{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 2. Background Remvoal with SVD" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Our goal today**: ![background removal](images/surveillance3.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Load and Format the Data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's use the real video 003 dataset from [BMC 2012 Background Models Challenge Dataset](http://bmc.iut-auvergne.com/?page_id=24)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Import needed libraries:" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Imageio: 'ffmpeg.linux64' was not found on your computer; downloading it now.\n", "Try 1. Download from https://github.com/imageio/imageio-binaries/raw/master/ffmpeg/ffmpeg.linux64 (27.2 MB)\n", "Downloading: 8192/28549024 bytes (0.02260992/28549024 bytes (7.9%5455872/28549024 bytes (19.18790016/28549024 bytes (30.812189696/28549024 bytes (42.7%15687680/28549024 bytes (54.9%18898944/28549024 bytes (66.2%22134784/28549024 bytes (77.5%25518080/28549024 bytes (89.4%28549024/28549024 bytes (100.0%)\n", " Done\n", "File saved as /home/racheltho/.imageio/ffmpeg/ffmpeg.linux64.\n" ] } ], "source": [ "import imageio\n", "imageio.plugins.ffmpeg.download()" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true, "scrolled": true }, "outputs": [], "source": [ "import moviepy.editor as mpe\n", "import numpy as np\n", "import scipy\n", "\n", "%matplotlib inline\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "np.set_printoptions(precision=4, suppress=True)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "video = mpe.VideoFileClip(\"movie/Video_003.avi\")" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100%|\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2589| 350/351 [00:00<00:00, 914.11it/s]\n" ] }, { "data": { "text/html": [ "
" ], "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "video.subclip(0,50).ipython_display(width=300)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "113.57" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "video.duration" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Helper Methods" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def create_data_matrix_from_video(clip, fps=5, scale=50):\n", " return np.vstack([scipy.misc.imresize(rgb2gray(clip.get_frame(i/float(fps))).astype(int), \n", " scale).flatten() for i in range(fps * int(clip.duration))]).T" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def rgb2gray(rgb):\n", " return np.dot(rgb[...,:3], [0.299, 0.587, 0.114])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Format the Data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "An image from 1 moment in time is 120 pixels by 160 pixels (when scaled). We can *unroll* that picture into a single tall column. So instead of having a 2D picture that is $120 \\times 160$, we have a $1 \\times 19,200$ column \n", "\n", "This isn't very human-readable, but it's handy because it lets us stack the images from different times on top of one another, to put a video all into 1 matrix. If we took the video image every hundredth of a second for 100 seconds (so 10,000 different images, each from a different point in time), we'd have a $10,000 \\times 19,200$ matrix, representing the video! " ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": true }, "outputs": [], "source": [ "scale = 0.50 # Adjust scale to change resolution of image\n", "dims = (int(240 * scale), int(320 * scale))\n", "fps = 60 # frames per second" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": true }, "outputs": [], "source": [ "M = create_data_matrix_from_video(video.subclip(0,100), fps, scale)\n", "# M = np.load(\"movie/med_res_surveillance_matrix_60fps.npy\")" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(120, 160) (19200, 6000)\n" ] } ], "source": [ "print(dims, M.shape)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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AZ/1IKgOMOmVUpAygs1ug2lB0pge6dq5ImBzNfplcx1mMhiv2sTNvryNiTH12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\nSUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(np.reshape(M[:,140], dims), cmap='gray');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since `create_data_from_matrix` is somewhat slow, we will save our matrix. In general, whenever you have slow pre-processing steps, it's a good idea to save the results for future use." ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": true }, "outputs": [], "source": [ "np.save(\"movie/med_res_surveillance_matrix_60fps.npy\", M)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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X63WcPHkycP4krcBkE4DskJDquex3YKWyQOny+TzGx8e9Z7Ozs5iZmfHy2h7u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\n1tu5KqzQNayrm4Xiur/UzcJGgddffx2XLl0azTncY2NjmJ7uLN+t9rZt2Lx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IaH92ahbA\nG2C9GHXeBXAXEY1n5TmLzrtArBeMpEhdUOP6ZXTaJ7fHXAhRyQ+AjwL4LwD/DeCzg5aHP6WX993o\nDO/8J4Aj2eej6MyJeg7A2wD+BcB1yjWfzfTjGICPKOfvBHA0++/PkO2oyp/h/QD4GQDfzn6zToz4\nB8CPA3glqy/+EcC1rBf8AfB7AN7KyvRvADRYL0bzA+Cr6MzlX0FnVOzRInUBwAYAf4/OC5YvA7jJ\nJxNv7c4wDMMwDMMwJVLVKSUMwzAMwzAMsyZgg5thGIZhGIZhSoQNboZhGIZhGIYpETa4GYZhGIZh\nGKZE2OBmGIZhGIZhmBJhg5thGIZhGIZhSoQNboZhGIZhGIYpkf8H5q/6DjTH/QQAAAAASUVORK5C\nYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(12, 12))\n", "plt.imshow(M[::3,:], cmap='gray')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Questions**: What are those wavy black lines? What are the horizontal lines?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Singular Value Decomposition" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Intro to SVD" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\u201ca convenient way for breaking a matrix into simpler, meaningful pieces we care about\u201d \u2013 [David Austin](http://www.ams.org/samplings/feature-column/fcarc-svd)\n", "\n", "\u201cthe most important linear algebra concept I don\u2019t remember learning\u201d - [Daniel Lemire](http://lemire.me/blog/2010/07/05/the-five-most-important-algorithms/)\n", "\n", "**Applications of SVD**:\n", "- Principal Component Analysis\n", "- Data compression\n", "- Pseudo-inverse\n", "- Collaborative Filtering\n", "- Topic Modeling\n", "- Background Removal\n", "- Removing Corrupted Data" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": true }, "outputs": [], "source": [ "U, s, V = np.linalg.svd(M, full_matrices=False)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is really slow, so you may want to save your result to use in the future." ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": true }, "outputs": [], "source": [ "np.save(\"movie/U.npy\", U)\n", "np.save(\"movie/s.npy\", s)\n", "np.save(\"move/V.npy\", V)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the future, you can just load what you've saved:" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "U = np.load(\"movie/U.npy\")\n", "s = np.load(\"movie/s.npy\")\n", "V = np.load(\"movie/V.npy\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "What do $U$, $S$, and $V$ look like?" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "((19200, 6000), (6000,), (6000, 6000))" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "U.shape, s.shape, V.shape" ] }, { "cell_type": "markdown", "metadata": { "heading_collapsed": true }, "source": [ "#### Exercise" ] }, { "cell_type": "markdown", "metadata": { "hidden": true }, "source": [ "Check that they are a decomposition of M" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "hidden": true }, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#Exercise: \n" ] }, { "cell_type": "markdown", "metadata": { "hidden": true }, "source": [ "They are! :-)" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "hidden": true }, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.allclose(M, reconstructed_matrix)" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": true, "hidden": true }, "outputs": [], "source": [ "np.set_printoptions(suppress=True, precision=0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Properties of S" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "s is the diagonal of a *diagonal matrix*" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "np.diag(s[:6])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Do you see anything about the order for $s$?" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 1341720., 10528., 6162., 4235., 3174., 2548.,\n", " 2138., 1813., 1558., 1346., 1163., 1001.,\n", " 841., 666., 0., 0., 0., 0.,\n", " 0., 0., 0., 0., 0., 0.,\n", " 0., 0., 0., 0., 0., 0.,\n", " 0., 0., 0., 0., 0., 0.,\n", " 0., 0., 0., 0.])" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s[0:2000:50]" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "6000" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "len(s)" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "3.2309523518534773e-10" ] }, "execution_count": 36, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s[700]" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": true }, "outputs": [], "source": [ "np.set_printoptions(suppress=True, precision=4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$U$ is a giant matrix, so let's just look at a tiny bit of it:" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[-0.0083, -0.0009, -0.0007, 0.003 , -0.0002],\n", " [-0.0083, -0.0013, -0.0005, 0.0034, -0.0001],\n", " [-0.0084, -0.0012, 0.0002, 0.0045, -0.0003],\n", " [-0.0085, -0.0011, 0.0001, 0.0044, -0. ],\n", " [-0.0086, -0.0013, -0.0002, 0.004 , 0.0001]])" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "U[:5,:5]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Finding the background" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "((19200, 6000), (6000,), (6000, 6000))" ] }, "execution_count": 39, "metadata": {}, "output_type": "execute_result" } ], "source": [ "U.shape, s.shape, V.shape" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": true }, "outputs": [], "source": [ "low_rank = np.expand_dims(U[:,0], 1) * s[0] * np.expand_dims(V[0,:], 0)" ] }, { "cell_type": "code", "execution_count": 360, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 360, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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7OQB4BwAcAMBPD8PwocPjbwCAXwWAEwDwxwDwzkFwp5cuXYKHHnqITKMlTrUH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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(12, 12))\n", "plt.imshow(low_rank, cmap='gray')" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "data": { "image/png": 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j1pNlmV89jbKioqLiLcRcME3KZaYR6msgCa44ekKlfqoMxQXVfedwZ3IfoGu+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\n3idayeJgbmxsdBQkmeH/NM9M7+tL2/dMFJFLo4+/ra2t1NRF25Qxcjd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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(np.reshape(low_rank[:,0], dims), cmap='gray');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "How do we get the people from here?" ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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/zufM2Az5vlfPJ/cliwM1eLt4FLutbKRLPemHnjRba28B8ETv/SOttTeqc3rv\nvbUmR661dhuA2wDg7NmzBwY7CoxVBnAeIH4wmeqrMkotUSEOavL2WOIo8XufGb5/UTZr20Hi+2B9\nZZXKJt6TJ0+GORXNieEnMDYX2ETrbzSboG1iNbOJybC5ubk74RvYfOAnJXZCWX+t7Y2Njd36+Fpb\nOM+5c+d227fgcVb3/XjxJJk5qqIy/li0meLYsWO48cYbAew5fl7zmtcA2Fu0zp49C2Bn8rRjvEHC\nY/TQe8dN9Dz5yYQXh0x9zRyNs+qvcowucQj5Mbb/7f7lNjzBmumfwoWo598H4JbW2mcB/CaAN7XW\n/gWAx1trZwFg9fmEKtx7v6v3fnPv/WZbWQuFQmHdcWim2Xu/A8AdALBimv9L7/2nW2t/H8DbANy5\n+nzfgjp3P5fM/lEYkCHLk6mCaqMAdlUuOscbrhl+C+ZMW9nWvqhurteYJqCZN7CnmvrxsnK8gnv1\nzpgWs1wvAzNfxdAjzYBZX+99tz5mpRYGtL299/4fbsvq39zcPMC0jM1an7y6HQVgK/OBCrzm/hiz\nt9AjY8/f/M3fDGDHUcWalQpjG6mZ3kFiYPOXv5eY1ap6Z1jkyOmkwNn7Z9pRpgpmwLwR4bDhRsDF\nCW6/E8APttYeBPADq++FQqHwXwSek+D23vvvAfi91f9/AuDNh6gjNfaOjN1AHLiuzle2nVFgeNYm\n5zsEDtrbFLuKWIvvSzQGLIMKuTCoAHMeLw4i9+WUY8TKsH2XV3Nvn40SR2xubh5wcnBIj/9UTNB/\nnjt3bl8+SV/e2LN/l7l9+t98mVOnTsmgbN8nFTqTaRJ2z3zLt3wLgD2Wy1s7s3FTbc1sKoigrv3M\ndkjFrFUuV/Xp71vO1JRpZUoGFYjvP9kezf/PoLZRFgqFwgKszTZKDp2IAs3V+ZGNTiWwyFb+iEn4\nc6PQJbbZzSJiAN6uyEyOV2Vfx0wWal6NFUuwlT56X48fc96KyO9h8anmIvl8mxzQzUzAJzqxT2Nt\nfozM/poFhvM1j+RUTEfZMiOm6bUXPmap4CzI3Wybp06dOnCNrE8qZ2x0b3uv8gzjHGl3vR98AyaP\nidKiIvatnlN1zdguyfeHD22LIh38NTusXbOYZqFQKCzAWjHNw4JXF8UGR3bBzB61JMA2Q7bNTSVO\niOSKmJNi6NyWZwnctpV9/PHHd+MDLRCb61VMVKVns7bZvhXZZf05bLdUNjo+198DzMoM6npGGoQd\n93F/zPCCq5d+AAAgAElEQVSVFqO2yho4FZzJ87WvfQ3AXvztmTNnwqQZ6v7g/vmog8ibr+6PSMtT\n48ZagGeDWVpCRsTMvVY1sj2qzSd8v6mEOmXTLBQKhYuItWGaETLby+z2pyzObEm5rJ6R13RUT7Rt\ndGtr64CNkFduz3hGLFnJZavvAw88AAD4pV/6JVx//fUAgF/4hV8AALzwhS/c15bvNyf8iFhuJodn\nCRHrVvYt/uQywB7rMLunl3eGmdt33uWjGHuklahoCEu0YjZcY5rGan39tsuKkfXBxyiO4hOVXZa/\nq3Mi7an3g0l3ontya2trqLGpc1SflPal2p6dOxTWZtLkANyoU5mKnG1hnDVK+3PVQz+aSGcM7CoU\nKnJUqaBqDi3xfcleBWzgic/KW3D7s88+u5tpJ3pXkOoz16u2rLHMKpcAByRnqhWHBqkJLXoJnlch\nRw+tz+EZjV8WkqYmQoMF5NuY2wK1tbV1IHg/e2mgIXN4jSYNdW8uIQLKmWuIzGj87Ef1jd4ioNqI\n5obMgTZCqeeFQqGwAGvBNI0hqRAOf46HCq9hxuNXsijTtC/DjGYmH2Gk1vnVMwqNmjGMqzajPvjz\nZhKH2PhZQovHHnsMAPCWt7wFr33tawHsJeGYcYZxKFTGwJRzIBpLZYbgMpmjKWJM2fuNZswZGaLM\n8j4sxswuto3S7g8b8+c973m78jHjVHKz48uPW8SKMwaaOZgibUBd14zlmbxRTlw/jiPGq+4zpS1y\nHcU0C4VC4SJiLZgmcNAGMmMvytgPoEN6DrNKqTpHIRKKDWV2lojBKjlm+pCNm8EyrH/gAx8AsPf2\nwxMnTuxu6fu2b/s2AHvvxYnkzX7r/eA7n/hcrzmMQmh8gDjb+DhEx//PjqZsa97M/acQObO8Pdac\nOsY0LZjdsn2pjP5ZfYbI5jojf8aeFfPPEohYfbzhY4lNUt0DM6FQ0TZK1lI841/qFCqmWSgUCguw\nNkwT2L+iRV4wf27GznzZra2t8N3oM55xFQQd2Vf8KjiylczYy3zoRpRI1ssZMSPVliWnsFAjs2k+\n//nP32WhlijXgt1V28zyWF6f9o3lybytzBIyO6/aJhhtOzWboQ/Mt4ByTpZsyNILztoB+fcoWkBt\nRYzCbbJk3F6GKOHHTAC6SpiSRSsAOxEBH/rQhwDs2WO/4zu+A4DWWqJn18trx6Jn2Zfj+0v187Bh\nR8U0C4VCYQHWimkaPGNSqZyAPA5MJR7l5A2RLUYdU0wzY8BcfuS5zNr0qzDLzDYZP24MddxYlb1X\n6N577wWw88oIG/eHHnoIAHDdddfta1PZH41RWFkfAxl5LzOPf8SW/bWPElFkNitjzadOndqV0WJU\njQWp1GRRtIZB2eaUrTC6D5TdzRDZ5H0/VUSIklPJkG0vVO9Cis6xMXrooYfwB3/wB/va/MxnPgMA\nuOWWWwDsf5cUv54is/9z+jg/RzDzVf2z7yOfSIS1mjRnAtczI3cUWpLV6wd55ORRYUSHmQhVf7NQ\nkGyvuR8bX27keAEO5nP0N5rdiJ///OcBHMy16T85PIQfYp8hPeqvknUmIDnaFKBkVW1HEws/fFl+\nU49oDHzZ0T58X0fUlgpti94llREMFR7Gk7dyMEUTtNVz44034pWvfCUA4Pd///cB7JmBLGP9rbfe\nCmDHXMI5T/n+UM4x1ZfI6aqemaV7zg2lnhcKhcICrAXTzJwAKqsLI3LOqFWFc/IZfLiCP8bfM+bG\n35kBKPUrYkz+nGgVzljNTKhMZPz3+3w/97nPAdjb6mfqq2LfHFzNqrySy49x5MiIWJGvm1Xn8+fP\nh1skVb+jjEX+M9ogsSQUx/8WhcMoDSLLyMPlonyTwMENFks2QRgyJ6wdv+KKK3aD9s3BaHvrf/u3\nfxvA3uuW3/CGNxxQtfnaeRbJ/fJvVc2cah7RvTaDYpqFQqGwAGvBNA0z7IjZmz8WlffG8plciJGN\n1GPkEFL18HG/YrPsKtlFlCjC93PGxmp46qmnAOwZ6K1PTz/99G6g+6c//WkAe44Ss0f5MY9YvD8n\nsjV5RKyH7VrK4cLvY8/svOptlAYOyFZ2Z3UP8rmRfdHLEY2FehNBxJx82WjrptfkolyqfoxGz5Ny\n3qktr1dccYWU1e67++67DwDw3d/93Qf6q5hsZJfld9Wremb8CbMoplkoFAoLsBZMk0Nl1KrCK+z2\n9vaBlTXyKvs3HRpG4S3+nMzTO2OHypjmTCq3KD3bzOoZ2fOAPVb15JNP7vu+ubm5G9zOKc0yW9HM\nO6WzyIaRnSxjqWxP3dzcDIPt1Vs3ObQtCoHx8nB+Tf9bZKNWv0XwdlRmiplWpn6zY2b/yzZKZAH5\nfE5mN7ZNBNG7zO2+e+aZZ3bPNfA18+WsDyrNYKQl8r3gj83YdT2KaRYKhcICrAXTtJVrJtYu8vj6\nYypGMfKMq8DwyKbq7Xcj1qe2DnIy3MyuoliCgVfsjIGpoHI7zxJE/ORP/iQA4Jd/+ZcB7HjKjWlZ\nedtyqeyokWfSxzhGmwpUf/mYYmtR3KJnUJG31dfP9kN+s6a3X0YB9V6m0X0GHGRRHA3B19efo7SL\nzLNuiGIvVRB4pj1ZXdG9p2JDowTUtkX32Wef3d1wEEXL+PhRto97xsgaAifu8OM3M24KxTQLhUJh\nAdaCaRrUahDZ7WbiD7NzVVsjr7myMUV2OO/JVnGj9j1iQcrbGq2wavWMtvx51mApyl7xilcA2FuV\nT58+vbvF8pOf/CQA4A//8A8BAD/6oz8q61VjoVbwyIvr+xHZ/Jj9+f+zd6Uze1G7aUayKLm4PpUE\nItOeouMqciJKGKLYaPZs8DXh7/4VIIphWv0z9liL6eXxt/rttR4nT54M7//sPUBqlyBv5eUyme9h\nFms1aWaOjOxmjJwymYrLD29mUDf4wY1Ce7wKETkFlBxROAW3m/XTq1Ysn+8nBwDzBPZDP/RDuxlp\nfv7nfx4A8OCDDwLAAbXd94nND6qf3Kds0o0mKa8q87kK0W9+YYvKqGvOap0fRw5/UfdddC+rkK1o\nO+BMP7O959y2l48R7e/35ZV8/MI9dsDZFt2vfvWru6FsrPb7ezwK4lcEg9tURCoyeYxwQep5a+3K\n1tp7W2t/1Fq7v7X2va21q1trH2ytPbj6vOpC2igUCoV1woUyzX8E4AO997/eWjsJ4BSAnwVwd+/9\nztba7QBuB/DOwzYws9Iym5opk4VaROf4zChRGJH/ZGaiZMgYiX1GyTeUOqtYmS97/vz50KD+mte8\nBsDO9rYbb7wRwF4yD2vDmKZybCgHhpU1OSInVmttl6VFzNoz4pFKpZi6Yq5RCJT6ZM1BMf7oPVC+\nnyMWZGPst/plpqPIfOPv3+hdPgbVT4a/ZhHT97L4kCIlp4W1PfXUU7tOSbsHlNaSyWyIshxxGdWH\nWRyaabbWXgjgvwHwaythnu29fxnArQDetTrtXQB+5LBtFAqFwrrhQpjmDQCeBPBPW2uvBfARAO8A\ncLr3/ujqnMcAnB5VZCu+Sj3FQcuKySkDOtdvUMZjQ2Sf9OBzmCEqVhjZRhXTZBaStWWYCZBXY2Cf\nlozj2muv3f20bZP2jqCzZ8/uK2Pwb3TkLY3e5hQxJT9OHC6yNOg4QsbQo7yN/Knsn+q6zrAhDqSP\n7L2KWWf3X3T9VagWM2Bvb4zuM38NM+3J2rQ8rebwsez41q+bb74ZwE6uVrUN08uu7iH1LPNckF3f\nbPtlhguxaR4H8J0A/nHv/XUAvoYdVXwXfUdSeQVaa7e11j7cWvvwl7/85QsQo1AoFC4dLoRpPgLg\nkd77Pavv78XOpPl4a+1s7/3R1tpZAE+owr33uwDcBQA33XRTj1au6A17KvxnJn1W9ka8kRfNr0hR\nQPkSBuBX9YiBLfF8KllVvWxbOnfu3L7vl1122a696ZprrgEAnDlzBsBBNnn8+PEDdjz2xtuKrmSe\nSZjC56rroFhpxDL8fTKyF3Pb/tzMZh6FvGxsbKTbc7lM1NbMePkyPE4q5MvKRM+Vrz/aJurDlYxZ\n2r3E8lnijs3Nzd1QIbbF+2cnYubq2isfA9fLbc3i0Eyz9/4YgM+31l6xOvRmAPcBeD+At62OvQ3A\n+w7bRqFQKKwbLtR7/j8DePfKc/6fAfwP2JmI39NaezuAhwH8xExFEWuK7HmKvfGql52fbeuLknl4\n7zm3yauysleqLZjRVjo7d2NjQyaY4LaUrP43/51ZAb9/++mnn96txxIp2G9qbO2YBZgz4/cee0O2\nuquxZPAx9XbGKG7RX/vIbjqyXatj3kYalZ+x03o5+T5VER2RtuPZbeZ998f9mMzIruIp7dxPfOIT\nAPaSD7/xjW8EsJeow37/1Kc+hde//vX72lBJavjeZhkiGbke/wnoVHwZLmjS7L1/HMDN4qc3X0i9\n/kaI9qJ6BwSDB1eFgvi2rN7RxDwTpuDr4PpULsPIAeFvbjbWR44Dpe6rF9NxedsZZDs4zp8/v/si\ntde+9rUA9iZPU+UtGHl7ezvMgu0XCz+BWt99f72MM+FchixwnctnDr5sR1bWDpeNJiN/nUchPcpk\nEU2M/p6KwoqUms/9UvdQ1Ae/uYBlNRm+8pWv4OGHHwawt+Psx3/8xwEA5sP41V/9VQDAPffcg5tu\nugnA/vuKxyTrn/VhdnHwbWSvZ1aoveeFQqGwAGuxjXJmdfPnAnpVMcxsW1TtjPJWqv3kmSMi6oMy\nbkdllBob1eszkUfhFK3t7c+1/lqo0Zve9CYAO84dY4+cE9Gy0fgtclEf/Cev6orZzYQlAfvZGo97\nxmANavvoKE+l35PNyK49f59xWvjjS+7t7F5iTUuZbexzhmVHDiBTxT/wgQ/gi1/8IoC9V/baO4OM\nTX77t387AODjH/84PvvZzwLYC3FTGOXPVYjuKeXYm0UxzUKhUFiAtWCaGZTx3jAy9CtGFjGJLJxI\nBRtHtla/Gkas1P/OfcgcDhlLtvr5HA6x8m1aOXPyGItsre3aHnncebX3bSo7lH2PZFdOD3bq8MYG\nz6jZDurtXpld186JNBmGOp45FzKHRGQ/VY6XGTtvxMx9mVFIlWJbmQOIN5/YW0uNXd5999149atf\nDQB43eteB2Dv2li42vXXXw8A+OM//uNd++fLXvYyAPptkdE7qJRjdUYLHYUYRiimWSgUCguwNkxT\nhegAOqAZ2Fl1ZlJfqXY8/Iqkwjk8lEc2YhTZSub7OeONz5iqr897qaO2lW1OhWOp3JX+XN9OZGdT\nb0OM+qK2NHI/s2BwFfydMd8IESPLIjrU+b5f/HvktVXyRZpIFg2h7vGIgSlGxpoVt6meVQs3M8b5\nyle+Et///d8PYE+TsXMsqP306Z0d1rfccssuw1xyrVWfIrZ9WFapUEyzUCgUFmBtmKaHX104ANvg\nV+nMPglozywj80Z6ux6zliiY2Z8T2VWicizXiHl59qcYF8vAdk4+14/XKBZWnRvJoNo0qMiELAYz\nsgMaMmaxlOnb54jFKBap7G+jmFCWM+tfxkq9nBE7jjzu/jcVD8nPhsX12vFTp07tbr21Z9fOffnL\nXw4AeOlLX7rblrHRyFfg6442pnimGd1D6tovZaHFNAuFQmEB1oJpWqyf8rZG73dRW+Bm7CF8Lsvh\nkdlMuJ4sxi5a0ZStaUn8XRa/yPXN2OGsjGf10ZY6306Wki5qQzGAiMWrOjImbWWjlHnewz6Kk1Vs\nbyYCg+3Gvky0VVBpL8qW78v6ckoO/j1KvaY0gCgyxD8Hdq9Y7OUNN9yw+z16N5DFCXsPOTNzxgwD\nzsob/Fhw32exFpOmQeVfjNQwry7xTcw3o9rmpjIiKceK/65UqwjqhlcT10hVjupW56gbXgV7R/Wo\nySCahGfUwqxN5QiacYyYDDPOJ77G5ojwD/zMBM19iUwzqry6jhxOY+XtuA9En8kRG7WlwvN4IckW\n02jjhp/4eSwsbO3yyy8/MN68KNvvimAoROPt6591Is6YoEI5Fp1dKBQK3+BYG6bJRtxIjcjU6ogN\nZQzRs5lsVTJZIpanQkHYMZI5L6IVVsmV9YGRmQRmmGqkgioGxqxWjUkG7kfkWPLMJDsn658vo+pR\n50TIzEGKzfM2zmhrqXLsZWMZaQ7+N75uEdNW9WaajH1a8peNjY3d/zkQXgWuj8a5972toBFT9+ap\n0TOjzEGzKKZZKBQKC7BWTNOwvb29u6rwKqzCdSI25M+NVp4lIQgzNs2MdXCwsF8ZeaugYt2RXHb8\n+PHjB9JnzdjfMiYRGd293S1ypnh7beacUHV4GbhMdg38uEVjkLGaw4T/ZL/xOUpzYEdJZofOnCAz\nrCqC8hXw+CnNgcfW2GVr7UCoEbPTaHurL6P6wPe42kQROXl8opkRG41QTLNQKBQWYG2YpmJddtxD\nsUg+psJPGCqxb8b2ovJR+EiGLEEuH8882VyfYgmq/hnGNbLd+t+j9GwZe1F9YZvVjGc360PEsr3s\nUTC1lfXv317iYc+iDaJro+z3WRu+TPabr4exhG2p1HiRPba1vaQvUTSK2pThtSaWc/Quc3+NsigN\nRtk0C4VC4SJibZgmoIOXI+95tsKqlXzkDc5WYw9ebbOEHQxmR/51FzNtR1s2PTvKbLaZbFxm1gbp\nvfEzHt4ookCVi665ihPMGHUEX48h0jZU5ITScFTwuYe3tUZ2RvUcRFD3H/dB9TOCujeYfXuZsueT\nWSgzT8/io+uZtWVQDF+9Wibq39I4zbWaNBWWGO0jNd0bfVmd9udEN4C6iaPdJln4jwqPiXY1qfIj\nJ4Of+Fk1XaKSA/n7ZlimaBL3k9xMSEl0Y1v9PmRlJkQoUuOU82TkNFLXI5soRo5HJVfWVgRFHlQ9\n0aQZjZH/n8fCm9J4IvTOzuh5jHZC+baiXKoZvAofXQfl+L1kr/AtFAqFb0SsBdM0hpQxk2y1Y8ys\nnupztj5fLttqFtWjmKsyO9g5IyO+QWV+UqaKiAFkjClrM9qiZ9/VFsTIOeDPiUwCvs2Req3OycJ/\nIgar7je1zZahWNbInDQD5UyMtJ4spGeGyWW/2TX2oTz2yeU4qD/TCgyHVadn2KPaSj2DYpqFQqGw\nAGvBNA1qVYlshJ4lRMxSbZE0cGCtD3vwbURyqS1v/lxlN1NOpJGDCjjoVIjCY3y5yM7o+xKFSSnH\nWWY/jlha5ohQ9WVvqvTHfZv8PqEMfB0U088cS9HYZm3N2IAzlhVpIMoOmG01ZmYZ1acSp/D2R2X7\ntvKWhMPyY3J/fHnFOEcJVDwyjdLA94c/JwphGqGYZqFQKCzAWjBNW/H9Shmt6ioEIfKQeTYU2aO8\nXWq08mQe1IwJR57Ura2tqTCdjEH4ttW4ZbbWjDnNsKlIDoO/HiNvtGdVEcv1bJCZpio7slMq1sdQ\nGy2UvdPanPEQM9NiZuePz7CgKHenZ6BsZ+b+qS3H0diqsbJ6n376aQA76d+4bnsnurHRTDtgZpz1\nV2GUV3P22VMoplkoFAoLsBZME9iZ7T0jGKUX8+wxYiTKK5l5Rw0R01E2MIaKmeTf1PcZRhG1PRN7\nqVgkr9h+5Y1+m2mL5fLXKlrVs7FVjJFtkGZv8+yKPbt87VXqtahtFYGh+hTFQ3rmk0Vw+M/sHvd1\nMTPkc48fPx5eNxXXOAqEz2z8XnZmt2YbVVERI1tmFkWSbcdU9QD5O8ZGuCCm2Vr7O621T7XW7m2t\n/UZr7Xmttatbax9srT24+rzqQtooFAqFdcKhmWZr7VoAfwvAq3rvT7fW3gPgrQBeBeDu3vudrbXb\nAdwO4J1ZXb3vJBjN7G2GzCMewduGmKEoe5To627ZUUydX+mYiaiYwBFjzdoy+KQjWT32fcSAM/A4\nqu2FS+pX/WRvMMdD+uuZbY/LkklY/RHLY5tw7/1AEgn1XvDIpuzPidL3qftF2Sf9uRnr84zOZGeZ\nfYo/X5blUGOTYWtrazc1HI8JXzt1D8zYO7mf3vPP9WRxqZd6G+VxAN/UWjsP4BSALwK4A8AbV7+/\nC8DvYTBpmqNAGX9nJsboYqoQlUy1jdQc5VSJ5MrUicgYn/VBqWiRvJkzxZ8TbVHjBcXLHG0vVKpc\nthEhcxbNOoL8gpSFMkWqnroXov3RmVqd9ZPHZ+ZdTdHYKHmyxZ7b2NraGjqL1PXknLZ+zKMFzY+R\nCvNR2NzcDBdaNbbcB19m5NDz43AYZydwAep57/0LAP4BgM8BeBTAU733fwfgdO/90dVpjwE4rcq3\n1m5rrX24tfbhP/uzPzusGIVCoXBJcSHq+VUAbgVwA4AvA/hXrbWf9uf03ntrTU7jvfe7ANwFAK96\n1au6X+HUaqBUtyhPosEzjZkEFKPVzq9kmVOH5eP6M3U/YqdZPZm6pBxoM9l/Rg4R5VDLWG6kUs3k\ngxyNtT/m2x45Ez1Ls092GqlAeJbX1zEy8ahjEYPKNBt1v0RJZFTbXJ+/HiNGp8px4PvW1tZuuUjV\n9s80s9Ls+ZwJz4u+eywxN3hciCPoBwA81Ht/svd+HsBvAXgDgMdba2dXwpwF8MQFtFEoFAprhQux\naX4OwPe01k4BeBrAmwF8GMDXALwNwJ2rz/cdpnJmltHv/L+HCihmO2AGFQISBWkrBhbZtZRtLpJT\nsZfMBhmxqxnW4r+zrD73YVbWH8sYmGJKI5amWG3E0P3Y8nX0Njp2hLCDRDHqLM1elAZNaU/MpJmR\n+RR4LJ9qk78veZuAOjeyGyuoZ2Wkrcw8w9nv6vpGNm7VduTnGOHQk2bv/Z7W2nsBfBTAJoCPYUfd\nfj6A97TW3g7gYQA/cdg2CoVCYd1wQd7z3vsvAvhFOnwOO6xzMfzKFtlV1OowY4sctanqnrF18Lme\naUThITPMKbLnqXPVih1t7+z94LtuuGxmC1Z2vAh+PLP+2DnRbyyv3wKXyRP95kNUItao7OOj66ja\nVp5nZpYsn7dNjrb2ZuM22n6r4Mc6KqfaVBsJONxnlLRFyaHu40yu6Drytc/C/UaobZSFQqGwAGux\njbK1tm/m9+/OiVY0FbDu6/PHFRNT9sDIO5oxiYwBjOxumadSxUryOdF39ZtnkVGUgbfnRYHhS218\ndjzy7CpE56j6s/qi9GeefWS2X3+ualtd35GHN7PjsQd5a2trWI+y3Spb5GzERcYiZ6IEvHZhiTmU\nvTMqZ8jSFaq2TK4oUQqPkffuL8VaTJrA/v2nanIy2KB4R44Z7dnQr5wyBnXDRxOhV7FGqpmfHExV\nidQktfeZ4SccfiCjyc+fO5q4FWbCnPwkE/XPy8cyc8jRzGTq+x+FMClDv3JMRXWz7H4co/pmnFnZ\nTjY1pnZ8ZBLIrpW61pF8M7kls3rV7hzeaz4TDjRadFT7M6Y6/p6VGaHU80KhUFiAtWGas7O9YoYG\npub+e8TK1MoThVgoxspy+c+IuXpWOmKPXrbItHDYbaeGmQBglj2TTyFjxbPIysywP5bT5zvg0CAV\nYhXVk7GXjO2ZhsR72tX2Xy6bXXs7x/chylplyMxN6v6N7iFTydXWyKgPwFym9hlk4x5hxuHrUUyz\nUCgUFmCtmKZiLJHNytvSojfqZeEKbIP09UQOBP/biF2pJBXMhLPVUIX/zKyIke1yZuXNnBQGNaZL\n3jEdOdeWrvaGjFkwI49s1QqZ42qGUUdymdPT1x1tflCOKr4vZvqt5Ir6ou7bjOFHtlB/zSNnZ5bD\nc8YGP8OAGYdhooximoVCobAAa8M0fTDs1tZWyAL8yhuFiagykT3Q1xetbpltVDFWf1z9lsl7IczL\njxkzAN/PEQtdsmLPyqkiByJE11Udz2ylHFyttITITsmYYeEekR3as6rIjq2uVRSu45+DKP2bb2PE\n+pRWleUNXfI2UG5zqS09ukZKk2RkZZaimGahUCgswNowTUDHVWaeymiVVJ7xyDbEbES16VevKBM0\nQ9mjFIMdBX1nCXxZXs/QmQFkiSO4ngyqLyPm5CMJuC3V7xnNIWNyvt2s3hl7pWKlo6gI/38WnRHV\n5+/NUfpDz1xnWFZmawX2s0iu18cdj2Jg/f0fybUkgiKz3XpZlrxB07CUda7VpKkmuejG3N4++FL7\nzMidPQzcZqaqsVrCzqOZMAp/YUd9iOSIfo9ujpmQkixkhhcZX4ZzKqp+j8J0Zm5c34eZnJEGO5df\n+TDz8CunTDQZK6dd9rCOcoy21g4sqtmilS2uozwIngREphS+f4GDDrPnwtFy2PL+PmNk91uFHBUK\nhcJFxFoyTTXzZ4ZhVvVs1fSqKaupql61knp5fJgT/2bIssR4NdraGYXFHMZhMovIIK9YVRR+4reL\ncr1K1mzFn8koD+zPcsS/+c9RfgBlNoiYZqYeZkxdhQixtsLqr2fzUYibv8czU4B9j+rh4+peUiat\n6FlVpoUIvp8jTUS1oTDanlshR4VCoXCJsTZMc2RHmVnpGZm9Uq1s0SqX2SmzfkRt+Xqjldo7t2YN\n6jO2Td+fiOWqseB6fZloc4FvbxTy4bUB7hfDn8vMImNp/Kpj7/SYYZYju7iqRzlpZsaU+89JL1T4\nT4SZ4HQvW3b/8/eM8TMrNignYOTUXbpFOMpuFH2qPoxQTLNQKBQWYC2YpvfAGma8mSMPpT83srup\nlTELyxh5KtW2zJlQkIwNcPKILLTKkOUCjUKgvAxRwDTL5NvifmXMVaVBi3J38vt6+H+PEydO7NbL\nNmSG0kD8b+p8/5nZ3lljMGShbQb/vvFRyJFvQ7FQ+x7d28wGFbtV93GWYCaSL3vjZKQJerki5qpY\n44z2aVhq3yymWSgUCguwFkyT4ZPMZsjsk+o8/5tKmhqxIc9UmKVlyVuXeOqiCADVv8hrruLUZgKI\ns8QVo3hI75nlczJGxinYvG1UbTjw525vH3y3T1TG94HHRtlaGcounrFlBjMmFQfJ8LG/fG347Znb\n29tp0gyrJ7IXzzxnHHly/PjxRUlnRpsKWmu7GkL0HGRJcwwqSoDhn8mRphqhmGahUCgswFowTWXP\nmnSxbpUAABMkSURBVPHejmxzflXJ7JT8P5fPEkVE3kPFFLk+FZ/GZfzxyCbk5YtYUGajVLGro3hU\nf+4Mmx3ZmHxyCuVZZ9mjCAD/+wxLHsUFZrZgxdJGnnAf4zhKvKuSEGe24Ij9ZXJmTJt/UxET2U6j\nTCPi46ZF8HuF7PjGxsaQFfvnaQQ/JyzZzgmsyaTJD6lXS2byL47Ucw+e1BRdjy6OCu+I5FNb6pRK\nGRnU/UQWTWDKcRJluvE3d7T1Lctwk+23Vk4Ef24WcuTVTd6SOrNFL3LyqHAWFfjMzg5emFQ/ud6Z\nPexermjSzdTN6HW/KlRLLQRcz4Vs3/WTU+YYVc+YP0dtF802loycdYoARWTJt1MhR4VCoXARsRZM\n0+i+XxWiIFVfxsArfRZQHLHITFWO2sngmSvLpVgoI3MwzWRE4nPszYBebbL+Rm/znEHm5PFB7yON\nYXNz8wDry675EuN9tkV1FEakwmyyMhH7VKai0dZGLzuHnSm5GEqL4tC7TOXNTDIRe1fPXATVT4Z6\nDiKTSsaW1ZgvdQDtyn2oUoVCofANirVgmkDMImaM0Qy12vOKk4XrZHaVyPmkVlVmt1lgLbMNxWIy\nhsng0BQV6ByNrZI5sgVvbGwckFnZo7NAfG4zGmMfZL0khGZJ2zOsj+v1ZTgEaobdRiy3tTZkaxn7\n9vVG9mF1bgT1XHKokHpWuLxiqXzuTCb46JnJ+qNY6XNu02yt/Xpr7YnW2r3u2NWttQ+21h5cfV7l\nfrujtfaZ1toDrbW/vEiaQqFQWHPMMM1/BuB/A/B/uWO3A7i7935na+321fd3ttZeBeCtAG4C8GIA\n/7619m2996kXiMwEzHoWOfKMebYUre6GzF6ZBS9HbNK3EXnPve02CpRWtlGWy/fBpwwD4qz2CmrF\nVkzJ18/9UecqtpbZDiO5lsCPRcTelW2Or5U/HrFu5aXOmM5IS/Ee/GicsrC1GVtdptFEcs2wUZXg\n2RDZqv0bB1SiDm4/08pGkRxLogQiDJlm7/3/A/CndPhWAO9a/f8uAD/ijv9m7/1c7/0hAJ8B8JcW\nSVQoFAprjMPaNE/33h9d/f8YgNOr/68F8IfuvEdWxw6gtXYbgNsA4OzZs/tWabVKKQYwa+NTtiEV\n9zYKnvXMkFmHst9EtkMvFzOTmXdxZ175iGVkbM8+VTq6CErOaDXf3NxMPbEMn7DCn+NTu/G4Z/bZ\nLEIhs2FGmPG08zFfJhqnbFtmFP2RbS/MNIbMrhp5p70nf6S5qe2i2b0ZsUelWc5EOIxYsmfoM1tJ\nPS7YEdR77621xb773vtdAO4CgJtuuqnPOFao/PBcfzxTsSNEoUz8v6rXX5RILj9Rz6hUI1Xb7zaJ\n3l20vb19oDw7LzY2Ng6oUiyfmsBVqJFvW7VpyFRRw4yJYQkylXS04EX1RJOIf/ijMVVtRiqud+yM\nHEvqGhkyE0o03tvb2+FmgKUmrKifPPn5cLpoocsWpKid7NwIh737Hm+tnQWA1ecTq+NfAHC9O++6\n1bFCoVD4LwKHZZrvB/A2AHeuPt/njv/L1tqvYMcR9HIA/3GmQl5do5XHr9iz4ROZ8Vcx1owtjJiH\ncuDMsNysD5HKnoVlZCw3CsE5bBhG5OjyxyNmno0/l/HshvvALNebUkb3hzpH9XEmjEVpHPx9JjtS\nhMxRqFRaw5I8DQw1fpkzhuvmerK2Mi2C+5XJFUGp50sdQcNJs7X2GwDeCOCa1tojAH4RO5Ple1pr\nbwfwMICfWAn9qdbaewDcB2ATwN/sk57zQqFQ+HrAcNLsvf9U8NObg/P/HoC/dxhh/My/xNjOyOyL\nWaC5IVuVRyEzM/IpZhIF1ANzgb5chlmub5NXbOUEsW2XhpnVPdtmONqaqZKh+DYYKvlGdG6meUTs\nJ3NiZNc4Ggt/PaK61bkj+6d66yOXycKv+L1J/lqNWKn6TYX5MTJ7cVaGtYqM1UfjdZQ2zUKhUPiG\nxNpsowT2rxQzq90oCcRSW4WBmd1MSI9iGKNtgX41zthftLJy8gUfQuPb4M9o3BS7jzKiew/5iHWr\nfmbe+YhBqPfFs5yZTS3bYhmdM2MP92w3C9OJ+sdtee1Dsc/oHK7fX+eRh91jlAleRaVw2z7/JY9T\nthGE6/HjGD3XmQYxSmZyGBTTLBQKhQVYC6bZ+8EEDAZlb7PvUVCqYlBmo5tJe5