PSTw9kTCh1FrF1u61OqvWs7koOYvXmc5D0r6zdP1deQPpSCwNBgNz5szhqaee4plnnvF4xEHg\nfIRgeiG//e1vKSgoYMuWLTYrtLt373Lw4EEyMjK4efMmMTExxMXF0b9/f5svp/XK0517bkoNCTrb\n1LultZ4teR6lOj1JYumqKIR0A1lbW+vU74BUS2yxWGzE0mg08txzzzF58mTmzp3rlO9ZTk4OS5Ys\nwWQyMX/+fFasWFHvmMWLF3P48GH8/f3ZuXMnQ4YMASA8PJzg4GD5xu3kyZOtHo9ACKZXUlNT0+gX\nu6ysjOzsbNLT0/nhhx8YPXo0U6ZMITIy0qF4SntuzhbPtjBxu6pUpynlQi193OrqakwmEwEBAYpa\nzbhaLOsifQek8G1LQ+eOxLKmpoYFCxYwevRokpKSnPJemEwmBgwYwNGjRwkNDWXYsGGkpKTY9KDM\nzs5m06ZNZGdnk5+fz8svv8wXX3wBQN++ffmf//kfunTp0uqxCH5COTGzdkRTJpGgoCASEhJISEig\nsrKSnJwc3nnnHS5fvsyoUaOIj4/ngQceQK1Wy2IgTRwGg0HuPdla8bR271GaWLojMUnKapZCvc7o\n7lH3mitJLD3hPGT9HajbXaipoXNH17y2tpbnn3+eESNGOE0sAU6ePEm/fv0IDw8HYPr06Rw4cMBG\nMLOyspgzZw4AjzzyCCUlJRQVFRESEiKPWeBchGC2Afz9/Zk6dSpTp06lurqaI0eOsHnzZs6dO8fI\nkSOJj49n8ODB9cSztrYWo9FIZWVli8yxrfdyxMTdOHXFU7qBkVYtTRFP61WOuObNR6VS2bTmk0Ln\nBoPB4erfkViaTCZefPFFhg0bxqJFi5z6XhQUFNCnTx/557CwMPLz8xs9pqCggJCQEFQqFWPHjkWj\n0ZCUlMSCBQucNrb2jBDMNoafnx96vR69Xo/RaOTYsWPs2LGDs2fPEh0dTVxcHMOGDUOtVssTh3W2\np3VPz4bEs7kZpd6EN7jgtKSvpzfaCzYVbxDLujjq7VlZWWmTOCflAtQVy8WLF/Pggw+ydOlSp78X\nzblptcfnn39O7969KS4uJiYmhsjISGH47gSEYLZhtFotEyZMYMKECdTW1pKXl0dqaiorVqxg+PDh\nxMXF8Ytf/AKNRtOshth1m+IqaeL21sJ+STwdhc59fHwwGo2KvEHxRrGsi/Xq37pky3r1/+233xIa\nGoqfnx/Lly/n5z//OcnJyS55L0JDQ7l27Zr887Vr1wgLC2vwmB9++IHQ0FAAevfuDUD37t2ZMmUK\nJ0+eFILpBJSz4SRoFT4+PowZM4YtW7Zw4sQJnn76aQ4ePMiYMWNYunQpeXl51NbWyiGrgIAAgoOD\n0Wq11NbWUlZWRnl5OdXV1ZSVlaHVahVjdSdhMBi8UizrIoXOAwMDCQoKks3ITSaTfENjNps9Pcwm\noQSxrItkRWmxWFCr1QQGBqLRaPjTn/7Efffdx+jRo7l58yYvvPCCyz7/Q4cO5eLFi1y5cgWj0Uhq\naip6vd7mGL1ez+7duwH44osv6NSpEyEhIVRWVlJWVgbccxw6cuQIUVFRLhlne6PNrzBv375NQkIC\nV69eJTw8nL1799qYnkvMnTuXQ4cO0aNHD86ePSv/ftWqVWzfvp3u3bsD8Ic//IEJEya4bfyuQKPR\n8Pjjj/P4449jMpnIz89n3759vP7660RFRREXF8fIkSPRarU2Iavq6moMBgOAjUG5tyf6WNcqKs1E\nHe5da6mBspTp2ZyEFU8hiaXSanLtZSBrNBrWrVuHn58fN27cwGg0Eh4ezvDhw5k/fz7Tp0936hh8\nfHzYtGkT48ePx2QyMW/ePAYOHMjWrVsBSEpKYtKkSWRnZ9OvXz8CAgLYsWMHADdu3GDq1KnAvfcg\nMTGRcePGOXV87ZU2X1aSnJxMt27dSE5OZu3atdy5c4c1a9bUO+6zzz4jMDCQ2bNn2wjm6tWrCQoK\nYtmyZe4ctkcwm82cOnWKtLQ08vLyGDBgAPHx8YwaNYqcnBz++7//m927d+Pj49Pqnp7uQsklLw2Z\nKbir1rOlKFks7RlBmM1mVq9ejdls5q233kKtVlNRUUFubi41NTXCAq+d0OYFMzIykry8PEJCQrhx\n4wZPPPEE58+ft3vslStXiI2NrSeYgYGBLF++3F1D9grMZjNfffUV+/btY+/evdy5c4dXX32V2bNn\no9Pp5OPqTtxN6enpLpRcftGcfWJX1Xq2FKWKJdi3GLRYLLz55puUl5fz7rvvKuqmS+Bc2vw7b12X\nFBISQlFRUbMfY+PGjQwaNIh58+ZRUlLi7CF6JWq1mkGDBhEQEEBtbS07duygpKSE2NhY5syZQ0ZG\nBhUVFfLk7O/vT1BQEDqdTjYwLysrk0Nb7r4vkzJKlVh+Udd5qLGxSwkrOp3O7ntQVVVFbW2tW94D\nKcu0LYnlH//4R+7cuSPEUtA2VpgxMTHcuHGj3u/ffPNN5syZw507d+TfdenShdu3b9t9HHsrzJs3\nb8r7l6+99hqFhYW8//77Tn4F3sl7773Hn/70Jw4fPixn3VksFv71r3+RlpbG3//+d7p160ZcXBwT\nJkwgODhYPteTqx4lNKx2hDOdh9xt0O8N5TotxZFYrl+/nitXrvDee+8JsRS0DcFsiMjISD755BN6\n9uxJYWEho0aNalZItjl/b2tUVFRQU1NjN0kK7k0oly5dIj09nUOHDtGxY0fi4uKYNGmSzTnW4llb\nWwvgsp6eUn2oVN+oRLF0lfOQtTm5sz2GlSyWBoMBo9FYTyw3bdrE+fPn2b59u8e3FwTeQZu/ZdLr\n9ezatQuAXbt2ER8f36zzCwsL5f/v37+/XaVnBwQEOBRLuBcK7NevHytWrCAvL4+NGzdy9+5dEhMT\neeqpp9i1axe3bt0CkEOGgYGBctF9VVWVU0OGre044klcLZaAXOcZGBgol0oYDAZKS0uprKzEaDS2\n6D1oi2K5detWzp49y7Zt24RYCmTa/Arz9u3bTJs2je+//96mrOT69essWLCAQ4cOATBjxgzy8vK4\ndesWPXr04D//8z957rnnmD17NmfOnEGlUtG3b1+2bt0q74kK7GOxWCgoKCAjI4OsrCzUajWxsbHE\nxsbSvXt3l/T0dLWJuivxdK1ia/p6Kl0sDQaDTamRxWLhgw8+4Pjx4/z1r39V3GsSuJY2L5gCz2Kx\nWCgqKmL//v1kZmZSW1vLk08+SVxcHD179nRKT093rM5chafFsi7N6espiaW3G0HYw5FY7t69m48+\n+oiUlBSveD8E3oUQTIHbsFgs/Pjjj2RmZpKZmUllZSUTJ05Er9fTp0+fFvX09DbBaQ7evjprqNbT\nbDYrViwle8S6YpmSksKHH37I3r17FXfjJXAPQjAFHuP27dtkZWWRkZFBSUkJEyZMIC4ujvDw8CaJ\np2RKIMTS9VgnbhmNRgC5RtQTtZ4txZGXcGpqKhkZGezbt88pTcQFbRMhmG6gtfZ8TT1fydy9e5cP\nP/yQ9PR0ioqKGDduHHFxcfTv39+ueBqNRsxms5zI4syG2K7GWw3gm4LRaKSqqgqdTicLKLSsr6e7\ncXTdMzIy+Nvf/kZGRoaNKYdAUBchmG6gtfZ8TT2/rVBWVkZ2djbp6en88MMPjB49milTphAZGYlK\npWLnzp0MHjyYBx54wGbPrSU9Pd2N0sWy7tjdXevZUhxd96ysLD744AMyMzPx9/f34AgFSkAIphto\nrT1fc85va1RWVpKTk0NaWhqXL1+md+/enDp1iqysLCIiIuTjHGV6epN4SokmbUUs7eHKWs+W4mjs\nhw8fZvPmzWRmZhIYGOiRsQmUhRBMN9C5c2fZbchisdClSxcb9yFr7Almc85vq1gsFpKTk9m7dy+j\nRo3i3LlzjBw5kvj4eAYPHmyTwWnd07O5ZRKuwl5WplJo6arYeuVpMpnk98CdNzGOMnlzc3PZsGED\nmZmZNg5VAkFDeH+2gUJoyJ7PGpVK1arJorXnKxGz2cwLL7zAP//5T/75z3/StWtXjEYjx44dY+fO\nnXz55ZdER0cTHx/PsGHDUKvV9Rpie6olltJbi7UmhCz19ZSaYksrT0eNyZ2NI7H8+OOPWbduHQcO\nHBBiKWgWyvr2ejG5ubmcPXu23j+9Xi+HUuGec1CPHj2a9ditPV/pqNVqhg4dykcffUTXrl0B0Gq1\nTJgwge3bt3PixAn0ej2pqamMHj2a5ORkjh8/jslkkhti+/v7ExwcTIcOHTCZTHJDbIPB4LJmzFIW\nb12PUqXgzIbb0k2M1Jjc19fXpjG5s98H6yxk67F/9tlnrF27lv379zslcS4nJ4fIyEj69+/P2rVr\n7R6zePFi+vfvz6BBgzh9+nSzzhV4F8r6BiuU1trztfb8tsD8+fMJCgqy+zcfHx/GjBnDli1bOHHi\nBNOmTePgwYOMGTOGpUuXkpeXZ9N6rK54lpeXO33SrtuEWIliKYWQnb3f6ugmxvp9MJlMLX58RyU7\nx48f54033iAjI4MuXbq0+nWYTCYWLVpETk4O586dIyUlhW+++cbmmOzsbL799lsuXrzIe++9x8KF\nC5t8rsD7UNa3WKGsXLmS3NxcIiIiOHbsGCtXrgTg+vXrPPnkk/JxM2bMIDo6mgsXLtCnTx+5g7qj\n8wX10Wg0jBw5kv/6r//ixIkTzJkzh9zcXGJiYnjppZc4evQoRqOxXluyupO2JHYtQerD2RbE0tVj\nr/s++Pn5yZ7ALWkPJ4Xe64plfn4+r7/+OhkZGXTr1s0pYz958iT9+vUjPDwcX19fpk+fzoEDB2yO\nycrKYs6cOQA88sgjlJSUcOPGjSadK/A+xB6mG+jSpQtHjx6t9/vevXvLXrYAKSkpzTpf0DAajYbo\n6Giio6Mxm82cOnWKtLQ03nzzTQYMGEBcXByjR4+mQ4cO8r6mdYG+db/PSJxppwAAEnpJREFUpjbE\nVnLTavBscpLU11Myz7d+H6DxWk9HjatPnTrFr3/9a/bv3+/U7YyCggL69Okj/xwWFkZ+fn6jxxQU\nFHD9+vVGzxV4H0IwBe0CtVrN8OHDGT58OGazma+++op9+/bx9ttvEx4eTnx8PGPHjkWn0zmctBvr\n6Sk1rQYUK5ZGo9ErkpPqiqeUcVtVVWW31tORWJ45c4bk5GQyMjLo2bOn08fYFEQhQttBCKag3aFW\nqxk8eDCDBw/GYrHw9ddfk5aWxoYNGwgNDSUuLo7x48cTEBDQqHj6+PjIK09JLKX2ZUrCm5OTVCoV\nGo1G7nEq1XpWV1fLbk+1tbX1xPLs2bMsXbqUtLQ0uQG6MwkNDeXatWvyz9euXSMsLKzBY3744QfC\nwsKoqalp9FyB9+Fd3wyBy7l9+zYxMTFEREQwbtw4SkpK7B7nKINv1apVhIWFMWTIEIYMGUJOTo67\nhu4SVCoVUVFRrF69Wk4KuXLlClOnTiUxMZG9e/dSWloqr3h0Oh1BQUGyK4zU07OsrAyLxYJOpxNi\n6WKs+3r6+fnJxvCVlZX8/ve/Z8+ePfzjH//gpZdeIjU11Sb06UyGDh3KxYsXuXLlCkajkdTUVPR6\nvc0xer2e3bt3A/DFF1/QqVMnQkJCmnSuwPvw/m+HwKmsWbOGmJgYLly4wJgxY+xa7DWUwadSqVi2\nbBmnT5/m9OnTTJgwwd0vwWWoVCoiIyP5zW9+w6effspbb71FUVER06ZNIyEhgT179lBSUiKveKRQ\nocViQaVSYbFYKC8vd1pDbHegNLG0RlplSglDQUFB9OnThz179sgRgo8++oji4mKXPL+Pjw+bNm1i\n/Pjx3H///SQkJDBw4EC2bt3K1q1bAZg0aRL33Xcf/fr1IykpiT//+c8NnivwboTTTzujKTZ7J06c\nYPXq1fLqURLVlStXsnr1agIDA1m+fLnbx+4pLBYLV69eJT09nQ8//BA/Pz/0ej3R0dE888wzvPTS\nS8ycOROVSmW3p6e3+aqCraGCEsVS6oFat1PNxYsXWbBgAVu2bOHChQtkZGRw5MgRli5dyuuvv+7B\nEQvaAsr6lghaTVFRESEhIcA9Q4SioqJ6xzjK7JPYuHEjgwYNYt68eQ5Dum0JlUpFeHg4y5cv59ix\nY2zbto0ff/yRxx9/nF69elFVVUVxcTEWi0VeeQYFBclCVF1dTVlZGZWVlbKQepK2KpaXL19mwYIF\n7Nq1i4cffpjp06ezd+9eCgsLWbBggQdHLGgrKOubImgSMTExREVF1fuXlZVlc5wjm72GVkILFy7k\nu+++48yZM/Tq1atdrTTh3rUxm83s3r2bf//3f2f37t34+vqSlJSEXq9ny5YtFBYWyuIp7bVJBgAG\ng8Gj4tlWxfL7779n7ty5fPDBB/VCmzqdziVJP4L2h8iSbYPk5uY6/JsUiu3Zs6dDm72Gsv+sj58/\nfz6xsbFOHLkyeOGFF3jxxRdZsmQJcO8m4vnnn+fWrVtkZmayePFiKisrmThxInq9nj59+tTzVa2p\nqcFgMFBZWSmHbV3d0UNyH6qtrVW0WPr5+dmIZUFBAXPmzGHbtm08+OCDHhyhoK0j9jDbGcnJyXTt\n2pUVK1awZs0aSkpK6iX+1NbWMmDAAD766CN69+7N8OHDSUlJYeDAgRQWFtKrVy8A1q9fzz/+8Q/2\n7NnjiZfiMaqrq/Hz82vwmNu3b5OVlUVGRgYlJSWMHz+euLg4+vbtW68htjvakrUlsdRqtfLvCwsL\nSUxM5M9//jMPP/ywB0coaA8IwWxn3L59m2nTpvH9998THh7O3r176dSpE9evX2fBggWy89Dhw4dZ\nsmQJJpOJefPm8corrwAwe/Zszpw5g0qlom/fvmzdulXeExXY5+7du3z44Yekp6dz8+ZNYmJiiIuL\no3///m4Rz7q+tt6UfNQUHIllUVERM2fO5N133+WRRx7x4AgF7QUhmAKBGykvLyc7O5v09HSuXbvG\n6NGjmTJlCpGRkTZC5qyenkoXS7PZTHl5eT2xLC4uZvr06bzzzjtER0d7cISC9oQQTIHAQ1RWVpKT\nk0NaWhqXL19m1KhRxMXF8eCDD9ptiC2tPpva07OtiKW09ytx69YtEhISWLNmDSNHjvTgCAXtDSGY\nAoEXYDAYOHLkCOnp6Zw7d46RI0cSHx/P4MGD64mnJJwNiWdbFcs7d+6QkJDAG2+8wahRozw4QkF7\nRAimQOBlGI1Gjh07RlpaGl9++SXR0dHEx8czbNgwh+Ip2cNJYVupt6dSxbKiogKtVmsjlnfv3iUh\nIYHXXnuNmJgYD45Q0F5RVqqcQPGIDvWNo9VqmTBhAtu3b+fEiRPo9XpSU1MZPXo0ycnJHD9+HJPJ\n1GBPz5qaGnx8fJzWENtdOBLL0tJSZsyYwSuvvCLEUuAxxApT4DZMJhMDBgzg6NGjhIaGMmzYMLlc\nRSI7O5tNmzaRnZ1Nfn4+L7/8Ml988UWTzm3rmEwmjh8/TlpaGl988QVDhgwhPj6exx57DB8fH2pr\na/nLX/7Cr371K3Q6nbz6bG5PT08hiaWvr69N2U55eTkzZsxgyZIl7bLuV+A9COMCgduw7jIPyF3m\nrUXPUYf67777rtFz2zoajYaRI0cycuRITCYT+fn5pKWl8frrr3P//fdz8+ZNysvLmT59uiyQze3p\n6SkciWVFRQWzZs1i0aJFQiwFHkeEZAVuozGP2oaOsdehvu657QmNRkN0dDTr1q3j888/5/r163z7\n7beYTCaWLl3K4cOHMRgM9dqS6XQ6LBYLFRUVlJeXy2YGngw0ORLLqqoqZs2axfz585kyZYrHxicQ\nSIgVpsBtiA71zqempoZZs2ah0Wj46quv0Gq1fPXVV+zbt4+3336b8PBw4uPjGTt2LDqdzqYhtmTR\nV1VV5bHOKtZiab1nWV1dzezZs5k9ezbTpk1zy1gEgsYQgilwG6JDvfO5ffs2Xbt2Zffu3fLqbPDg\nwQwePBiLxcL//u//kpaWxoYNGwgNDSUuLk7uFanRaGSDeE+Ip7TS9fHxoUOHDvLzGAwGnn32WaZN\nm8bMmTNd8twCQUsQIVmB2xAd6p1PSEgImzdvtuttq1KpePDBB1m1ahXHjx/njTfe4MqVK0ydOpXE\nxERSU1MpLS21aYgttSVTqVRUVVVRVlbmkobY1mLp5+cni6XRaGTevHno9Xpmz57tVLG+ffs2MTEx\nREREMG7cOIet6RxlY69atYqwsDCGDBnCkCFD5H6xgvaDyJIVuBV7HrVSd/qkpCQAFi1aRE5ODgEB\nAezYsUM21XbkbytoHhaLhUuXLpGenk52djbBwcHExcUxadIkOnXqZHOsyWSSs23NZrONRV9LxUwS\nS0mkpcepqalhwYIFjBo1iueff97pK9vk5GS6detGcnIya9eu5c6dO/UaDzSUjb169WqCgoJYtmyZ\nU8clUA5CMAWCdozFYuH7778nPT2dgwcP4ufnh16vZ/LkyXTp0qWeObzkMNRS8XQklrW1tSQlJfHo\no4/y0ksvuSQMHBkZSV5entzi7oknnuD8+fM2x5w4cYLVq1fLq0dJUFeuXMnq1asJDAxsdz1gBT8h\nQrICQTtGpVLxs5/9jGXLlnHs2DG2bdtGTU0Nc+fOZcqUKbz//vvcvHkTi8Ui9/Ss2xC7tLS0SQ2x\nJbFUq9U2YmkymXjxxRcZOnSoy8QS7nU3kTrrhISEUFRUVO+YxjK5N27cyKBBg5g3b57DkK6g7SIE\nUyAQAPfEMywsjMWLF3PkyBH+8pe/4OPjQ1JSEnq9ni1btlBYWFhPPIOCgtBoNBiNRkpLS6moqMBo\nNNqIp7VY6nQ6G7F8+eWXeeCBB1i2bFmrxTImJoaoqKh6/7Kysuq9VnvP1dDzL1y4kO+++44zZ87Q\nq1cvsdJsh4gsWUG7JScnR94TnT9/PitWrKh3zOLFizl8+DD+/v7s3LmTIUOGABAeHk5wcLBsfn7y\n5El3D9+lqFQqQkJCWLhwIc8//zy3bt0iMzOTxYsXU1FRwaRJk9Dr9fTp00cWTynbVtrzrKqqkstY\nampq6oml2Wxm+fLl9O3blxUrVjhlZZmbm+vwb1IotmfPnhQWFtKjR496xzSUyW19/Pz584WRQjtE\nrDAF7RKTySQnF507d46UlBS++eYbm2Oys7P59ttvuXjxIu+99x4LFy6U/6ZSqfjkk084ffp0mxPL\nuqhUKrp168b8+fM5dOgQ+/fvp0ePHqxYsYKJEyeyfv16Ll++LK88tVotAQEBBAcHy0bwJpMJi8XC\nl19+SXFxMWazmeTkZHr27MlvfvMbt9R96vV6du3aBcCuXbuIj4+vd0xD2diFhYXycfv37ycqKsrl\nYxZ4F0IwBe0Sa5s+X19f2WrPGns2fdb7Xu01X65z5848++yzHDhwgIMHDxIeHs5vf/tbxo8fz1tv\nvcWFCxewWCwYjUZeffVVSktLCQoKwtfXl4yMDKKiovjlL3/JpUuXWLhwodtMElauXElubi4REREc\nO3aMlStXAnD9+nWefPJJAHx8fNi0aRPjx4/n/vvvJyEhQbZfXLFiBQ899BCDBg0iLy+P9evXu2Xc\nAu9BhGQF7RJ7yR35+fmNHlNQUEBISAgqlYqxY8ei0WhISkpiwYIFbhu7N9GxY0cSExNJTEykvLyc\n7Oxs/vCHP3D16lVUKhVBQUF0795dXnmuWrUKuGdIoVaruf/++3nooYeYNWuWy69hly5dOHr0aL3f\n9+7dm0OHDsk/T5w4kYkTJ9Y7TqoPFrRfhGAK2iWtten7/PPP6d27N8XFxcTExBAZGcmIESOcOUTF\nERgYyLRp05g6dSrTpk3jhx9+oHv37kycOJEnnniC+Ph4srKyMBgM7NmzB7VaTXV1NUePHuXKlSue\nHr5A0ChCMAXtkpba9IWGhgL3ViUA3bt3Z8qUKZw8ebLdCybcq6d85plnqK6u5rPPPqNDhw4YDAaO\nHDnCmjVrKCsrIzc3V26E7efnx+TJkz08aoGgaYg9TEG7pDU2fZWVlZSVlQH32k8dOXJEJIBY8fDD\nD5ORkSGbqXfo0IHY2FgyMzP56KOPZLEUCJSGWGEK2iXWyR2S1d7AgQNtbPomTZpEdnY2/fr1k236\nAG7cuMHUqVOBeyuqxMRExo0b57HX4k34+PjwH//xH54ehkDgEoQ1nkAgEAgETUDERgQCgUAgaAJC\nMAUCgUAgaAJCMAUCgUAgaAJCMAUCL8FR42KJ8+fP8+ijj+Ln58c777zTrHMFAkHrEUk/AoEX0FDj\nYoni4mKuXr1KZmYmnTt3lrtlNOVcgUDQesQKUyDwApribdu9e3eGDh2Kr69vs88VCAStRwimQOAF\nNNa42FXnCgSCpiMEUyDwAlrTscNd3T4EgvaOEEyBwAtoiretK84VCARNRwimQOAFNMXbVqJunl5z\nzhUIBC1HeMkKBF5AU7xtb9y4wbBhwygtLUWtVrNhwwbOnTtHYGCg3XMFAoFzEWUlAoHAa7h9+zYJ\nCQlcvXqV8PBw9u7dS6dOneodN3fuXA4dOkSPHj04e/Zss88XCFqCCMkKBAKvYc2aNcTExHDhwgXG\njBnDmjVr7B733HPPkZOT0+LzBYKWIFaYAoHAa4iMjCQvL4+QkBBu3LjBE088wfnz5+0ee+XKFWJj\nY21WmM05XyBoLmKFKRAIvIaioiJCQkIACAkJoaioyK3nCwQNIQRTIBDYpTXetuHh4Tz00EMMGTKE\n4cOH2/wtJiaGqKioev+ysrJsjlOpVK2uTxU1qgJnIrJkBQJBPUwmE4sWLbLxp9Xr9TbZt127dmXj\nxo1kZmbWO1+lUvHJJ5/QpUuXen/Lzc11+LxSKLVnz54UFhbSo0ePZo27tecLBA0hVpgCgaAerfG2\nlWhJeoRer2fXrl0A7Nq1i/j4eLeeLxA0hBBMgUBQj9b606pUKsaOHcvQoUPZtm1bk89buXIlubm5\nREREcOzYMVauXAnA9evXefLJJ+XjZsyYQXR0NBcuXKBPnz7s2LGjwfMFAmcgQrICgaAerd37O378\nOL169aK4uJiYmBgiIyMZMWJEo+d16dKFo0eP1vt97969OXTokPxzSkpKs84XCJyBWGEKBIJ6tNaf\ntlevXsC9sO2UKVM4efKk08coELgbIZgCgaAerfG2rayspKysDICKigqOHDlCVFSUy8csELgaEZIV\nCAT1aI237c2bN5k6dSoAtbW1JCYmMm7cOE++HIHAKQinH4FAIBAImoAIyQoEAoFA0ASEYAoEAoFA\n0ASEYAoEAoFA0ASEYAoEAoFA0ASEYAoEAoFA0ASEYAoEAoFA0ASEYAoEAoFA0AT+P0uhlJEsM5H8\nAAAAAElFTkSuQmCC\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(8,8)\n", "from mpl_toolkits.mplot3d import Axes3D\n", "gcf().add_subplot(111, projection='3d')\n", "gca().scatter(vl[:,0], vl[:,1],arange(len(vl)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Recovering Low Dimensional Structure of Views of Real Objects" ] }, { "cell_type": "code", "execution_count": 84, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "359.0\n" ] } ], "source": [ "frames = cv2.VideoCapture(\"bunny.mp4\")\n", "print frames.get(cv2.CAP_PROP_FRAME_COUNT)\n", "data = []\n", "for i in range(350):\n", " _,frame = frames.read()\n", " gray = cv2.cvtColor(frame,cv2.COLOR_BGR2GRAY)\n", " gray = gray[::2,::2]\n", " data.append(gray.ravel())\n", "data = array(data)\n", "del frames" ] }, { "cell_type": "code", "execution_count": 85, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(350, 20)\n", "[ 3853.40952636 2180.11119734 2171.40068491 -206.92715815 215.6530972\n", " 2157.56203323 316.11037864 -2269.19097953 -1318.46861416 35.84289751\n", " -594.64097527 1022.32363534 -29.46706416 308.2711417 229.60280484\n", " -712.37283502 -170.98457044 1484.92789905 -1202.73114523 160.54615569]\n" ] } ], "source": [ "from sklearn.decomposition import RandomizedPCA\n", "pca = RandomizedPCA(20)\n", "lo = pca.fit_transform(data)\n", "print lo.shape\n", "print lo[0]" ] }, { "cell_type": "code", "execution_count": 86, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 86, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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//POz3i87O9to0qSVYbffYPj53WPY7RcZ33zzTen3e/bsMYKD6xtW678NeN6w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\nYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "mds = manifold.LocallyLinearEmbedding()\n", "vl = mds.fit_transform(lo)\n", "scatter(vl[:,0],vl[:,1])" ] }, { "cell_type": "code", "execution_count": 87, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 87, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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ZsgVdXV04ePCg+jtPPvkkzj77bADAggULsHbtWhQKBezZswe7d+/GzJkzPb1G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\ntZON6ibaOC3VOtLL6uWY2o0J3beX4+V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M9PT8e7VupyqYPXtuu8AJlvTT4OhLRqxSiZDQ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\nIBDYwP8Hh5S/us0AmvUAAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "figsize(8,8)\n", "from mpl_toolkits.mplot3d import Axes3D\n", "gcf().add_subplot(111, projection='3d')\n", "gca().scatter(vl[:,0], vl[:,1],arange(len(vl)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Image Normalization and Intrinsic Dimensions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Dimensionality for Real World Images:\n", "\n", "can compensate by 2D image processing:\n", "\n", "- 2D translations (2 dimensions)\n", "- 2D rotations (1 dimension)\n", "\n", "cannot compensate by 2D image processing:\n", "\n", "- translation in depth / scaling (1 dimension)\n", "- 3D rotations (2 dimension)" ] }, { "cell_type": "code", "execution_count": 89, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from scipy.ndimage import measurements,interpolation\n", "frames = cv2.VideoCapture(\"bunny.mp4\")\n", "data = []\n", "for i in range(350):\n", " _,frame = frames.read()\n", " gray = cv2.cvtColor(frame,cv2.COLOR_BGR2GRAY)\n", " gray = gray[::2,::2]\n", " y,x = measurements.center_of_mass(gray<0.3*mean(gray))\n", " gray = interpolation.affine_transform(gray,diag((1,1)),offset=(y-120,x-180),mode='mirror')\n", " data.append(gray.ravel())\n", "data = array(data)\n", "del frames" ] }, { "cell_type": "code", "execution_count": 91, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 91, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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FCqKionIW4vEowEVEpMzIK/cKHM6FReEsIiJlSV65pxnCREREXEbhLCIi4jIKZxEREZdR\nOIuIiLiMwllERMRlFM4iIiIuo3AWkTLvrbfeoXbt5lSr1oiRIx8nMzPT6ZKkjCvQ3NoiIiXdV199\nxV13PUpy8t+AFJ5/fiJebyQjR97vdGlShqnlLCJl2gcfTCY5OQxYC8SQmnqAMWNec7osKeMUziJS\npu3YsRmIBZ4D6gMj2LNnJ0lJSc4WJmWawllEyrSNGzcAEUAX4HvgcyCYqVOnOlqXlG0KZxEp0/bu\n3Qf8DNwKHATqAk34+OOPnSxLyjiFs4iUaWedVR1IAyYClwDRwBqWL1/uaF1StimcRaRMe+ONFwEP\ntju7OTAIuIgdO/Y7WpeUbVoyUkTKLGMMbdt24ffflwEpQAxggLMIDt5NRsZhZwuUUk1LRoqI5GLJ\nkiVZwTwV8AP3Yqd/OIIxAUdrk7JN4SwiZdaSJUuArsBFQDjwL+AI4CEyMsrJ0qSM0wxhIlJm1atX\nD1iDHRAWBmzIeiWRFi1aF18haWnwyiuwciV06gS33AJBajuVZbrmLCJlVmpqKhERVYF6QCfgK6An\n8BWTJ79Jv379ir6IQAAuvBB+/RWSk8HrhWuugffeK/pzi6N0zVlEJBcrV64kKCgMOwisEfA28Dvg\n57zzziueIhYtgiVLbDAD+P0wcSLs2lU85xdXUjiLSJkVFhZGWFgosBF4COgLXExkZAd+/fXX4inC\n7z+5Czs4+FhYS5mkcBaRMqtp06a0b98Ce815O5AEPENwcBIRERHFU0SHDhARcSygQ0OhXj2oXbt4\nzi+upGvOIlKmpaam0qVLd5YuTSEQGERExFyaNNnKokXxhIaGFk8R69fDrbfCunXQti28/TZUrlw8\n5xbH5JV7CmcRKfM2bNjAqFFPsGnTLho3rkOrVi1o3LgxPXr0wOPxOF2elFIKZxGRU5g3bx69el2N\nx3MRqakrCQS2AKEEB3u47rq+fPjheAW0FAmFs4jIKcTExHLo0GvAFUAAuBAoD8wDYObMT7nkkkuc\nK1BKLd1KJSJygu3bt/PCCy9w6NA+oGPWs8FZ3weAK4FkRowY6VSJUoap5SwiZYoxhg4dLmDx4kVZ\nz9QE+gDPAluw4RwJeIG1REWdxeHDu50pVkq1vHJP03eKSJnyz3/+k8WL9wI7gVjsXNqLAB926cgg\noBx2Ks8wwsKK6ZYqkeOoW1tEypRZs+KBq4Fbsp5JBVYAjbHXmr1Zr0UD9WnevGGx1yiilrOIlClJ\nSYnAa9hVqMpjry/PB/ZgA7otMBrbil5H27Y9HKpUyjK1nEWkTGnVqhV27eZEYC+2C/slbBg/BWQA\nTwARQCQvvfQRH374kUPVSlmlcBaRMiEjI4NvvvmGdu3aAZnY8O0BbALexa7p/Cq2m3s/tkVdAWMe\n4uGHn3akZim71K0tIqVeamoqF1zQm+XLEwkEvFnPpgGzgWrAACABmAS8AtyBHSjWBPCSkqJFKKR4\nqeUsIqXeW2+9xbJlYRw5spDkZC/2enMSdqnIF4CfsEtF1sC2ojOBMGAjoaFvM2DAdc4ULmWWwllE\nSr3NmxNITu6KnWTkALZVbLDXl4cAg7BrOdcBvs3aK4Xy5UMYPrwX//3vEw5ULWWZurVFpNTr0qUT\nXu8D+P2DgEuBJdjWcTBwFXBD1pYfAbWBKkA6U6Z8xPnnn+9EyVLGqeUsIqVe3759uemmiwkOrovH\nM5rg4HDs/cyZwK7jttyLbbPsBY5Qr1694ity+XKYNAmWLi2+c4prKZxFpNR77rkxvPfep4SENMGY\nGAKBR4Ao7DSdPwGDsbdTXZ61RyZhYdHUqlWreAp86SXo0AEGDoQuXeAJdaOXdZpbW0RKtG3btvHB\nBx+QlpbONddcTbNmzU56vWHDs0lJWQp0Ab4C2gC3Au8DFbArUvmxQd0BmE79+g1Zv/7Pon8De/dC\nbCykph57LjLStqSLs+UuxU6rUolIqbRp0yZatOjAI49sZtSoQ3TocAHz58/Psc3WrVsJD68P1MIG\ncPWsV6phl4dMxN5C9Q3QE3u/czgffji+eN7Ejh0QFpbzubAw2Lq1eM4vrqRwFpES65lnXuTQob+T\nnv4agcCz+P3P8s9/jsqxTePGjQkENgPx2Dm1BwLLgaZ4PPMJC2uDvc4cyNrmQZ5++kE6d+5cPG+i\nfn3weHI+l5EBcXHFc35xJYWziJRY+/YdJDOzbtajTCCB1av/5Oeff8YYw3fffcdXX33Fiy/+h+jo\na4mI+JLQ0J+pWPFymjV7jWnTPuW5527Marh+gW1Bf87TTz9PcnIxTTzi88H06VChAoSHQ3Q0fPEF\nVKpUPOcXV9KtVCJSYmRmZjJu3Hji4xfQsGEt+vTpzvTpj+P3twKGAivYs6cqXbt2p169huzeHQDa\nkpk5i1dffY6LL+5J5cqVCQ0NPXrMb775hsjItqSldT/6nDFRWdeqi2lFqq5dYc8e2LcPKlaE4ODi\nOa+4lgaEiUiJcdttd/PRR4vw+28lPPwH6tdfwW233cSjjz7FoUN+4GPs4K7JwD3AWuyI7OVERHTm\n8OH9hITkbJOsW7eOli27kJy8CDsJySK83kvYvTsBn89XvG9QyhQNCBOREi8pKYl33hmP3z8TGEhq\n6tVs2LCfkJAgRo4cjp3t64qsrdOBVthgBmhOZiYcPnz4pOM2bNiQZ555jIiItsTEdMLr7cXHH7+r\nYBZHqVtbRByVnJzMb7/9RlhYGG3btiX4hC7djIwM5syZw/bt27EzekUA1wEbSE09lxEjRnH//bdj\n2xrfAhcDdYF5wK9AOzyeV6hevRbly5fPtYa7776Dq666gs2bN9O4cWOqVKlSVG9XJF/UrS0ijtm+\nfTtduvRg//5IjDlCixa1mDNnKpGRtsWblpbGBRf05s8/D+Dx1MLvn4fH05qMjN3YKTjDgJWEhXXg\n7rvv5LnnXgZq4fHs4PLLezBnTjwpKX7q1GnMzJmTadSoUY7z7969mwkTJpCWlkbfvn1p3LhxcX8E\nUobllXsKZxEpMikpKSxbtoyIiAhatGhBUFDOK2l9+vwfM2Y0ICPjSSBARMTfePjhdvz73w8D8Prr\nrzN8+Jf4/dOwrea3CQ8fTlraeRjzFTagBwArqVOnGe+99wqBQID69etTt25djDEkJyfj9Xo50bZt\n22jdujOHDl1AILCdoKD5vPHGK9xyyy1F+6GIZNE1Z5EyJDMzk+efH0PnzpfSt+/1rFy5skjO8+WX\nX9Kr19/o1+9GFi1adNLr27dvp2nTdvToMZguXa6kR48+pKWl5dhm1ap1ZGRkT5kZTEpKL5YtW3P0\n9c2bE/D7u2CDGWAJqakZGDMHmIWdbnMkkMLmzQ/Qr98NdOzYkbp16wL2l19uwQzw3/++yIED/UhL\nW0cgEE56+hAGDryPCRM+KcCnIlI4FM4ipcxDDz3KI498xPz5dzJ1ajs6derGli1bzvg4aWlpZGZm\n5vrahAmfcMMNdzNz5uV88cU5dOvWmyVLluTY5rbb7mXr1qs4fHgpSUmrmT/fMGbMyzm2adeuJWFh\nH2DvUU7B651Ix46tjr7epUsnfL6PgB3ACuxay/WBt4D/w15/vh7bvX0jGRkVWb16db7e3+7dBwgE\nEoFoYBrwApmZ33LnnSPytb9IUVI4i5Qyr732Bn7/ROAKjBlOSsqVTJ48Oddt33nnPcqXr054uI8r\nrriOw4cPs2/fPrp2vZjIyCi83hhefvnVk/Z7+umx+P1vADcBd+H3D+eVV97Ksc2KFasJBK7KehRK\ncvLlLFuWMzhfeeVZmjZdgtdbl4iI2vToUZFhw+46+voVV1zBP/95MyEh9QkObocN0n7YAWGLgIPY\n9ZkB9pOWtpVK+Zy8o1+/XoSGTgMaAtkzdDXmyJH9+dpfpCgpnEVKGY/Hg52KMvtxIOu5nL7//nuG\nDh3JwYMzSEvbzqxZYfz973dyww23sWhRIzIz/aSm/s6DD45mzpw5Ofa118mOH1UdclIru2XL5oSE\nTAAMtlX8Oe3atcixzVlnncVvv/3A0qVzWL36V778cgIhISHs27eP5557jkcffZzLLruYI0cSefLJ\nx4F9wEwgFagHdMDjaUV4+J34fJ24444h1K5dO1+f07XXXsM999wKfIgd2b2XsLD7uPDCS/O1v0iR\nMi7holLKvMzMTJOenn7G++3evdsMHXqfufzy/zOvvPKayczMLILqnLdt2zazdOlS4/f7nS4lV//+\n9yjj9bY28KkJCnrSxMRUM1u3bj1pu0ceedR4PP8yYLK+tpiYmGomKqqyge1Hn/d4HjaPPfZ4jn3f\neusd4/XWNzDZwFsmMrKSWbBgQY5tdu3aZZo0aWt8vvomMrKqufzyv+X4d7Vs2TLz+eefm1WrVuXY\nb8+ePaZatfomPPxm4/E8ZLzeKmbatGmmUqXaBsYYiDFQxUBzExlZ0YwfP96MGTPGzJ49+y99XlOm\nTDHVqjUwkZHlTa9e15gDBw78peOInKm8cs81iVic4fzqq6+bWrWamZo1m5r//OfZYguRPXv2mE8+\n+cRMnjzZJCUlFcs5z9Sbb75tvN7yJigoxHTterHZs2dPvvY7ePCgqVmzkQkNvcvA+8br7WDuvntE\nEVdb/B5++DETEVHBREc3MxUrxprff/+90I49e/Zs06XLpaZNm27m1VfH/eV/l5mZmebVV183F110\npenf/1azbt26XLd76aWXTETEVQYys4J4pqlTp4WpV+9sA19lPRcwXu8lZty4cSft/8EHH5quXXub\n7t2vNPPmzcv1HOnp6WbFihVm/fr1Od7PqFHPGK+3uilX7goTGVnFvP76+KOvPfnkUyY0dOBxfzRM\nNw0btjFebwUDOw1kGJhngoKuNqNGjfpLn5GIGyicj/PxxxOM19vAwC8GFhuv92zz8suv5nv/jRs3\nmjZtzjNhYV5Tp05z88svv+Rrv7Vr15qzzqppoqL6mKioC039+i3M/v37/+rbKLCMjAzz3HMvmssu\n62/uueefZv/+/ebHH380Xm9NA8sNpJrQ0KHmoov65Ot4H3/8sYmK6n3cL9Q9JiQk3GRkZJxRXatW\nrTLNmp1jQkIiTL16Z5tff/31r7y9IhEfH298vvoGdme9x/dN3brNC+XYP//8s4mMrGzgYwMzjNcb\nZ15++ZVCOfapHDlyxDRp0sb4fL1MePgdxuutZGbOnJn1PisZn+8GExXVxbRrd75JSUkptPOuW7cu\n673uyPoc15qIiBizb98+Y4wx9913v4Enjvu3tNJUrdrA9O//dxMR0c/AWgPTTGRkJbN06dJCq0uk\nuCmcjTF+v98sXbrUXHRRXwPvH/c//tfmnHN65usYGRkZpm7dZiYo6BkDBw1MMtHRVcyuXbtOu+/F\nF/czQUHPZp0z04SFDTbDhz9Y0Lf1lw0YMMh4vRcY+MCEhQ02DRu2NKNGjTIhISOO+2z2msjImHwd\n7/333zdRUVcft+8RExwcZtLS0vJdU2pqqqlWrb7xeF4xcNjAxyYmptpf7mbcsmWLmTx5svnhhx8K\npXdk7NixJiJiyHHvMd14PEEmEAgU+NiDBw818N/jjh1vGjfuUODjnk5SUpJ5++23zYsvvmj+/PPP\no8+vX7/evPPOO+bzzz8/o59hfsydO9fExJx73Hs1Jjq6sVm+fLkxxph58+aZyMjqBr43sN5ERl5q\n/vGPYSYpKcncdNMQU6lSHdOwYRszc+bMQq1LpLiVuXA+cOCA+eKLL8y0adNMcnKyWb58ualcuY6J\njo4zQUExBp4+7hfDONOjx1X5Ou6WLVtMZGS1HL9UYmJ6munTp59237i4TgZ+OG7ft8zVV99U0Lf6\nlxw+fNiEhERmBaD9YyE6uqsZNmyY8fl6GAhkPT/L1KjROF/H3LVrl6lQoUbWHyBzTWRkb/O3v918\nRnWtXLnSREU1POHz7XLKLtO8fPvtt8bnq2TKletjfL7G5pprbixwQM+aNcv4fI0NHMiq7zNTs2b+\nPp/TueOOYcbjeSxHV26zZp0L5dhus3PnTuP1VjTw09H3Wq5c1RyXeiZM+MTExjY1FSrEmsGD7zKp\nqalFUsuRI0cK/Y8PkfwqU+G8YcMGU7lybRMdfbGJju5iGjduYxo2bG3gjaxfBL8Y8BqPZ7jxeB42\nPt/JA1nuKImqAAAgAElEQVSO9/vvv5uOHXuYWrWam/79/25CQ33HDZZJNj5fQzN//vzT1nXHHfdl\ndcmlGNhvfL6O5tVXXy+U93ymEhMTs95H6nEtlx5m0qRJpkOHbiYq6lzj9f79aDdnfq1Zs8b06nWN\nOfvsc83w4Q+f8S/UnTt3mvDwmOO6jQ8br7dmjhZdflWqVMvAd0d/TlFRrczUqVPP+Dgnuuuuf5rI\nyComJuYcExNTzSxcuLDAxzTGmOXLlxufr5LxeP5jYJzxemuaTz6ZWCjHdqNp06YZn+8sExFR2ZQv\nX8388MMPxXr+/fv3my5depqQkAgTEhJhHn30yWI9v4gxZSyce/W6xgQFZbeMM01Y2N+NxxNq4MjR\nIAoNvcl0797TPPjgw3n+4t+2bZspV65qVrD/bsLDrzcNGpxtfL76JjT0PuPztTdXXXV9vlpkfr/f\nXHbZtSY4ONyEhISbO+6494y7Q/ft22dmz55tFi9eXOBW4MUXX2kiIq4xMMcEBz9mqlatZxITE01a\nWpr57LPPzLhx404aRVscHnjg38bna2RCQ+8xPl9Lc9NNQ874GIFAwHg8QQbSj/7MIyNvM2PHji2U\nGteuXWt++uknk5iYWCjHy7Zs2TIzYMBg06/fTWbatGmFemw3SktLM9u3b/9LdwYUVN++15uwsCFZ\ng8u2G6+3ifniiy+KvQ4p28pUODdt2vGE7uO3jc9XzcAHWY8PGp+vufn6669Peyx7HfXa446VYoKD\nw8z06dPN6NGjzaeffnrGAev3+/9SF91vv/1mypevbmJizjdebx1zzTU3Fehap9/vN3feOdy0bHme\n6dv3erN58+a/fKzC9u2335pnn33WTJky5S//ERIX18EEBT2X9XNbb7zeGnn2kEjZUqlS3ayBZdn/\nbz9l7r33n06XZczevcb84x/GXHSRMY8+aoy63Eu1MhXOQ4bcYyIirjOw0sAEExHR2tx//4OmQoUa\nJiamg4mMrGZuu+3ufP3SnzRpkomK6maO3Wqyw4SERJzxCOTC0KhRGwMfZtXhNz5fezNxYunt9iyo\n9evXm7p1m5uIiLNMWJjPjB37mtMliYucfXaX4/5gD5iIiD7mf//7n7NF+f3GNGhgTFhYdnePMVfl\nbzyMlEx55V6pW8/5+eef4scfL2D58vZAG9LTtxIcHMGmTStZvnw5FStWzPeycL1796ZGjafYvHkA\nqann4PWOZ9iwB09ab7Y4JCSsB3plPYokJeVC1q1bV+x1lBT169dnw4Y/2LNnDzExMYSHhztdkrjI\nO++8RLduvUhLe55AYB/R0cH07/+Gs0V9/z3s3g3Zi4MkJ8PXX8OBA1ChgrO1SbErddN3ejwe1q9f\nBywAfiAQWMGYMeNISEigc+fOZ7Rea2RkJIsWxTNyZDMGDlzLW2/9iyeffKTIas9LXFwrgoLeznq0\nl4iIr2jdurUjtZQUHo+HKlWqKJjlJO3ataN79+5AFIHAUxw61I0LL7yM1NRU54oyBk6cZtXjgVMs\nPiKlW6lbz3nTpk00b34efn/C0ediYi5mwoR76dWrVx57nrlly5bx8ccTCQ0N4dZbb6FevXqFevzj\nbdiwgW7derN/fwrp6QcYNuxuRo9+osjOJ1KaJSYmUqVKLOnpuwAfYIiO7sTkyU/Ss2dPZ4pKSoK4\nONixAzIyICICunWDGTOcqUeKXF65V+q6tWvUqEF4eCZ+/5fAlcAS0tOX0Lx580I9z88//0zPnn3x\n+4cQFHSEMWM6sWjR9zRp0qRQz5PNdtP+yaZNmyhfvny+V94RkZOlp6fj8YRgl5oE8ODxeMnIyHCu\nKJ8PFi6EESNg7Vo491x46inn6hFHlbqWM8CCBQvo1asfKSmZQDLvv/8W11xzdaEcO9sFF1zO999f\nDfwdgKCgJ7jxxu28++5rhXoeESl8xhguuuhy5s+PISVlCMHBc6lc+QNWr15CuXLlnC5Pyogy1XIG\n6NixI7t3b2bnzp1Urly5SK45Hj6cBNQ8+jgzsyYHD64p9POISOHzeDx8/fWnDB8+kp9+GkmDBnV4\n+eV4BbO4RqkMZ4CQkBBiY2OL7Pg33ngVq1c/gN9fGUjG632SAQOeK7LziUjh8fv9TJw4kcaNa3PH\nHbfSsmVLp0sSyaFUdmsXB2MMTz01mtdee5eQkBBGjhzGbbcNcrosETmNpKQk2rc/ny1bqpKR0YCQ\nkIl89tm79O7d2+nSpIzJK/cUziJSprz66quMGPEtyclfAB7gO2Jjh5KQsNLp0qSMySv3St19ziIi\nedm7dx+pqXHYYAZoRmLiPidLEjmJwllEypQePboTEfEe8CuQSHj4A/To4dC9zSKnoHAWkTKlS5cu\njBv3LBUqXElYWCw9eqTy3nu6BVLcRdecRUQk/5YuhTey5iEfPBg0jfBfpgFhIiInWLNmDRs3bqRp\n06bUqVPH6XJKhkWL7JSifr997PXCnDnQsaOjZZVUGhAmInKcZ555ntatz+O6656lWbP2fPzxJ06X\nVDKMGnUsmMF+P2qUc/WUYgrnEuS7776jdevzadCgDSNHPk4gEHC6JJESZ926dYwaNZrk5CUcPDgb\nv38uAwf+g8OHDztdmvsdH8zZkpKKv44yQOFcQvz222/06fN/LF16Dxs2jON//5vNgw86s3ylSEm2\nceNGwsJaADWynmlBSEhFduzY4WRZJcPgwbYrO5vXa5+TQqdwLiEmTfqc5OQhwNXAOfj943j/fXXF\niZypuLg40tKWAb9nPTOLoKAj1KpVy8mySob+/eGll6BJE2jcGP73P7jhBqerKpVK7dzapU1kZATB\nwds5tqLdPsLDI5wsSaREio2N5d13X+eWWy4kKCiG4OBkvvrqUyIjI50urWQYONB+SZFSy7mEGDjw\nVsqV+4rg4OHA//B6r+eppx4qtOMvXbqULl0uoUGDNtx++70kJycX2rFF3GLDhg2MHz+ezMwMEhLW\nsXTpd+zatZkLLrjA6dLylpkJY8fClVfCsGGwf7/TFUkR061UJUhCQgJjxrxCYuIR/va3Plx88cWF\ndtzmzdtz+PCTQGsiIp6md+8oJk/+oFCOL+IGP/74I5deehXGXEZQUAK1ax9m4cK5+Hw+p0s7vdtv\nh/fftwOywsKgRg34808oCbXLKek+Z8nTm2++yT33zMPvzw7jI4SEVCIlJYng4GBHaxMpLE2bdmD1\n6uFAPPAZkMm1117Cp5+6fOxGWpoN4WPXtCA6Gt59F/r1c6wsKTjd5yx5ioiIwOM5cNwzBwgKCiEo\nSP88pPTYs2cXMBvYCvwJzOWLL35gxowZzhZ2OpmZkNsv8OPDWkod/fYV+vbtS8WK6wkNHQy8is/X\niwcffBCPx3PafUVKigsv7AZ8DfwHqA60JiPjXqZO/cbRuk4rIgJ697b/BQgKsl3b3bs7W5cUKYWz\nEB0dzZIlPzFiRDUGDPidN94YyWOPjXS6LJFC9fbbY/H5QoDVR58LDV1D5coVnCsqvz79FG67DZo3\nh0sugQULoGJFp6uSIqRrzuJqfr+fNWvWUKlSJWJjY50uR0q4+Ph4LrvsWtLTryc4eBdnnbWYpUt/\noVKlSqfeKfv3knqSpJDpmrOUSEuXLqV27Sacf/4AGjVqxUMPPep0SVLSbN8Ov/4KBw/C/v10a9iQ\ntfcP5ZcOv7Ki3jI2tIuj0nff2QD+6CNo29ausnTRRTaMPR7bjRwUBPXqwYEDpz9nYVi2DD78EH76\nqXjOJ66jlrO4Vv36Z7Nx4/3AjcBefL5OTJ06ngsvvNDp0qSo+P3wyis2BENDYf16SEmx38+YAYcO\n2SCNjISaNSE1FbZts4OmAKKiIC4OypeH336DfftswJ7ud0tQ0LFj5CU4GBISoHp12LgRpk+314Kv\nuQZiYk6//8KF8PPP9laoq6+2xzvR66/D8OG2JmPg73+3X7/8AtWq2Xudi/IuipQUePllWL0azj0X\nbr5ZvQZFpEhvpZo5cybDhg0jEAgwaNAgHnjggZO2ufvuu5kxYwZer5d3332XNm3anFGRUvZkZmYS\nEhKKMSlAKAAREbfz7LPNGTp0qLPFlTaHDtmwCw09+bVdu+zkF3v3wvnnQ/v28OqrdrGDCy6wITFl\nCmzYAB06wP33w+LFsHw5hITY/d5804Zo9+7w4IN2icGlS224bd1qJ9TweODyy20Ap6YW/2dwJlq3\nthOBDBliwzMkBCpUsO/J67Wt3shIaNHCBizAt9/CLbfAjh32uYgIu8zirFmwezc8+aRt5ffoAffc\nA8cvahMWdqwVHxICnTrBzJlFE9AZGdClC/zxhw1prxcGDIBx4wr/XJJ37pkCyMjIMA0aNDAbN240\naWlpplWrVmbFihU5tpk2bZrp1auXMcaY+fPnm44dO+Z6rAKWIqVQrVpNDUw09jfgAePzNTazZs1y\nuqyS49dfjfnsM2NWrTJm+XJjvv7amEmTjKld25iwMGNatTImLs6YkBBjgoONadnSmKAgY8C+fvXV\nxkRGGuPxmKwfQsG/CvNYTn5lf07ZX6Ghxtx5pzG1ahlTrpwxPp8xPXoYk5ZmzG+/GeP1nnyMqChj\nJkwwpmpV+zPIPs7pzh0Zacyll9qfX61axnTsaH++hWHuXFvXie8tMbFwji855JV7BZpbe+HChTRs\n2JC6desC0L9/f6ZMmUJcXNzRbb766ituvvlmADp27EhiYiK7du2iatWqBTm1lAGff/4BPXv2wZhn\nSU3dzMCBt9CjRw+nyyqYLVtg/Hg7sQTYFtIFF9hW44ldh4mJttWydCk0a2ZbL1n/r+Xq0CF4+mlY\ntcrus2WLbV1lZuZsiWVbujTn42XLjn2flgaTJ/+lt5in0tI7dmIXeHo6fP65bQVnf9Y//XSsiz4l\nJffjzJoFhw8fu2c5Pf30505Oti3nbAkJ0LIlrF1rr4sDzJtnezDq1rXd4Pmds8DvP3nb4GB7zvx0\n20uhKVA4b9u2LcdKLrGxsSxYsOC022zdujXXcH7ssceOft+tWze6detWkPKkhGvfvj2bN69ixYoV\nVK5cmQYNGjhdUsG8/LLtsjwxoP73P3ubzKuvHnsuORlq17a/uMF2/7Zta7uPy5c/+dipqdC5s71G\ne3y3cH6uo0rBhYfbP2iO/yMoOdn+wRMXZ7ujs/8gy5aZCXXqFM4fLIEA/Pe/8Npr8Mwz8MQTNvBD\nQ+2tV5MmHfvjb/Nme6kiPd12tbdufew4nTvbfbKv04eF2T8M1ZgqFPHx8cTHx+dv44I0ySdNmmQG\nDRp09PEHH3xghg4dmmObyy+/3Pz4449HH3fv3t0sXrz4jJr3IiXemDF5d+mGhhqzceOx7Z9+Oveu\n1C++yP34335rTHS08929JfGrcuUz2z63n+PIkcb07n2sexpsV/bYscbs3m1MlSo5X4uKMmbGDGMS\nEmw3ePYxj98mv+fO/mrQwJhp007uGvf5jPn5Z2N27DCmW7eT/01NnJjz39Lq1cace64xsbHG9Otn\nzL59Rfa/RVmXV+4V6FaqmjVrkpCQcPRxQkLCSfeinrjN1q1bqVmzZkFOK1LyjBxpfx3m5fiVhjZv\nPvl1Y2wLLDfp6e4fUevxnH4QU1iY7VbN73vJHih1Ku3a2eUN27e3rb+OHe0EHs89B6NG2ZbtqlW2\nOzg01NZXvvyxEeBHjthBalFRtnVcsSJ88AHUqmXrrFgR4uPtgK633rLHiYqyA74uuQT+8Q+oXNme\n56GH4M47YfZs2yNy6aUQG2tHb3fvbgeQDRpkz5Ob2rVtS/dUS1uuXw/XXZd713jv3naE+YmttsxM\nOxL8eI0bww8/2O7yyZPhrLOOvZaUZD/Phg3hwgvtZydFokCjtTMyMmjSpAnfffcdNWrU4JxzzmHC\nhAk5rjlPnz6dsWPHMn36dObPn8+wYcOYP3/+yYVotLaUVsbY0MlrLuSoKDsy2uu1jz/91C5if/w+\nPh/s2ZP7L+dDh+wv1b17c7++XJxuuw3atIFNm6BBAxue4eHQsydcdpm9xel4PXva65nVq9vvW7c+\nNgPWO+/AhAk2RKKj7UjlkSPhk0/g999tl+vo0ccCJDXVjjQOCbHXYXO51pqZmcmBAweoUKHCsfnj\nU1LsrUrG2K7dEz/jQMBeOz7rrGPHTE09OUjT0+2138hIe733r/zB9OmnNoQzMo790ZX9u7F8ebj1\nVvu5FNY91x6PPVd+rktfcom9np2aavcrX97eclW5cuHUUsYU2WhtY4yZPn26ady4sWnQoIF5+umn\njTHGvP766+b1118/us2dd95pGjRoYFq2bJlrl/bpmvciJd6VV9oR0Ll1R0ZHG/PHHzm3z8w05v77\nbbejx2NMtWrGbNiQ9zk2bzbmssuMqVfvWNdmUJAxo0bZ0b1erzFnnWW7K8PD7QjtiIiT64mNNebs\ns+32ISG2vsqVjWnd2ph77zXmvvuMmT7ddtWXL2+3693bmPh4W3defvvNHi8qyn61aGFMUlLe+3zz\njR2hHBlp9zn7bGP8/tN/5rmIj483MTFVTVhYjClfvpqZN2/eXzpOkUtNNWbRopNHeUdEGPP888as\nXGl/loUx+j0uLn81HTli/82c+G/3xG5xybe8ck+TkIgUB7/frsk7Y4bt8rzzTntPa4UKtiv0VC2s\n1FT7Va7cmZ/TmNyPa4xtYft8tqXu99vWXsOGxbM+8PbttnvV57Ndu6fqxs1Wp44deZ4tMhJeeMF2\nGZ+BxMREatVqzJEjHwE9gW+Jjr6RrVvXUu6vfL5Fbf9+25tw4kCy4GDbE/PMM7bbedMm2w3/V3pM\noqLsz75atdNvm9vSlVFRdiazvn3P/Nyi9ZxFpASLjrbXfrMFBcGjj8Ijj+Rv/1Wr4NpryVyzhtUZ\nQVyduZiVNAOgXLnWzJnzFu3atSuCwgvB8OH2D5HcREbaLv916+xljVGjzuzY1arZfc/kD7J77rGT\nyvj99o+qOnXs5YVTXQeXPCmcRaTkuuwyO4gquwXp9doeiPPPP/2+ycn22u+ePWAMmcA+zqIuW/CT\nSETE2axf/yc1atQoynfw1wUCdqBabr8bw8JsKzp7m6Sk0x/P44FzzoHrr7djA7KXocwvY+Dtt+0s\nb/Xrw4gRuv+5ABTOIlJyJSbauavj420L7cUX7ajm/FiyBLp1sy3LLAfxcEX4eSwOXssjj4zggQfu\nO/X+xtj70F9/3YbhoEH2uZgYOzLa67WDtkJCim60fKtWdpBbQX8/XnEFfPFF0c7LLWdE4SwiJV9m\nZv5nusq2aZOdBOS4Gbr8BNE+rCLNrujBpEkf573/mDF2dPjxrdLQUBvU1avb0du//mq7eMeMgcGD\nz6y+/NiyxY6SXr362DiC3H5Xnur58uXtTGXXX1/4tUmBaMlIESn5zjSYwXZp33wzxucjHTiMlwnc\nwsq09cyY8QPLjp+yNDfjx5/cXZyebp/bsMEGc2am7T4fNsxO2ZmeDitX2lndsiUlwV132S7lm2+2\nA/Lyq3Zte7yDB20r/lRd0bndA1+zpr3lKrdg/v57ePdd27sgrqNwFpHS7bXXWPPoozyCl5v4kEG8\nCUQD9di5c2fe++Y10CkzM+f0qGlpMHUqNGpkQ7hhQ3tPcmambfm++SYsWmTv0e7c2YbtkCF2QpPW\nre1kJHkJD4evvsp9nu7ateGNN47dJw/2+4EDcz/WnXfaiUmGDrXLQr78ct7nluJXRLdvnTEXlSIi\npcxll11hoJyBNw0EDHxjwGt27tyZ944zZtj7q/MzlabPZ0yjRjnvBfb57P3gJx4jOtqY7t1z3mfu\n8xmzZs3JNQQCxnz3nTFdu9r7048/Tni4MVdddWzbWbOMadvWmMaNjXniCbvviZYuPfn+6fBwYw4d\nKtiHLGcsr9wr0MIXIiIlwZo1W4HhwIvAEKAKQUGhp18d79JL7VrM775ru9XXrLEziXm9dnBY9mIl\nQUH22vbatTnvN05Ksl3SuV1X/P77nFNtZmTYUei7dtnBb5Ur21XJrrvOzsp1/O1k2dq2tfcZZ+vR\nw65GlZcdO05euzt77e3o6Lz3lWKjcBaRUq9x4zqsXbse+ANIB8ZQo8a7+dv53HPtV24GD7YhW6EC\n9OkDXbrYcMwOY58POnSw9xP/9JO9Nh0WZruht2zJGc7BwXZq04cesl3XERF2CdB9+3K/Tcrns7dD\nHd+VnR8tW548lazPZ+f5FtfQaG2RIrZq1So++mgCQUEebrrpxpK/9GUJs337duLi2nLoUAhQDwgj\nOHgRS5f+QvPmzQv3ZGvW2CBPTbUB2LOnncUrPd0u4/jLL9C8uV0o4733bBD7/bYlW62anRXs+CAO\nC7PXrE8M05AQ27JesSL3JURPZ/Zse3vakSN21Pm0aTa0pVjpVioRh/z222+cf/4lJCffCmTg9X7A\nggXxNGvWzOnSyowXXniBhx5aQVraS8A3wEZiYp4lMXFH0ZzwyBFYutROudqiRd73P3/9tQ3GqlXt\naO6qVXN2i4eH23DObmF7PPYe61tuscFepcpfr9MY+4dBcUzZKrnKK/fUrS1ShEaO/A9JSY8DdwCQ\nlFSVxx9/lokT33G2sDIkEAhgTATgBa4CNgDPFt0Jo6Kga9f8bXv55fYr24UX2m7y7