{ "cells": [ { "cell_type": "markdown", "id": "c95dd2a6", "metadata": {}, "source": [ "Title: Distance Transform\n", "Author: Thomas Breuel\n", "Institution: UniKL" ] }, { "cell_type": "code", "execution_count": 20, "id": "d00fcb37", "metadata": { "collapsed": true }, "outputs": [], "source": [ "\n", "from scipy.ndimage import filters\n", "def ims(image,**kw):\n", " size = kw.get(\"s\",8)\n", " if \"s\" in kw: del kw[\"s\"]\n", " subplots(1,1,figsize=(size,size))\n", " gray(); imshow(image,**kw)\n", "def imp(image,**kw):\n", " subplots(1,1,figsize=(6,6))\n", " gray(); imshow(image,interpolation='nearest',**kw)\n", "def imrow(*args,**kw):\n", " size = kw.get(\"s\",8)\n", " if \"s\" in kw: del kw[\"s\"]\n", " n = len(args)\n", " gray()\n", " subplots(1,n,figsize=(n*size,size))\n", " for i,im in enumerate(args):\n", " subplot(1,n,i+1); imshow(im,**kw)\n", "def rescale(image):\n", " return (image-amin(image))/max(1e-4,amax(image)-amin(image))" ] }, { "cell_type": "markdown", "id": "eba7f81e", "metadata": {}, "source": [ "Distance Transform via Grayscale Morphology\n", "============================================" ] }, { "cell_type": "markdown", "id": "8a5883cf", "metadata": {}, "source": [ "In nonlinear filters, we considered a special kind of grayscale operation:\n", "morphological filtering with a filter constructed from the distance\n", "from the central pixel. Let us look at this on a much simpler image.\n", "\n" ] }, { "cell_type": "code", "execution_count": 21, "id": "a498d68c", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "image = zeros((100,100))\n", "image[64,64] = 1\n", "image[30,40] = 1\n", "image[40,30] = 1\n", "image[50,10] = 1\n", "imrow(image)" ] }, { "cell_type": "markdown", "id": "8a17b334", "metadata": {}, "source": [ "We now construct a mask in which each pixel value gives the distance from the central pixel.\n", "\n" ] }, { "cell_type": "code", "execution_count": 24, "id": "51d8b289", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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bABUcqjGqRW24M+aG+JghIVDmzcQ4qjEjgHbu9nzOzhf5+pwVTou19avXBhPp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\n/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nnGrotej6zwZl/CWB/zcOk8tuYs5hSW4Y4aI4tpNbmhfJlzD5PNQ0KChCGDhWrpI3xZ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\n/w+ACb4ZtqVp9AAAAABJRU5ErkJggg==\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ys,xs = mgrid[:128,:128]\n", "r = hypot(ys-64,xs-64)\n", "imrow(r)" ] }, { "cell_type": "markdown", "id": "cee2e7dd", "metadata": {}, "source": [ "This expression will compute the distance transform now.\n", "\n" ] }, { "cell_type": "code", "execution_count": 26, "id": "03d5d2db", "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(128, 128)\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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erWoMquCPooGsHHpmpuPIUPk5gp8kY91oCJQh9hR582isG0/m8bGv+Jkt40Ga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\ndK8Az9JwnFR9rC+VeaNkZ3VF96gPVX9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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy.ndimage import morphology,filters\n", "print r.shape\n", "dt = morphology.grey_erosion((1-image)*amax(r),size=r.shape,structure=-r)\n", "imshow(dt)" ] }, { "cell_type": "code", "execution_count": 27, "id": "278239ce", "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.0 66.1891229735\n" ] } ], "source": [ "print amin(dt),amax(dt)" ] }, { "cell_type": "markdown", "id": "f006c5c1", "metadata": {}, "source": [ "(explanation)\n", "\n", "How does this work?\n", "\n", "- we start with an image having zero at the sources and a large value elsewhere\n", "- at a given location, we subtract the structuring element from each surrounding value\n", "- at zero pixels, this gives the distance from the center of the mask\n", "- elsewhere, it gives a large value\n", "- the minimum over the mask is then the closest distance to a zero pixel" ] }, { "cell_type": "markdown", "id": "a5e8f8d5", "metadata": {}, "source": [ "If you look at the output image (ignoring the top left and bottom left corners),\n", "the gray values are proportional to the minimum distance of each pixel from\n", "the white pixels in the original image.\n", "That is because we effectively placed a mask on each original white pixel,\n", "and assigned as the output value the minimum of the values in the overlapping masks,\n", "where each value represents the distance to the center of the mask.