atsNEKpYJqR7am\nGZuOSuA7E6fI46aSZ6i3PFrZJYlJWHa11ZJjTA2KxUeag0EFy6v+ju4p/390TXxfsqQgERRDjOyL\nHPuomJhikRFbzjYgcL0eh0lKw9+97ZZZ91K7c3SOIRvbiO36c5eimGahUCgswFowTeBgjBuzDLVK\nRXFgKm4tqi+zqUXJNDwi5pWxhNH5Hmq7aGZ343qYtWTe7kyuzEMeMRJ/LqcmWzKWhqys2qEyYpGZ\n7Eo21a8IUZtZH9W1mimnZOV6ZmQG9ttIWRPxfcoYppWJogRmGCvH3Xq5Il+BsnvORkcswVpMmq21\nA04NQ+SA8PRfqYMe/uEY5RUcyTk76MpYnoWURI4vhUyGkZFc9UFNiHzzRaYGfx2iBenYsWMH8nty\nX2ZMFb4ODjWK3pOj4B1LkQMum+zYvOH7OXJo+LEdmZeyhdzfLyOnhyIjUb2+zeiezFRbP45ZCJqq\n1yPbimvg8t4coZx0wP6FaTRuEUo9LxQKhQVYC6YJHMxKk6nagA5piFgCMM7erdRgtTqNVnPPaDlp\nxowTJWNcWf9myyjWrdjHSLWayR/qEZlSluT39MyFVXWVmGSU8ca3PaM5jJxFvfdQpVXtRG3OXGev\nMUX3tP/O4zTjXIzMIVm9WflMs+H6GJlKr1j8yGHrHclLVfVimoVCobAAa8M0PbIVw68qnJYqYooZ\nczWoQGIOBem9h6EzignPOANGNlLPDEf2ReXYUH3KUn7ZuSNn0RKGqAz0Kq2dgW1pitXy+C8N0zEZ\novFX4zaye2Y5Xg1ZALwK+I9ynypkzDVqy6BSzfnyS2VQds+ovN/AEaUXzNry9cwmQbkQR1AxzUKh\nUFiAtWSaQGz/MPhEqFxG2d2WhD9k7CNK4hrZXqN6rGxUzq/KM97GCMwwgHgV9+cyS5jZjhYxKA+2\n+Xm714iZKAYWyafslcquOuqX8vpnGsQMY2VWbG90tON+jLJk0txGhBkvvB+H6L7IjrEGoaJbIm+6\nr4ujaNRYR1qPyta/xGM/i2KahUKhsABrwzTVKm3H1feM9WX1ZCxySdByZg/kc7OA2yV2osjr7T8j\nxqoSidiqrqIQZuyKkdyq31Y+ipP1rDvyai4ZI9+mioLIynkZ/HW2Y/yubz9GS7ZaRv2LYpZZdqsj\nsj+r+MxoDJdudIjqyezFEfNUW15VX2YYdWTvj+TMzomwNpMmq7PshOHz1ADxzaKy4vANyQ+zL589\ntKPA5JkXS2WOGxXEH6kaKgA4Ghv/HiGVS5HlihYbf1PPTG78oKh6eYLma+XlZIcBn+MfbO6nGqfI\nFKAmngyRk82PJ8sRbcrwYXX8qeSysbD+Zk4R7rdfqCJn0YyqrFTk7F5keTLVXe0AYrkix1lElg6D\nUs8LhUJhAdaGaaqwICBne5H6G61wwMHV15+rQiFUGSVX5sBR76+J5OHjfuU25jVinr6cWsE5bGrG\nWTETdpIx66icYn/czxknm5Jn1Gam8qlxGzGdSI7oeMRy/bWPtB6ltjJDzJxGbCbxyLS7qD8zJq3o\nHvcyZCaGGZao7icg7pOSa4RimoVCobAAa8M02Y4WrTiZjcOQBQRHvyn7USQn16nqU3JmzCSyhW1s\nbIRMRBm9WT7O/pONgQow5z4YZt5bNOM4UMw8cgh5G+XI3qYcQTPsOEtEEWk2qr6MFUX3dpaU4jD2\nVP89CqCPHDC+vLJjR2ObOZSiMckcosyiWUYln+8nM+vD2qo9imkWCoXCAqwF0zSWqbY9+nPsNz7G\nUPa3iFGooN7IO+3ZUCSXWsGzMIiISSimaojCgRSD5eDsLHO9l2GU4T7aTuqPscfcy5ix5ki7iBKM\n+HOi/qh6PRvlMkrOkSdWjb/qS1Q+0l6yc2dYvB9b3nqc2YIZ6lmJnitvO48iL/zzPvJ6e7Y8g8ju\nn2kJsyimWSgUCguwFkzTGJxnFLy9S620ytblvys2FK2wihlmqaNGrNSvjNmWPy7PbSrGx6uo8sDz\ndkW1skZ2KR9sPIpMUGOr2uQxZO+tegfPyG6sxkIxusxrG42/YpUjj7GyxfO5SluJ5Mvsbsp7zuW9\nPXvUJpdVffD3pmKx1padw9eY2/TPJz/Dyu4b2dn9NYqYpYowiGJ9RyimWSgUCguwFkwTOLhiRvYr\nv7pEW9YUGxp5vVXsn4rL4xUxe3+36iPLEDElXyZKgZd5BLOdMoZsd84S20/GzqydiIX6vmQ2Qj6e\n3RdeJtUHfw7Lnr12JLPDKhlHx0dxh1kCClVHFuEw6qfSqqJdOr4eHhM/1lGsJB/39doWVRVBkZXj\ntjOth88fXQfG2kyagL4Jo44p1YXP9ep6FBKRDVgWNhHtP1Yy8sWO3peT9cUjChPxi0M0mSt1juX0\n6tzMjTWjErEzR5WZnTTVw6HCYyIzi78X1AvZfJkZdT8bi+y+GDk7/WIzYyrKnIqjbYqZKSBbkLKx\njdT7DFHQvVps1HXIAvt9me3tg1nSZlHqeaFQKCzAWjFNv9qz+qBWzxkVyDBSM9VKq1ZG+2309kPP\nnDI1OArP8eo/r/SRAdurrRljmskBGjllFNsYmRiUKSVjEoboOmTXytfLjD66dqp95YhgJv3ss8/u\nO9dvRBiFMilw/VnY2oyGk4VoRVsuMxmV8yfbSGLbYXm8+b5VzJXb9OOfaSSRJpNpsUtCmYBimoVC\nobAIbakR9KII0dqTAL4G4EtHLYvDNVgveYD1k6nkybFu8gDrJ9M6yfOS3vuLRietxaQJAK21D/fe\nbz5qOQzrJg+wfjKVPDnWTR5g/WRaN3lmUOp5oVAoLEBNmoVCobAA6zRp3nXUAhDWTR5g/WQqeXKs\nmzzA+sm0bvIMsTY2zUKhUPh6wDoxzUKhUFh7rMWk2Vr74dbaA621z7TWbj+C9q9vrf2H1tp9rbVP\ntdbesTp+dWvtg621B1efV11iuTZaax9rrf3OUcvTWruytfbe1toftdbub6197xHL83dW1+re1tpv\ntNaed6nlaa39emvtidbave5YKENr7Y7VPf5Aa+0vXyJ5/v7qmn2itfZ/t9auPEp53G8/01rrrbVr\nLpU8zxWOfNJsrW0A+N8B/BUArwLwU621V11iMTYB/Ezv/VUAvgfA31zJcDuAu3vvLwdw9+r7pcQ7\nANzvvh+lPP8IwAd6798O4LUruY5EntbatQD+FoCbe++vBrAB4K1HIM8/A/DDdEzKsLqf3grgplWZ\n/2N1719seT4I4NW99/8KwKcB3HHE8qC1dj2AHwLwOXfsUsjz3MC2Ix7VH4DvBfC77vsdAO44Ypne\nB+AHATwA4Ozq2FkAD1xCGa7DzkP3JgC/szp2JPIAeCGAh7CygbvjRyXPtQA+D+Bq7GwF/h3sPISX\nXB4ALwVw72hM+L4G8LsAvvdiy0O//SiAdx+1PADei52F97MArrmU8jwXf0fONLH3ABgeWR07ErTW\nXgrgdQDuAXC69/7o6qfHAJy+hKL8QwB/F4DfGHtU8twA4EkA/3RlLvgnrbXLj0qe3vsXAPwD7DCV\nRwE81Xv/d0clDyGSYR3u8/8RwL89Snlaa7cC+ELv/T/RT+swPlNYh0lzbdBaez6Afw3gb/fev+J/\n6zvL3yUJNWitvQXAE733j0TnXEp5sMPmvhPAP+69vw47W173qb6XeHyuAnArdibzFwO4vLX200cl\nT4R1kMHQWvs57Jih3n2EMpwC8LMAfuGoZHgusA6T5hcAXO++X7c6dknRWjuBnQnz3b3331odfry1\ndnb1+1kAT1wicb4PwC2ttc8C+E0Ab2qt/YsjlOcRAI/03u9ZfX8vdibRo5LnBwA81Ht/svd+HsBv\nAXjDEcrjEclwZPd5a+1vAHgLgP9uNZEflTwvw85C959W9/Z1AD7aWjtzRPIcCuswaX4IwMtbaze0\n1k5ixxj8/kspQNvJEfVrAO7vvf+K++n9AN62+v9t2LF1XnT03u/ovV/Xe38pdsbj/+29//QRyvMY\ngM+31l6xOvRmAPcdlTzYUcu/p7V2anXt3owdx9RRyeMRyfB+AG9trV3WWrsBwMsB/MeLLUxr7Yex\nY+a5pff+FyTnJZWn9/7J3vu39N5furq3HwHwnav760jG51A4aqPqauH7q9jx7P0xgJ87gvb/a+yo\nUZ8A8PHV318F8M3YccY8CODfA7j6CGR7I/YcQUcmD4DvAPDh1Rj9PwCuOmJ5/lcAfwTgXgD/HMBl\nl1oeAL+BHZvqeexMAG/PZADwc6t7/AEAf+USyfMZ7NgK7b7+P49SHvr9s1g5gi6FPM/VX+0IKhQK\nhQVYB/W8UCgUvm5Qk2ahUCgsQE2ahUKhsAA1aRYKhcIC1KRZKBQKC1CTZqFQKCxATZqFQqGwADVp\nFgqFwgL8/9iW1dnk7C5IAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(np.reshape(M[:,0] - low_rank[:,0], dims), cmap='gray');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "High-resolution version" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "data": { "image/png": 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qpmnpZDXrlvfD8wsePnwYwBYzZn8nH5NRfL7GY24Wk/NmP3JGoX231v3NsMQe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\nBjAZpgns1Nx5jMmKTmr/R0a0qkd365s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Lku2o75/FYL1t1UZ8nZEO0mqjHnuXDDizgXJG\nCN5r90gzabHe3pdbLWao1S3y2ektGNjNYpZimoVCoTCAyTBNHbVbRpemYTETnV/kd7MighYry9pp\nfRGzZ7u1SifyRe7G98vY3NxcGPGjVTAeLD2kx0YjNtNbhSXTjPinNjc3FxiYV2/LLqssTm99h92z\n2fNDWxt3eNshWtdHao+MLjKzuYd3/6xZRrTE0WOYFjKfrMhsULLs6qDJvDTltHFZkap3LpI/RA+A\n7giS0meE5j27optm7ajUk4tYtow4+i17My/f3tRKXut9SjkKFllpe9NWed6795YUyntRWwNJRi4V\nQddLt43clT0KbPTkeZHtlk2eu2VEwhQNbNqWiNTodJ7NnL8eXEbE+1nU9LxQKBQGMBmmSUTmdISl\nDdYIHklSRsr1julRdGRDi4xI2JoiWEEoT7CrWZKVtudOsMq2rs8e99L0puVWgEpDMpUeA47ajWEF\nCBnRTELfI8sNwRgJAFlM3VtkYE2ndT+VzFVPafm54rJPnTo1T+sFMIelOR2XgOX2igK/1nMI7Ozb\nvam7bD9vMUsPxTQLhUJhALRMoGDPjSB6GMATAB7Zb1sEDmFa9gDTs6nsiTE1e4Dp2TQle57dWjvc\nSzSJlyYAENGtrbVr99sOxtTsAaZnU9kTY2r2ANOzaWr2ZFDT80KhUBhAvTQLhUJhAFN6ad683wYo\nTM0eYHo2lT0xpmYPMD2bpmZPF5PxaRYKhcJ3AqbENAuFQmHymMRLk4heRURfJKIvE9EN+1D+5UT0\n10R0OxF9nojePDt+kIjeT0R3zv5efIbtWiWiTxHR+/bbHiK6iIjeRURfIKI7iOiH9tmeX5rdq9uI\n6B1EdM6ZtoeI/piIHiKi28Qx1wYiunHWx79IRD9xhuz5rdk9+ywR/W8iumg/7RHnfpmIGhEdOlP2\n7BX2/aVJRKsA/huAVwO4BsBPE9E1Z9iMdQC/3Fq7BsAPAvj5mQ03APhAa+1qAB+Y/T6TeDOAO8Tv\n/bTn9wD8RWvteQBeOLNrX+whomcB+AUA17bWXgBgFcAb9sGePwHwKnXMtGHWn94A4Pmza35/1vdP\ntz3vB/CC1tr3AfgSgBv32R4Q0eUA/iWAu8WxM2HP3oCXMO3XPwA/BOAvxe8bAdy4zza9F8CPA/gi\ngKOzY0cBfPEM2nAZth66VwJ43+zYvtgD4EIAX8HMBy6O75c9zwJwD4CD2FoK/D5sPYRn3B4AxwDc\n1msT3a8B/CWAHzrd9qhz/xrA2/fbHgDvwtbA+1UAh86kPXvxb9+ZJrYfAMa9s2P7AiI6BuBFAD4O\n4Ehr7fjs1AMAjpxBU34XwK8AkAtj98ueKwE8DOCtM3fBHxLReftlT2vtPgC/jS2mchzAo621v9ov\nexQ8G6bQz/8DgP+7n/YQ0esA3Nda+4w6NYX2SWEKL83JgIieDuDdAH6xtfaYPNe2hr8zIjUgotcC\neKi19vdemjNpD7bY3IsB/EFr7UXYWvK6Y+p7htvnYgCvw9bL/FIA5xHRz+yXPR6mYAODiH4NW26o\nt++jDecC+FUA/2W/bNgLTOGleR+Ay8Xvy2bHziiIaA1bL8y3t9beMzv8IBEdnZ0/CuChM2TOjwD4\nSSL6KoA/A/BKIvrTfbTnXgD3ttY+Pvv9Lmy9RPfLnh8D8JXW2sOttVMA3gPgh/fRHgnPhn3r50T0\ncwBeC+DfzV7k+2XPc7A10H1m1rcvA/BJInrmPtmzFKbw0vwEgKuJ6EoiOgtbzuBbzqQBtLUP1R8B\nuKO19jvi1C0A3jj7/xux5es87Wit3dhau6y1dgxb7fHB1trP7KM9DwC4h4i+e3boOgC375c92JqW\n/yARnTu7d9dhKzC1X/ZIeDbcAuANRHQ2EV0J4GoAf3e6jSGiV2HLzfOTrbUnlZ1n1J7W2udaa89o\nrR2b9e17Abx41r/2pX2Wwn47VWcD32uwFdn7BwC/tg/lvwxb06jPAvj07N9rAFyCrWDMnQD+H4CD\n+2DbK7AdCNo3ewB8P4BbZ230fwBcvM/2/FcAXwBwG4D/AeDsM20PgHdgy6d6ClsvgDdFNgD4tVkf\n/yKAV58he76MLV8h9+v/vp/2qPNfxSwQdCbs2at/tSKoUCgUBjCF6XmhUCh8x6BemoVCoTCAemkW\nCoXCAOqlWSgUCgOol2ahUCgMoF6ahUKhMIB6aRYKhcIA6qVZKBQKA/j/9STVMHpHEB4AAAAASUVO\nRK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(np.reshape(M[:,140] - low_rank[:,140], dims), cmap='gray');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Make Video" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I was inspired by [the work of fast.ai student Samir Moussa](http://forums.fast.ai/t/part-3-background-removal-with-robust-pca/4286) to make videos of the people." ] }, { "cell_type": "code", "execution_count": 70, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from moviepy.video.io.bindings import mplfig_to_npimage" ] }, { "cell_type": "code", "execution_count": 75, "metadata": { "collapsed": true, "scrolled": false }, "outputs": [], "source": [ "def make_video(matrix, dims, filename):\n", " mat_reshaped = np.reshape(matrix, (dims[0], dims[1], -1))\n", " \n", " fig, ax = plt.subplots()\n", " def make_frame(t):\n", " ax.clear()\n", " ax.imshow(mat_reshaped[...,int(t*fps)])\n", " return mplfig_to_npimage(fig)\n", " \n", " animation = mpe.VideoClip(make_frame, duration=int(10))\n", " animation.write_videofile('videos/' + filename + '.mp4', fps=fps)" ] }, { "cell_type": "code", "execution_count": 296, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[MoviePy] >>>> Building video videos/figures2.mp4\n", "[MoviePy] Writing video videos/figures2.mp4\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "100%|\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2589| 600/601 [00:39<00:00, 15.22it/s]\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "[MoviePy] Done.\n", "[MoviePy] >>>> Video ready: videos/figures2.mp4 \n", "\n" ] }, { "data": { "image/png": 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MpqF/h4MLjqcVW4shqTqpHRMX/qBjOAj2YpPs05oBLQt50sC93fKYFuEeiqnL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\ns+y7i8aYjxljvuT/XmC//Zwx5svGmC8aY/7CVqOpqKio2HFswjR/EcD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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "make_video(M - low_rank, dims, \"figures2\")" ] }, { "cell_type": "code", "execution_count": 554, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100%|\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2589| 600/601 [00:00<00:00, 858.48it/s]\n" ] }, { "data": { "text/html": [ "
" ], "text/plain": [ "" ] }, "execution_count": 554, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mpe.VideoFileClip(\"videos/figures2.mp4\").subclip(0,10).ipython_display(width=300)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Speed of SVD for different size matrices" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import timeit\n", "import pandas as pd" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "m_array = np.array([100, int(1e3), int(1e4)])\n", "n_array = np.array([100, int(1e3), int(1e4)])" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true }, "outputs": [], "source": [ "index = pd.MultiIndex.from_product([m_array, n_array], names=['# rows', '# cols'])" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": true }, "outputs": [], "source": [ "pd.options.display.float_format = '{:,.3f}'.format\n", "df = pd.DataFrame(index=m_array, columns=n_array)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# %%prun\n", "for m in m_array:\n", " for n in n_array: \n", " A = np.random.uniform(-40,40,[m,n]) \n", " t = timeit.timeit('np.linalg.svd(A, full_matrices=False)', number=3, globals=globals())\n", " df.set_value(m, n, t)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " 100 1000 10000\n", "100 0.006 0.009 0.043\n", "1000 0.004 0.259 0.992\n", "10000 0.019 0.984 218.726" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df/3" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2 Backgrounds in 1 Video" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We'll now use real video 008 dataset from [BMC 2012 Background Models Challenge Dataset](http://bmc.iut-auvergne.com/?page_id=24), in addition to video 003 that we used above." ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from moviepy.editor import concatenate_videoclips" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "collapsed": true }, "outputs": [], "source": [ "video2 = mpe.VideoFileClip(\"movie/Video_008.avi\")" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[MoviePy] >>>> Building video movie/concatenated_video.mp4\n", "[MoviePy] Writing video movie/concatenated_video.mp4\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "100%|\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2589| 300/301 [00:00<00:00, 481.76it/s]\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "[MoviePy] Done.\n", "[MoviePy] >>>> Video ready: movie/concatenated_video.mp4 \n", "\n" ] } ], "source": [ "concat_video = concatenate_videoclips([video2.subclip(0,20), video.subclip(0,10)])\n", "concat_video.write_videofile(\"movie/concatenated_video.mp4\")" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": true }, "outputs": [], "source": [ "concat_video = mpe.VideoFileClip(\"movie/concatenated_video.mp4\")" ] }, { "cell_type": "markdown", "metadata": { "heading_collapsed": true }, "source": [ "### Now back to our background removal problem:" ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "hidden": true }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100%|\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2588\u2589| 300/301 [00:00<00:00, 533.88it/s]\n" ] }, { "data": { "text/html": [ "