NnQgoPh/vvt\nylvG2HnYZ82y3eIF5fEomF1Mt1KJFKGDB48AtY4+NqZW1nNSXPr27UtY2KfAK8AsvN4bGDz4VqfL\nyt1nn9mu8Kgoe4vV55/bObOTkmD3bjtPeGEEs7ieWs4iReiGG/qydOlI/P5a2G7tx7nhhn85XVaZ\n8dlnk7j55kGkpCTj8TxCaGg4PXueyzPPnOEiEcWlfHnb1X2ikJC/dm1ZSiy1nEWK0B13DOFf/7qR\natX+RvXqN/D000O58cYBTpdVJqxdu5abb76d5OQnMaYyxrxHWtoHzJq1lHfeec/p8opXSgp8840N\n/oMH8942OdlOnlK5sp1QZebM4qlRctCAMBEplT755BNuu20Shw9HAucD2fNeT6N9+xdZtGi2g9UV\no4MHoVMnu+azx2Nv0Vq40C73mJsBA2x3enKyfez12tvAWrcuvprLCM2tLSJlTmxsLIHAEmA+kHjc\nK4mEh4c5VJUDnnrKzgN++LBdnWvfPjtt56lMmXIsmMHeFjZjRtHXKTnomrOIlEpdu3YlLq4aixcn\nA6OAVOyI7cd48MHTrEZVmqxZc2z0N9hbtdavP/X2Xm/O2chCQ+0ANSlWajmLlBLp6em89tpr3Hvv\nP/noo4/K/GUij8dDw4ZNgSrABcAOYDXQivj40ywyUZp065ZzFrGICDjvvFNv//zzx7YPC7PXnm+8\nsUhLlJOp5SxSCqSmptKkSVu2bDmIMZWJjJzGN9/E07Vre3bv3s2ll15K+/btAZgxYwabNm2ibdu2\ndOrUyeHKi1ZwcDqwAngd6J317Of8+uu7jtVU7O66y04L+skn9ppz587wwgun3n7AAHsb1/TpULGi\nnaJUI8WLnQaEiZQC559/MT/8kAQ8CSzDduMm4/H0wBg/Hs8CLr30YsqXL89XXy0kM7MLMBWfL4ID\nB/YQGVmO8eOfp3///o6+j8LWokVXli/fClwEvA0YgoJu5I47qvPyy885XF0xO3zYzjR21llOVyJZ\nNH2nSCm2YcMGGjRoAuwEKmY92xA7K9l9WY/vISjoM0JDQ0lNXQlEAu2woTUciAcGMX/+HDp27Fis\n9ReVQCBAuXJ18PtfAh7HXnNOp0KFDDZt+oNy5co5XKGUdRqtLVKKTZ06FQgF/Mc9m4IN32xtycyM\nwZj62EFRe4FN2GksqwP/B3RizJiXiqXm4jB79mzS04OBB4BHgeuBHUya9I6CWVxP4SxSwoWHhxMc\n3Bi4Angf2xJOxOMZBRwGdgEvERKSjMfzO/AtEI4N811ZR8kAEti9ezfNmnWibt2WPProk2RmZhb7\n+yks7777AenpTYCO2HucXwIMFSpUcLawkio11S5RWaUKNGiQ+0xmUmjUrS1Swu3bt49mzdqxZ09j\njPETHLyOu+4awMcff8Hu3ZsBDxDJ3/7Wj8GDB3DNNTdx8OAuIiIqkJLiBW4C4gkK+oPQ0HBSU98B\nquD13sWIEZfz+OMlb7rRjRs3Ur9+HPa9V8De61wbeIkmTd5j1arFjtZXIg0aBB9/nHNyknnzIGug\noZw5dWuLlGIVK1bk999/YejQllx7bSPee+8F0tPh0KE2wCFgD5GRZ9OpU1v++9+xBAJViIrqR1CQ\nhz592lK79me0aRPg6quvIDV1OHAZ0AG/fyzvvfeps2/uL7rrruFANNAS6IkNZoA7WLPm9xLdI+CY\n42cNAzslqFrPRUa3UomUAtWrV+ell46NPv7Pf14hJeU/2OvLXpKTh/DRR2+zalUqSUmLsNeoZ7Fg\nwT/YudNOSPHAAw8THLznuOWEdxMZGVm8b6QQZGZmMm3aVMBgr63/hu3C9wLfUalSLYKC1C45Y14v\nHDhw7HFoKERHO1dPKad/oSKlUN26sQQH/5j1yBAW9hM+Xwjp6edggxmgC/v2bTu6zx13DCEq6iOC\ngkYA/yUy8laeeebhYq684ObMmYMN5mggCtiNHb3eBejHJ5+8TUZGhoMVllAnTk5SsSL8/e/O1lSK\n6ZqzSCm0ceNGOnbsRkpKcyCJKlUOMHbsf7n66kH4/fOA+gQHP0bbtj+wcOGco/tt3ryZV18dx+HD\nfvr378f555/P7NmzefPNj4mMDOe+++7g7LPPdux9nc6ePXuoV68ZSUnXAuOxgfw0sBhYA3yAx5OM\nxwPXX38zb7/9KqGhoXkdUo73ww8wdSpUqGAHh1WsePp95JR0n7NIGXTgwAHmzp1LSEgIPXr0wOv1\n8tprbzBs2L1kZhqaNDmbb775nJo1a57yGFOmTOH662/H7/8XHs9BvN4XmD9/Li1atMixXXJyMvv2\n7aNatWqEhBTP1bJVq1axfv16mjVrRr169QCIj4/nyiv/zcGDdYGvgDpAGBAL/IgdIBYH1Mfr3c59\n9xmN+vsAABPVSURBVJ3HE0/8u1jqLZVSU+1158OH4cILT73SleQqz9wzLuGiUkRKtYyMDHPo0KF8\nbdu69QUGvjRgDBjj8TxpBg8emmOb9977wERElDORkdVM5cq1zZIlS4qi7BwefPDfxuMpb6CDAZ+5\n++5hxhhjVq1aZcLCzjIQYiDawD0GZhr4zMCTBqoaOGwgysCnpn377kVea6mVlGTM2WcbExV17Ovn\nn52uqkTJK/c0IEykjAkODiY6nwN50tLSsNdtLWOiSEk5tsLR6tWruf324aSk/AI0Izn5Yy699Cp2\n7NiAx+Mp5MqtdevWMXr0GIwZCrwIeHjppTfZuHEziYlJpKUdytoyGtu1vSPrPXwFHATSgFCCghZT\nu3b1IqmxTBg/HtautaO2sw0cCCtWOFdTKaIBYSJySkOH3ozXOxQ7cclneL3/YdCgG46+vnTpUoKD\nzwWaZT1zPQcOHGD//v1Ht0lPT+df/xpFhw49uOqqAWzYsKFANa1fvx5jKgGfAmuxE63cwtSpP/DD\nDzuB5thBbweAVtgpSttirzt7gWsICooiJuYDnntuVIFqKdO2bcsZzAC7dztTSymkcBaRU/rHP27j\nuefupVWrpzjnnDeYNOkdzj///KOv161bl0BgMZCY9cxi/r+9O4/Oqr7zOP5+sm+EQCRPLEllBgmy\nhCRDKAJNJwwmjlIiCjOiiAic1gWXeoYqTDuj04EaHJcqWlPa4sTjlOOcqiXHQcZYwUGPqCwBqiBY\niSZkEQgRUrLnN3/8SCQEMGzPvTfP53UOR+6Sh6+/E/Lh3t8WFuYj4YRdjBYsWMgTT2xk8+YfU1Iy\nknHjvseBAwcAqK6uZvXq1axZs4bm5uYef35zczNLljzEhAl/z5w5P6SmpuZ4f3cFdsnRwdgfYw8e\nryEfG8pt2H7mHcB3gYXYKVUtDB9+mKioY9TX1zJjxlwqKysvaJsFjZO3ooyIgBO+N+Q8BfD1+hm5\nqBQROQv33PNjExOTauLjrzExMZeYV155tetaW1ubCQ2NMPBVV791bOwMU1xcbMrKykx8vN/Exd1g\n4uImmdGjx5uGhoZun11QMMtER0818JoJC/uxGTx4mDl69KgJC4syMMlA2/HPfclAtIFlBsIN9DfQ\nYeC7BiINDDIQY0JCYkx0dKKB/zPQbEJDHzajRn0n0E3WdyxfbkxEhDEhIcbk5hpz+LDTFXnKmXJP\no7VF5Lxt27aNyspKxowZw2UnjNhtb28nKiqWtrb9dO6YFRdXQFHRjfziF79l8+bZwALAEBV1Iw8/\nnM2DDz4AwJEjR0hMvJS2tkNAFAD9+k3md7/7J6ZNmwkkH//My7Ajsf8CJGCfoKOARcB9wOPYLTTD\niIz8NiEhmTQ2vnS8QkNoaDRffXWI2NjYi9lEfVdHB7S12SdnOStavlNELqqsrCymTZvWLZjBDj77\nwQ/uJCZmGvASYWEPEBf3J6ZOnUpVVRVw5fE7fTQ1jefzz6u6fb0dU3biD68OfD7f8cFmf4WdwzwL\nuA27VGc5UICdPvUoEA88hp1CFUJzczk+3y6g9fjnfUJYWLgnV0JzjZAQBfNFoHAWkYvqmWceZ+nS\nWVx11X8zd+4xtm59l4SEBHJyJhIZ+Rg2KGuJjX2e3NyJXV8XHx9PQcENREffALxKePj9DBjwJbm5\nueTn5wGbgd9hFxdZiQ3lcGAydsvMEcCN2GAOBQyxseHk5FxOXNwkoqLuICbm7/jlL1doOU9xHb3W\nFhFHHDlyhOuuu5mNG9/E54MHHljM0qUPdZuC1draytKly3n77Q8YOjSVRx55iKSkJFpaWhg+fCzl\n5RVAOzaAB2N3nwoHLgEGAtOBocC/AQ0kJPTj4MGDlJSUUFVVxZVXXsnYsWNPLk0kILRCmIi41rFj\nx4iIiDjrlcWMMQwfns3evQ1AJvAa9nV2KHa09v9i93IG+A/gX5g0KZt33nnnlJ8nF1hlJWzfDt/6\nFmRlOV2NK50p97QIiYg4KubE6ThnwefzcejQl9gn5xuAt4BHgDpsX/SBE+6uAUKYp40aLozqanj5\nZTtQ/vrrISWl+/XXX4eZMyEszA4Wu/VWeO45Z2r1KD05i4hnTZw4hffe2wEMB34CXHP8yveBjcA/\nY4N5FRDF3Xf/IytWrHCk1j7js89g7NivFyCJiIAPPoDhw+2xMdC/v11vu1NsrA3snJzA1+tiGq0t\nIn3Sr371C6AZ+Bwow07Lugc7avsIsAz7urs/kMSmTVucKbQv+elP4cgRG85NTTaEH3zw6+sNDdDY\n2P1rfD7Yty+wdXqcwllEPGv06NFkZKRjA/oJIBsbxPux858fw06p+k/gCAMHaovD81Zba+c2dzLG\nnusUFwd+f/ev6eiAzMyvj//0Jygqgldesa+9pQf1OYuIZ/l8Pv74xxJSUkbT1LQa+DZ2SlU7dvnO\nfwX+GtiNz9fG8uX/7mC1fcT118OmTXDsmD2OibHnOvl89hX2VVfZp+j2dnjiCRgzxl5/+WWYM8f+\nPjTUviJ/803bPy1d9OQsIp6WmJhITEwUdheqm7ALknyBXWP7IPZ192ESEwfQePLrVjl7CxfCfffZ\