\n", "\n", "This is a common and very useful operation, but there are much more efficient\n", "ways of computing it." ] }, { "cell_type": "markdown", "id": "a65dcc7c", "metadata": {}, "source": [ "Distance Transform via the Brushfire Algorithm\n", "=============================================" ] }, { "cell_type": "markdown", "id": "5a0297c7", "metadata": {}, "source": [ "The operation we hinted at above is called the *Euclidean distance transform*.\n", "It assigns, to each input pixel, the distance of that pixel from the nearest\n", "white (or black, depending on the definition) input pixel.\n", "Here is an illustration of that.\n", "\n" ] }, { "cell_type": "code", "execution_count": 28, "id": "7a36d057", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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u+Bpsf82IJSOyEk0hhBDiYDBClNVfLZo2diRVXk5VQUJ9MWNmBI+V\nvei+V8ebM0b0IsEdmVvUXzUHRCSZFZCIZjs+kWSyC+0ZYbOLfVtm41fELZLbjFWSOfr10dGvDFeI\nPljwrmf6mBVMD/Yr4qzojnxldkOiKYQQQhyMTBbseX89Iw9Mm0isItGz16OSyQpm1oc3TjQ2Zg4z\nAY3kF403m6NsPqO5QeMfpboY7vtjZBPlh3Y9I2nayMbL9IuE1/Zziq+tRnPFCMip/xZzhOpcZqDn\nIvvV1spXYKMPTdjXAuqz8iFNj0RTCCGEOBhVubTXmShW+kdlkXDaGIwURfcYWaoKLMrT69fe88rZ\neUDx0L1ojCNj3ks0WUYX1fYcxbT3Znc0UT1WePaSTDQPKM4e+bJkMSvPuz1y2+KyH5RE9UdF1WuL\nylH/2e6/h0RTCCGEOBiRZDB10XV2nyn3+hiRqb5uVI7ENhKpipgyMbL5YOpEc8LOFXOezUH0fEH3\nVsF8HXZGNntmpa2PyS7ebZ9VwYq+asv03/fJ9r33LmaUx6lyyPpGosd+DTWTUEYKo77Zr9iOjEGi\nKYQQQhyMimh6ZdVrJmZW5kmTV4eRuqiOvZ/FQvlVjjY3JJeRdKL5RDHRfFYlMxoTc72CymK+Kphs\nnx6z5V4dOxZbz+aIYq6QLy8XlG9FTiuwY0Tztgd934yMsTvp7K4nilOVzaoQe0g0hRBCiINx0UXT\n5hWJYiRRTFtbPzsi0azEQTHRPCCx9GQ3+4n6HhHOc4gmu3PJyuaWFyND/Ti8XU6bh3efLe/rRHkw\n9fr6o6JVnSOm31MKYJbLaF3vcc+kLXpu9jHZdh4zH55EZZUcJJpCCCHEAWHFgKkzIxOsZCFhGpVM\n239VQNlYWRkaSyaRaJ4yUG4rJdMbN7quwu7+2PuzO25IIr2Ytn62izciWFXBrMREnOMrqD0zHwKw\n8S2jcUYkr89hdrdytP7IV2yjOZJoCiGEEAcjEoPq9QqRQG1YyUT1vXqMTFVEM6vnjTGLZ+cgGiuq\nGxH1y0g0mi80Nq/vCtHfoGWL36iOVw/lGO1eRtK5Ut5YeR1pNypnpwJJka3j3a/En2nnfWhROfZt\nR+L084JeLx4VKa5+fVeiKYQQQhwMVoTQtRdjRCCyPrb7nsxUBHJUMhnhZI52jJnARsKIRNCrF7Fq\nPkfnYARmNzPboYlib/llO5B9fVuWydAoNq/KPDJf/Yxi27JTCynqM8pzRfyRGCue36NxRndBbdvq\nrmeERFMIIYQ4GJ5URkJwEUSzP18pRXsIJ3uPmUNWPL06mbhG90fnk52XGSpf6/PqV3f1GHFk4qN2\nDHvJnieZ3k4h+9ViRmp7qnN1yt1KFKtndPeyKpXVr8ZWy2bbIiSaQgghxMFAC/9ICCIZqfRXrcP2\ngwTLK+vrVM7RPS/PGdGcnVNGLqM23jirc5TNQUS0u1JtZ8uqX4Ht7zOL9FOIExO3zwuVeeVRzHN8\ntXbPOao8ZlakvefCzI5mtW32FVZ2N7JSjl6XERJNIYQQ4mAw0siKplfG9FkpR8Lj5YEkc1QsmRhR\n/ZFjNh9ovEgwI+FE0onqjUpmRaIjKn+fhr7GyogYU9e2O4eI2Rxaw8Jsy07NqefIm4+RfGy97IOP\nlcI5Equ6a1opr+Yj0RRCCCEOBiONFdH0rrM+Z8szkerrjEqmV45E07abOVbmIavLyGsmoux8VI4M\n7NcNM9m0/VZ2NStfbaxQla5MeJEMjcQ6N+jDgYuyW7xCBjO8mJk4svJb2a1kyxESTSGEEOKAsJKU\n1c/uMWVsHU+ckPyw4pidR/3YnLN7Ud2qbKKxovqoLaqH+rQxsrEg0WUWxBnMV2X7a29MUdnI12EZ\nvJjZmCu7qZXc9xKyLXZP9Bhk9c5FPz+MXO0hnRGjX31lYlXLPSSaQgghxMGoSpI9965H72c5orJM\nMm2cPSWTmc8Z0WTnjpVNez8SUVTujYMRT5QX83eQPWghXYmZ/b0dS/W57UnmiFxFohy1Qf3P5mHZ\nc0dxtk7WfoP9MGPkA5KRr7ZGfyfJfHgz8zea1XG2JtEUQgghDkdFKpEknEo07U4NK5mjYtmfVyWz\nIpJI3lbNH4rBCiRqi3KuCKeNG31N0MIstNG113dWfgqpqfxNpV30M/GjeCgPltnxjxD1uTqf6vMz\nghVKRkCjHcvqV19HdjLZ8Us0hRBCiINREclZ0RwVJGYBtNVbJZlIXiv1vbGzQmvLvbGuBgkkK6Ss\nfEZjYMYVLZq3GCt3NPtyxB6SmX2l9iJ9rfScjD5mTFzvq7LRhxrZ85eRvBlxZdsy4orijn4lWKIp\nhBBCHIwR0fTqRPFQ+Wie/b1IhkYkCAlkVgfFtv1HIpmVZeNn5ochqxsJJ5qvyrh6qot3e53Jm83j\nHPLGSGal/Tm4CDmsZFT4ECOiVhXRrH7lq7HVHdftXoREUwghhDgYmWhG4nhq2fTiZDl4QjQrmUg0\no7mcFU1Uv0ok5yifaI6RcHrts+dXRvY3cn1M7yuoe33FkhHYiFtR0Oy4bsUxWCIJy2CkrbKbWZVL\nlkr9iqi2lr+OJJpCCCHEwZgRTebe3qK5HZEooXIkdTOSmQkoiuH1be9F9VeSSWU0z1HdbL4zoh0U\nJD2ZYHqMzOmp/kYwwutrj/5H5nR1/3v0bYWpQuXvJ2d3SUf/5nLPv9Hc7rcWz51EUwghhDggmSDZ\neqg9e13JiamHBBLlgqSwIpmMVDJx0ZizDwC861UwcaM5GpmvCtFuZh/T29VE8bY6qyTmlJLZ99mz\nh2SeUzBb2/9fr52RwtFdytFdzZm/m1z1N5r66qwQQgghICMSUBXLPYSoIsVVARqRTC+PinBFY2Cl\nDMle3+8eRLEr47eMLqy93ZXb4audtyPnfIysIDHPxVU7kzPs9TeaqA9GNlvLP4iQaAohhBAHw0oI\nIwIVsdxrMYZy9kQPtZ+VzKjfkfrRuGxZNqaRcq/uqvqRZGZ9VBe1ti6b/6zonEOaVuR9rn7YmKv7\njgRz1S7mXkQfvoy0Z+tmssnElmgKIYQQB+N2EE2vT+/a/vTtqpLp9YViZve8tigeMydsPRY0f0gs\ns7K+DsqH2Y1BY6pKSUVkorm7XXZN0eOxuo9zzFffLxImW7e6U7gHValj/0az0u9sLImmEEIIcTA8\nIVgpm3suwLw+I+FE7UckM5NWr25UJ2sfjdu7v/fC1/bLSCczHx79Ahf1n+1uRlQk86LIZL/QXx33\nooyxtf3yQR9ezLxu9hBO5h/uGem3Io2rZFOiKW5r7rzzznbXXXe1t7zlLe2uu+5qr732WnvppZfa\nyy+/3F5++eX26quvnjtFIYQ4OYzw2PPK9amEB4lMfx1JT9bWjimS3L2O3piz60gA9yCLm81ta7V/\nYbYv88pXScopBAzJYzbmlf2fUzL3HmckaewOIcu5/paTEVOvbn+vNf91xMim/kZTHJa3ve1t7d57\n77358+KLL7bnnnuuPffcc+2rX/1q++Y3v3nuFIUQ4uRkUsmcR9enFE3bXyRaXnlFOCNRtccZsczy\nZ6+RbHryPQsjm15uSDb7sou027aSc0ve7czo83rF33DadtWj7bNaH+UxMs5ZGZdoituat7/97e2B\nBx5o73rXu9q73/3u9