" ], "text/plain": [ "" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "concat_video.ipython_display(width=300, maxduration=160)" ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "collapsed": true, "hidden": true }, "outputs": [], "source": [ "scale = 0.5 # Adjust scale to change resolution of image\n", "dims = (int(240 * scale), int(320 * scale))" ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "collapsed": true, "hidden": true }, "outputs": [], "source": [ "N = create_data_matrix_from_video(concat_video, fps, scale)\n", "# N = np.load(\"low_res_traffic_matrix.npy\")" ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "collapsed": true, "hidden": true }, "outputs": [], "source": [ "np.save(\"med_res_concat_video.npy\", N)" ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "hidden": true }, "outputs": [ { "data": { "text/plain": [ "(19200, 1800)" ] }, "execution_count": 45, "metadata": {}, "output_type": "execute_result" } ], "source": [ "N.shape" ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "hidden": true, "scrolled": true }, "outputs": [ { "data": { "image/png": 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LV1ZWIjvjOqN1OVc9wdk3WeXu7m60zPM8tusuc9evX08kEI5JwzPdZcnDkznn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\nvrj44P1TZ3RXNLu7jbbrriAa9uYO3AyxdCarOUbdAdiZsPbLjRWqdD8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l6fzovp/jZ35+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\nYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(np.reshape(N[:,200], dims), cmap='gray');" ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "collapsed": true, "hidden": true }, "outputs": [], "source": [ "U_concat, s_concat, V_concat = np.linalg.svd(N, full_matrices=False)" ] }, { "cell_type": "markdown", "metadata": { "hidden": true }, "source": [ "This is slow, so you may want to save your result to use in the future." ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "collapsed": true, "hidden": true }, "outputs": [], "source": [ "np.save(\"movie/U_concat.npy\", U_concat)\n", "np.save(\"movie/s_concat.npy\", s_concat)\n", "np.save(\"movie/V_concat.npy\", V_concat)" ] }, { "cell_type": "markdown", "metadata": { "hidden": true }, "source": [ "In the future, you can just load what you've saved:" ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "collapsed": true, "hidden": true }, "outputs": [], "source": [ "U_concat = np.load(\"movie/U_concat.npy\")\n", "s_concat = np.load(\"movie/s_concat.npy\")\n", "V_concat = np.load(\"movie/V_concat.npy\")" ] }, { "cell_type": "code", "execution_count": 50, "metadata": { "collapsed": true, "hidden": true }, "outputs": [], "source": [ "low_rank = U_concat[:,:10] @ np.diag(s_concat[:10]) @ V_concat[:10,:]" ] }, { "cell_type": "markdown", "metadata": { "hidden": true }, "source": [ "The top few components of U:" ] }, { "cell_type": "code", "execution_count": 51, "metadata": { "hidden": true }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 51, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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3vbhk4saNG+0MTXbM2TQSp7stM/K+sw3IEjz3oKZMi5JSaPkHBwedMDlfFahs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\npqiztDtEnGWoIy7byXGZ5AnK/jzk0J1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tmO6d44jsZ84wnR1EejeH2uYW6ShV65h5BCO9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\nAPD1r3+9vT/i9ddfB4CWcWZsoZTSYU6ZIiCqs5abRR1FNk1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wftcHbTfej5soGIFDk8po\nNAqDCIDus9PvosnU2ycjNZq1atXM7XV5XlFRUbEC1oJpllKwtbU1t5Oix/VGBnCfhV0Wo8dGYXuO\njGnq7BVl8NHydEZ0aUuf8Jfok/+4xEUZDr/3+4zkQH3SIIfHPDv707jybGkUyaYixpPtlxTVy8+P\nMqT3ica9LTJoXXwZHOXXjMTnWodSSierjgu71cTjzCly0Pm9R+3vTpnsHA15zZ65Lr0Jl+tFUiEP\nQdZMRmT4bn7wd1nr2pdjl8i2Lvbrr4LKNCsqKipWwFowzeFwiNOnT7ezzO7ubioOJpQ99tnv+HeW\n5V0lJ1liB62nXl8/fcYupXScFJH9MmOdei23dXlYpbIGZ5q+b0/UPl4HtRdzNva9obUuPNZthpoT\n1PeZcZYQMb7s2auTzRNaRNf0fJqE7hAQCcsVapP17OvqmIhE8cBJ+K9KZzzfZNSXvF78m/c7mUxa\nG6HacxWRrZXwFYkyTT3f7zcL7VUHziJRfOSfiPorj8l8F2rbjMT/Wi/aTpVxRtn0+1CZZkVFRcUK\nWAumSbuYeswzGYufp5/OPKMEINm5OntlHrdlQiOjemY5AtVjn3nR1d6jeTgVLkAH5kXewAn72N/f\n77Btn901IYbbPz2zuTJ0r4eylyjphn4q6+OxrLPbxDRJiCMKP+V53o59/SKT8ej5bnudTCadTOsu\nS1LpTBaySezv73f6oK/A1Bfg7ZXZ/vT+ohUSr+X7xWtbOAP2ZCaRAsD/1jbNMvETUZ909UGULpLH\n6p5KwFH/zXYnWITKNCsqKipWwFowzel0irfffnsuHDBjEjozZrNK5qlVZEkOtBz/VI+92wXdFqaZ\nw33mV9ufz5qR/cdFwUxrF9nfeC3XG6rX1cPt3Gur9lgXfZNhMtWeMk0e64mU1b7l+/9oUo1s5eCJ\ncg8ODhbqCyOBuP8WeVu977CeBwcHaTishk46++G1mFIwykDuDJP3e+rUqTRVnWocXdMc3bfbIF28\nrwzd29IZ3mAw6Ni4na1Np9NOUAg/eS/qTXc7rydXiZQOXk9t20zvybbe2NhIU8wtQmWaFRUVFStg\nLZhm0zRzwfs6q2QzRh9DdPantitP0BCF8fUx1cw+06fp9PJ935jo/iLG6faeyHbrKeoYNbRM1ISy\nSteW8vmQBSmbdPtflDBCdwHUY/j3wcFBWw69mWQzvAdl44uUExrB46xKQy79GbiqQu/Fv/P7Ho/H\nHZtoxCqzZC9eF0204bY54vDwsK2P2yC1fNc7OuN0dYOW45+j0ah9Nt4v9F4yW3fmBdfvPK2fok/z\n6+wx0oT6savuRrkWgyYwvyyIhOtRQ2dZcFz+MBh0txPtE0xntN3rqNfqG+wicTCv4wO1v7Tj8biz\nROt7sX1g8JdXr5VNAHqelxMJ/32Z6S/6eDxuX7IsNFWXv9nL6hOUtoXfmx7nscosb2Njo2M2IHiM\nypUiKY+ilNJZIvN8NUtwOe2DXbaFsf7Ge4i29M02kCulLJxwI/G3DzjaJ30ZHZm0PLjD3yudBH2L\n3b5s6m460YxXi0Ii9f13x+CyqMvzioqKihWwNkxTEYVpEVESh8w50xeuSEThWZ4xRyU5mazGoULn\nvswy2R4rekyWVScSGLvZgbOwMkdnHdFSpk/4rvc/GAxSsbfeg5fHNlYm5sskMru+dswcOVoPZ7fK\n6HhNZ8KeZEKZZsZudXmuOwxouWo2WCSDGw6Hc2J9/SR0G+hsD6PRaNSaQdwJ6KsyDfPMQhtns1kr\n1vdQXn9ntF4eBqzOLV8FeN/UPJ/eJl6unhftb+TtsyiZjKMyzYqKiooVUDJGd1crUcqrAG4DeO1e\n10XwANarPsD61anWpx/rVh9g/eq0TvV5rGmaBxcdtBaDJgCUUr7QNM1H7nU9iHWrD7B+dar16ce6\n1QdYvzqtW32WQV2eV1RUVKyAOmhWVFRUrIB1GjQ/fa8rYFi3+gDrV6dan36sW32A9avTutVnIdbG\npllRUVHx+wHrxDQrKioq1h5rMWiWUn6wlPKVUsozpZQn78H1Hy2l/Eop5cullC+VUn7y+PuLpZTP\nllKePv68cJfrNSyl/JtSyi/f6/qUUu4rpfx8KeXfllKeKqV89z2uz58/fla/V0r52VLK1t2uTynl\n75VSXiml/J58l9ahlPLJ4z7+lVLKH79L9flrx8/si6WU/7OUct+9rI/89lOllKaU8sDdqs+7hXs+\naJZShgD+JwB/AsC3A/ixUsq33+VqTAD8VNM03w7gDwP4M8d1eBLA55qm+QCAzx3/fTfxkwCekr/v\nZX3+FoB/2jTNvw/gDxzX657Up5TyCIA/C+AjTdN8CMAQwI/eg/r8AwA/aN+FdTjuTz8K4Injc/7n\n477/XtfnswA+1DTNdwL4KoBP3uP6oJTyKID/GMDz8t3dqM+7A2YjuVf/AHw3gH8mf38SwCfvcZ1+\nEcAPAPgKgMvH310G8JW7WIerOHrp/hiAXz7+7p7UB8B5AM/i2AYu39+r+jwC4AUAF3EUCvzLOHoJ\n73p9ALwPwO8tahPv1wD+GYDvfq/rY7/9pwB+5l7XB8DP42ji/QaAB+5mfd6Nf/ecaeLkBSCuHX93\nT1BKeR+ADwP4DQCXmqZ56fin6wAu3cWq/E0AfwGABijfq/o8DuBVAH//2Fzwd0opp+9VfZqm+SaA\nv44jpvISgBtN0/zze1UfQ1aHdejn/zWA//te1qeU8jEA32ya5nfsp3Von6WwDoPm2qCUcgbAPwbw\n55qmeVt/a46mv7siNSil/BCAV5qm+c3smLtZHxyxue8C8LebpvkwjkJe55a+d7l9LgD4GI4G8ysA\nTpdSfvxe1SfDOtSBKKX8JRyZoX7mHtZhG8BfBPDf36s6vBtYh0HzmwAelb+vHn93V1FK2cDRgPkz\nTdP8wvHXL5dSLh//fhnAK3epOt8D4IdLKd8A8I8A/LFSyj+8h/W5BuBa0zS/cfz3z+NoEL1X9fl+\nAM82TfNq0zSHAH4BwB+5h/VRZHW4Z/28lPKnAfwQgP/ieCC/V/X5VhxNdL9z3LevAvitUsrD96g+\nd4R1GDQ/D+ADpZTHSyljHBmDf+luVqAc5ZT6uwCeaprmb8hPvwTg48f//ziObJ3vOZqm+WTTNFeb\npnkfjtrj/2ma5sfvYX2uA3ihlPJtx199FMCX71V9cLQs/8OllO3jZ/dRHDmm7lV9FFkdfgnAj5ZS\nNkspjwP4AIB//V5XppTygzgy8/xw0zSaRfmu16dpmt9tmuahpmned9y3rwH4ruP+dU/a545wr42q\nxxPfn8SRZ+9rAP7SPbj+f4SjZdQXAfz28b8/CeB+HDljngbwLwBcvAd1+z6cOILuWX0A/AcAvnDc\nRv8XgAv3uD7/A4B/C+D3APxvADbvdn0A/CyObKqHOBoAfqKvDgD+0nEf/wqAP3GX6vMMjmyF7Nf/\ny72sj/3+DRw7gu5Gfd6tfzUiqKKiomIFrMPyvKKiouL3DeqgWVFRUbEC6qBZUVFRsQLqoFlRUVGx\nAuqgWVFRUbEC6qBZUVFRsQLqoFlRUVGxAuqgWVFRUbEC/j/uMTLjeQJ2KQAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(np.reshape(U_concat[:, 