nfuTYWLj9dli0qPs96el2Y4zdu6Guzt7TacEC+9q7sdGG95YtsGZNYP8fPEADwkTE8+bMmc+LL76H\nXZCkCbgVG87bsUt3zgP+h379fsi+fR+TmKjX247o6IDw8O6vxaOj4bHH4K67nKvLIRoQJiJ92m9/\nW8Rll/mAaOwAsNeA5UAs8ANsD951hISksWPHDucKDXYhIfY19smvsCdNcqYeF1M4i4jnRUREsHfv\ndnJy/gaYje1zvgQ717n6+F1HaG39jKSkJKfKFICSEjs4LCQE+vWDVasgI8PpqlxHPfAi0icsX/4E\n775bBviBQ9gn5huAsUA+sbHvM3v2TEaNGuVkmZKcDB9+aAeKhYY6XY1rqc9ZRDzvmWee4Z57HgSu\nBdKwI7UXA+GkpQ1m3rybyMrKIj8/v9va3SJO0traItJnvfHGG1x99XXY+c1t2AFhLUAkYWEh7Nv3\nESknLy8p4gIaECYifVZBwT9g5zcXAR3AK9gpVHfR1gbJyclOlidyTvTkLCKe5vMNBJZit4UcC6w9\nfsUAkRw9WkdcXJxT5Ymclp6cRaQPa8MG8xzsyOzO5SA/AwzR0dFOFSZyzhTOIuJxR7Fray8HUoG/\nBRYC44AOPvnkEwdrEzk3CmcR8bTk5EuBRuBTbH/zfOAF7K5UYTR1bm0o4iEKZxHxtLy8q7D9yznA\nd4Al2B9t7UAE6enpDlYXxFpbe+5gJb2mcBYRT7vjjjuwP8qagTjgISAdu5RnC7/5zSoHqwtSr74K\nCQkwZIjdPnKL9tE+WxqtLSKe5/NFYHelqgIisUH9LaCF7OxsPvxwvZPlBZcvvoARI77eUhIgMRGq\nq+2mF9JFo7VFpI/rABKAiOPHEUAMAAMG9HOopiC1c2fPEG5shKoqZ+rxKIWziHheVFQEdgDYT7H7\nN/8EqAfgyScfca6wYJSaavubT9TRAYMGOVOPRymcRcTz1q9/CzgG/BfwfeCXJCREsGvXh9roItDG\njLF7M8fEQHy83a+5qMgeS6+pz1lE+oStW7cyf/4CGhoaWLjwLu6//36nSwpuW7fCvn2Qng5paae/\n78ABKC21r8KvuQaCaDU3bXwhIiLus3cvXHkltLTY44EDbagnJjpbV4BoQJiIiLjPffdBfT00NNhf\n1dXws585XZUrKJxFRMQZFRXdFylpbYXPP3euHhdROIuIiDOmTLEDxjrFxEB+vnP1uIj6nEVExBlN\nTXDzzVBSAj4f3H47PP00hATHc6MGhImIiHs1N9tADrIVxM6Ue2EBrkVERKS7yEinK3Cd4Hh3ICIi\n4iEKZxEREZdROIuIiLiMwllERMRlFM4iIuKcnTth9my47jo7pUoATaUSERGn7NoF48bBsWNgjF2E\nZOVKG9ZBQGtri4iI+zz3HPzlLzaYwYb0kiXO1uQSCmcREXFGa2vPc5WV9leQUziLiIgzZszoeS4y\nEt5/P/C1uIzCWUREnJGTA2EnLVQZFhY0+zmficJZREScERkJhYV2IFh4OMTGwqRJ8L3vOV2Z4xTO\nIiLinCFD7H/b2uCSS+xo7SDZlepMNJVKRESc8dFHdipVY6M9Dg2F0aOhrMzZugJEU6lERMR93nvP\n7uPcqb3dLkpyqlHcQUbhLCIizvD7e77Cjo7uOUgsCCmcRUTEGddeCxMmQFycDeXoaPj1r7s/TQcp\n9TmLiIhz2tvhtdeguhomToQxY5yuKGDOlHsKZxEREQdoQJiIiIiHnHM419XVkZeXR1paGvn5+dTX\n15/yvvnz5+P3+0lPTz/nIkVERILJOYdzYWEheXl57NmzhylTplBYWHjK++bNm8e6devOuUAREZFg\nc859zldccQVvv/02fr+fmpoacnNz2b179ynvLS8vZ9q0aezcufP0hajPWUREgsiZcu+cJ5PV1tbi\n9/sB8Pv91NbWnutHdXn44Ye7fp+bm0tubu55f6aIiIgbbNiwgQ0bNvTq3jM+Oefl5VFTU9Pj/LJl\ny5g7dy6HDx/uOjdw4EDq6upO+Tl6chYREenunJ+cS0tLT3ut83V2cnIy1dXVJCUlnV+VIiIiApzH\ngLCCggKKi4sBKC4uZvr06ResKBERkWB2zuG8ePFiSktLSUtL46233mLx4sUAVFVVMXXq1K77brrp\nJiZOnMiePXtITU3l+eefP/+qRURE+jCtECYiIuIArRAmIiLiIQpnERERl1E4i4iIc37/e4iKgtBQ\nGDcOmpudrsgV1OcsIiLOKC6G227rfm7QIPjyS0fKCTRtGSkiIu7j8536fFMTREYGthYHaECYiIi4\ny7vvnv5aiKJJLSAiIoH35z+f/lp4eODqcCmFs4iIBF5+/qnPr1kT2DpcSuEsIiKBl5wML77Yvd95\n5UooKHCuJhfRgDAREXFWSwtERDhdRcBpQJiIiLhXEAbzN1E4i4iIuIzCWURExGUUziIiIi6jcBYR\nEXEZhbOIiIjLKJxFRERcRuEsIiLiMgpnERERl1E4i4iIuIzCWURExGUUziIiIi6jcBYREXEZhbOI\niIjLKJxFRERcRuEsIiLiMgpnERERl1E4i4iIuIzCWURExGUUziIiIi6jcBYREXEZhbOIiIjLKJxF\nRERcRuEsIiLiMgpnERERl1E4i4iIuIzCWURExGUUziIiIi6jcBYREXEZhbOIiIjLKJyDyIYNG5wu\noc9TG198auPAUDs7S+EcRPSX7eJTG198auPAUDs7S+EsIiLiMgpnERERl/EZY4zTRQD4fD6nSxAR\nEQmo00VwWIDrOC2X/BtBRETEcXqtLSIi4jIKZxEREZdROIuIiLiMI+FcV1dHXl4eaWlp5OfnU19f\n3+OepqYmxo8fT2ZmJiNHjmTJkiUOVOptvWnniooKJk+ezKhRoxg9ejRPP/20A5V6V2/aGGD+/Pn4\n/X7S09MDXKF3rVu3jiuuuIJhw4axfPnyU95z7733MmzYMDIyMti2bVuAK/S+b2rj3bt3M2HCBKKi\nonj88ccdqDB4ORLOhYWF5OXlsWfPHqZMmUJhYWGPe6Kioli/fj1lZWXs2LGD9evX88477zhQrXf1\npp3Dw8N58skn+eijj9i0aRPPPvssu3btcqBab+pNGwPMmzePdevWBbg672pvb+fuu+9m3bp1fPzx\nx6xevbrH9+XatWv59NNP2bt3LytXruTOO+90qFpv6k0bJyYmsmLFChYtWuRQlcHLkXAuKSlh7ty5\nAMydO5c//OEPp7wvJiYGgJaWFtrb2xk4cGDAauwLetPOycnJZGZmAhAXF8eIESOoqqoKaJ1e1tvv\n5ZycHAYMGBDI0jztgw8+4PLLL2fIkCGEh4cza9Ys1qxZ0+2eE9t+/Pjx1NfXU1tb60S5ntSbNh40\naBDZ2dmEh4c7VGXwciSca2tr8fv9APj9/tP+hero6CAzMxO/38/kyZMZOXJkIMv0vN62c6fy8nK2\nbdvG+PHjA1Fen3C2bSy9s3//flJTU7uOU1JS2L9//zfeU1lZGbAava43bSzOuWjznPPy8qipqelx\nftmyZd2OfT7faRcgCQkJoaysjK+++oqrr76aDRs2kJubezHK9awL0c4ADQ0NzJw5k6eeeoq4uLgL\nXqeXXag2lt7rbTuevD6C2r/31FbudtHCubS09LTX/H4/NTU1JCcnU11dTVJS0hk/q3///kydOpXN\nmzcrnE9yIdq5tbWVGTNmcMsttzB9+vSLVapnXcjvZemdwYMHU1FR0XVcUVFBSkrKGe+prKxk8ODB\nAavR63rTxuIcR15rFxQUUFxcDEBxcfEpA+HgwYNdI18bGxspLS0lKysroHV6XW/a2RjDggULGDly\nJD/60Y8CXaLn9aaN5exlZ2ezd+9eysvLaWlp4aWXXqKgoKDbPQUFBbzwwgsAbNq0iYSEhK4uBvlm\nvWnjTlrB0QHGAYcOHTJTpkwxw4YNM3l5eebw4cPGGGP2799vrr32WmOMMdu3bzdZWVkmIyPDpKen\nm0cffdSJUj2tN+28ceNG4/P5TEZGhsnMzDSZmZnm9ddfd7JsT+lNGxtjzKxZs8yll15qIiIiTEpK\nilm1apVTJXvG2rVrTVpamhk6dKj5+c9/bowxpqioyBQVFXXds3DhQjN06FAzZswYs2XLFqdK9axv\nauPq6mqTkpJi4uPjTUJCgklNTTVHjx51suSg4ZqNL0RERMTSCmEiIiIuo3AWERFxGYWziIiIyyic\nRUREXEbhLCIi4jL/D41PaoVw3cvLAAAAAElFTkSuQmCC\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from sklearn.decomposition import RandomizedPCA\n", "pca = RandomizedPCA(20)\n", "lo = pca.fit_transform(data)\n", "mds = manifold.LocallyLinearEmbedding()\n", "vl2 = mds.fit_transform(lo)\n", "scatter(vl[:,0],vl[:,1])\n", "scatter(vl2[:,0],vl2[:,1],color='red')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "View \"Manifolds\":\n", "\n", "The appearance of a rigid 3D object (including all the pixel values) is a function of the six pose parameters.\n", "\n", "The appearance is usually piecewise smooth.\n", "\n", "If it were completely smooth, it would be a _manifold_." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [] } ], "metadata": {}, "nbformat": 4, "nbformat_minor": 0 }