1], dims), cmap='gray')" ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "hidden": true }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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aMlf2sGM/DdRlu5uGTahuH0cNaJAx26NwDg3mV/sq22WVtXFbVFJO+2u29EYr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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(np.reshape(U_concat[:, 2], dims), cmap='gray')" ] }, { "cell_type": "code", "execution_count": 53, "metadata": { "hidden": true }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 53, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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sJKvky/O8CshMPX/X2KBkzZpLk5aLoNReaVvkyHIUCAQCK8JkmKbmMFs6Dxy9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\nnZvrSzNbzHUyG+V7o+dzfL8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LwOJpr1THizF0mq0MrGQgsUJeraxCLSGIJSzFOVqwPu26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\nICbNQCAQaMD/B1jNh6cYA9n/AAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(np.reshape(U_concat[:, 3], dims), cmap='gray')" ] }, { "cell_type": "markdown", "metadata": { "hidden": true }, "source": [ "Background removal:" ] }, { "cell_type": "code", "execution_count": 54, "metadata": { "hidden": true }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 54, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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+uXPnFrZRLo9ZqLYlkkOVpM0wDw/i0Bu2SfIWSWaRecgPh02xXJxnaWlpwXyl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\nRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(np.reshape((N - low_rank)[:, -40], dims), cmap='gray')" ] }, { "cell_type": "code", "execution_count": 55, "metadata": { "hidden": true }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 55, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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HpZ09exbAJBty6Ib2PIesmKFinClv3LjRS3aRsZnIgBbt0uhuRBEjJLsmA3FD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\nPXFNtLSKzp1mgADywcxfdB2E/ZxoABsqf5qiWpetQ4YWHnc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RM7/mjRs3ev2C5fEc3rvW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\ngg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(np.reshape((N - low_rank)[:, 240], dims), cmap='gray')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Aside about data compression" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Suppose we take 700 singular values (remember, there are 10000 singular values total)" ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 1341719.6552, 10527.5148, 6162.0638, 4234.9367,\n", " 3174.0389, 2548.4273, 2138.1887, 1812.9873,\n", " 1557.7163, 1345.805 , 1163.2866, 1000.5186,\n", " 841.4604, 665.7271, 0. , 0. ,\n", " 0. , 0. , 0. , 0. ])" ] }, "execution_count": 56, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s[0:1000:50]" ] }, { "cell_type": "code", "execution_count": 57, "metadata": { "collapsed": true }, "outputs": [], "source": [ "k = 700\n", "compressed_M = U[:,:k] @ np.diag(s[:k]) @ V[:k,:]" ] }, { "cell_type": "code", "execution_count": 66, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 66, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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4ikxBiqIgFAoZ7swbCbOyREyM/d5pOCn0mtXBSRBHQADo6uqqEagJeEIxC55W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hW4CG0ZHByE0+kEAHoiaWlpKXJzcxNoACski4RJth3C4TD6+voQDAbR09ODD33oQwnvsc+yY0NU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\n/VUtIzf/VMtetSMOUpj08oM9Fz/LwhLRTbPob1BtvdFopnSr9JdhhsUj9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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(12, 12))\n", "plt.imshow(compressed_M, cmap='gray')" ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [ { "data": { "image/png": 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AZ/1IKgOMOmVUpAygs1ug2lB0pge6dq5ImBzNfplcx1mMhiv2sTNvryNiTH12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\nSUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.imshow(np.reshape(compressed_M[:,140], dims), cmap='gray');" ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 59, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.allclose(compressed_M, M)" ] }, { "cell_type": "code", "execution_count": 60, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.864899899979104e-09" ] }, "execution_count": 60, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.linalg.norm(M - compressed_M)" ] }, { "cell_type": "code", "execution_count": 61, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "((19200, 700), (700,), (700, 6000))" ] }, "execution_count": 61, "metadata": {}, "output_type": "execute_result" } ], "source": [ "U[:,:k].shape, s[:k].shape, V[:k,:].shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "space saved = data in U, s, V for 700 singular values / original matrix" ] }, { "cell_type": "code", "execution_count": 50, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "0.1531310763888889" ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" } ], "source": [ "((19200 + 1 + 6000) * 700) / (19200 * 6000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We only need to store 15.3% as much data and can keep the accuracy to 1e-5! That's great!" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "### That's pretty neat!!! but..." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The runtime complexity for SVD is $\\mathcal{O}(\\text{min}(m^2 n,\\; m n^2))$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Downside: this was really slow (also, we threw away a lot of our calculation)**" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CPU times: user 5min 38s, sys: 1.53 s, total: 5min 40s\n", "Wall time: 57.1 s\n" ] } ], "source": [ "%time u, s, v = np.linalg.svd(M, full_matrices=False)" ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(19200, 6000)" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" } ], "source": [ "M.shape" ] } ], "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": "3.6.1" } }, "nbformat": 4, "nbformat_minor": 2 }