vWvf7197nOfazdu3Ghf+9rXJJpCiEOSLfhnRdMr24NI8PprJFVod40Rzkwy\no3mtlKMxs9cMp5LNrY4dZ7TAZuKt3MHs2VMCbd6n7Lvv73YUXVbmLKN/h9jXX7mruTIH5nwkboZE\nU9zWvO1tb2sPPPBAe+9739ve//73t7/8y79sN27caNeuXWt/8Rd/ce70hBDiLFSk8lYQTe88k0sk\ni1kcRjJte9S/zRvFR2NG984tm+jHq7edVwWzbzeb78a5/qGaU/e9Us4vGlW53GC/alqdu5ldzUp7\nlK+XSzRmViL1N5pCtNbe/OY3t2/5lm9pd999d/u2b/u29uqrr7a3v/3t7a677mp33HHHudMTQoiz\ngoSpWo6uUX8rYQQzkh4k1EjoIsn0+otiMwKWjTmqF43lHKDxMn/r5cW6XWVJzIHkMvuHb0b/hnO0\nfRZ3pv6ouG51WsNfa698OCLRFLc1L7zwQrt69Wr7sz/7s3bjxt9+XfZzn/tc++pXv9pefvnlc6cn\nhBBnIZMkVM+eZ2Wo3kpGJQsJHyOo3tGeR0KbiaZ3jMbMzPu5ZNNbjHqSeOnSpfJO0QrRPLesnqP/\nc495NaeQuZl2e/2NJpvjiGxGY/VEFCHRFLc1169fb1evXm2ttXbt2rX2zW9+s129elWiKYQ4NJFM\nZtIZnXvX6N5Kst1IT/yyttluoieWXv9RfEY0vVyqc8zM/6q/KWP69nYwt/NNIE8pQ32fp+77XP3f\nLrKZCVJVyiIiIVy1uznyNVZUl4lVydMKpnY0xeHZdjSvXbvWnn766fbKK6+069evt+vXr7eXXnrp\n3OkJIcTZiHbnbB17npWhPvaGzSkTUbQ7WZHMSFpRvJHzaA480OLwFI9Rv1CNZBNdRzFXs7eIXQTR\nuwg5zMCIESNXDKu/FrvHbiZ6faG4qG4mqNrRFOLvePHFF9uLL77Y/vIv//LcqQghxIUB7bpF0hld\nXxTRtH15kujV8+5XyyMZtcdINL0xoHuI6sJ7BdWdEE827XE7z3b7bmXZzMZ0uwvvyE5uJGRRP6PP\n/equ5QrBXVXH1hv5Gi0zHoREUwghhDgYjAyhulGcavkeZLt9jIgiKbT3UQwkl7a+V9fLwZaPiiaa\nh1H6BaZdvHr5oAVp9BVaVN/b/WR/bhXsXNxq+Y+QjZEVtZF+94o5+rXVEflDY1ohm6298b0ly0Oi\nKYQQQhyMEcGMRHO0fC8iCezve+3Ytp5Een1n596RLcvGn5VXHxMkkLY8uo92QdCuZlU42XGw7Y4g\neaeS8Zm4FcHy+o3ae+XV3cpqLjPxvdeQJ47sOZPfKBJNIYQQ4mBURQctNNAuHLrO2lfwFq3VnbxM\nOJFgVmWyIpmVxyYaZwaqk+0mRfUzwYxAu5r9vT2Ec6TNrbxLynLucdnnlf0QY1Y4o/Jz75hWxBfF\nr8om+jDI9oVEHSHRFEIIIQ4GIzPbdSSaqE10nbWfBcmhrcMIZ1TmSaetn4kpc8zKsjmoUF0MR31l\ni2UUz15b4Ykk75xydMp+b2WxZeU82rFblUdl55ARrmrfK+JH9Tx5tG2QoK7a2ZRoCiGEEAejKppe\nmY3lXe8pmUhYKsKIhNP+eGWoDy+W7Wv2GI0Tla/apfF2llD/FSGKRHM7IkFhZBS1v5WlbWNPwT7H\n/GQ7dkwZK0h77F6u6iuTvhkZnJHNygcAEk0hhBDiYFRE096PxDKqu8dizouZLYI8WUSC6UmibWP7\nQe1tThUBze4hqrsjCG9OvR1NKyVocWrLvbZIHO31yI6m1xfzU427N9749+rnVFTFaeS5vVIuq/K3\nUhZRHq3h90ZW3rN8UUyLRFMIIYQ4IEiiZs4r9U6FJ4m2jJVMJK42VlSendt+sg8D0D22nNnh82TS\nCmd0b1T++vNoZ3NEOEfkiRHPEUFdyZ6yufe4qqLFSpxX194b6ZdtE8lfNq6KmFbPs3pbzjMyLNEU\nQgghDkYkR4w4ztQ/Fd7uWhUkgdGY+zqMRDJCm8nm6Px6i86obt9XJpzZDiaK711byezvzwjnqSRw\ndIc0i3luZnKwzwVGDEfun4Lq7uSMNGbXI7vATF+jsinRFEIIIQ5GJjfZeVU0vXqnwpM59sfm7kli\nFt9rj9pFfaEyW2cFNhba6bDXq+Up29X0yqLraDd0RAJXyh6zS3q7EEmmt/uX7UZmVESM3UGs7GZW\nJBC1RdettTfMG7Oju1I2o+emRFMIIYQ4GJEA2TqVetF1VYRGxMVbyI32b9swMplJKnPOHL3xrBZ5\nu+hkdjS9BW8fL9oF3fB2MrfzXjTtPeba9pPtdjLPvxkBROPPpHikH2a8I8wKcCZve+1UzgigF2eF\niI7Gj+bNE1DUNzMnnlxG+Us0hRBCiIPB7Jp592ZEs5LXdt4vaJgFbbbT50lilh9qb+sg8aycR/e8\nXLKxr6Kyo5l9QMB8gODJpieXVeFcvaOZxdhLVCt9VHKYkc2RtpGQ2efZCmalblQqVwt0JJFIFlGu\nrGx6HyAxr2WJphBCCHEwkLDssbNWXUx5fVSxiydGJqM6SGAjcUVzVZHMPUUzWuha8WAXnivxZDI6\nbueepKL4zA7f7NgYAV0hu6jv7N7Kxy4SbtSPFZctzqyEnYMZAc1ej4xEsnFHZdMry5BoCiGEEAej\nKppsGXvN5lZt21q8YIvE0CtHbat4EsoI556iaWEX6NHORnas5sMct/NeZqLrSPKiHFYKoM0/qsP0\n7Qk2I9l7fEDQcyrhq8pltNM3KosjconyaY2bu8puZCSqXr+sbGZINIUQQoiDgSRllWhGfYzkV5Gg\nFSJo70f1PTn1hHGVZGYfEsyCFsyelFQFslLf25mMjplk2thILBlpq+zYrSYTSHT/VPl5rH5ujpav\n7HtGQKvnTB5sP96HQyj+CtmUaAohhBAHZVRmovpe/Owem2cEK0aMJCLhnJFlGxvNKyOiXh8zC+xo\n0Rjt9G39rt7NtH2gXcztyEjmyG6mJ5wjoreqPhsTCfCMGI/mioSmCiteXt9ZzNW7mUz7TBhtHUZC\nvdgV8ay092J4SDSFEEKIg5EJ4yrR9Mr22HEY/bTdgkQQ1UHltq4nkF5/rGRmj9MojCjOyONIPvY8\nOjKSWd31Y4RtZi68WFm8VXPP5p7NXRZrtWRmO3F7MtIPEs9RwbV5ZO0YSUUfHkWxongbEk0hhBDi\nYGS7amwZI5pe+SkWhIjK7iQSRa/Ma4di2jqZZJ5KNDOiBT4jqSP92XN0ryKZ2a5flE8kqlmdCpl8\njghqpV973pd7MLttMx8AjYytImNsHLbujESifCvCvc2X15bNJYrlXXtINIUQQoiDcXTRnKmTiWe1\n7qxkjshmtOjMFsZo128PkAAicczO+3uRQGXilsmfrbNKCpl2I/2tfEyjDxlmXvdevGjXzeYS1a8S\nCV61ffR6q8gmqpOdW2n06m3lmXB6SDSFEEKIg4HkhJWaW1k02f6tJHrC2NdD11G/jGSOfACwGrSw\n7hf+kWDM9IuuZyTTjsHWs31GshYJJyuFVUZlNZPNyhgjst2yUeGrPreynbvReOhe5UMbdn6qstmP\na0Q80VgZ4fSQaAohhBAH4+iiOQuSTqYOEteKZI4+DpbRhbGVNW/Bbu+NCCgrmtuRlUxPqiLZtDlk\ncon6YttW2KP+aD6MRO1BRfYuEpXXGyubTP2K8G5E7wPRvEo0hRBCiAMSCaa9V5HRrK+sbpWRBWS/\nQPXOSp4AACAASURBVPKkrwI7fracme9o7lfNLVqs9n2g3a9VVEVzO7ISmtVnBLGSvy1D5VG/magy\njD5GXrvV8oZez95zb7bviqCuEtdIEFFOo7GieP18VsfECOaGRFMIIYQ4GIyorNxNu0g7mtliakQ+\nvZ1Irz1Tbut65/ae1xaNPSrf6niL774dirNSMr14rGjaoyeQUTx299HL0RtDVRyjWN4509+snHp5\nIDnpnzMzZDtqs3HRrl+1D6Z+JpCREEYyiK4jqdzOvf6z8qiNh0RTCCGEOCCssGRSetFEs/qpPENF\nNlEZOz9ITqNzr/9socjupKAFa3/dn6+UzYpoevcYyUR1ovtef5HUobF5wlmNUWFETrN8ItlE/TMi\nmsnYCjKxRJI3KqRebJRHFLsim63hr71GfbLzn82BRFMIIYQ4GNFOWbXc1ov6Q9enZqUM9TA7lqg8\nEkx7jWJ7+VSoCqa9Ht0hi/JB95DYViWzb5dJZpSXlycjbdGcMX2uks0Z2OeZJ5iMrEXCVIWVxxUy\naXPNBJHNlYmFXr/2vCK4NhaDRFMIIYQ4GJkojoimreP1l93bE7RA8qTNYybfSuxITtE16ofZEWEX\nqNE16qPPY1RwkEj259G9SOw8mYwkMGo7Mi5WdNlYbC7VfCtylPUXyRsrnbP5jDAjqMzrDYntKtn0\nrm381vzXKnqsUP0eiaYQQghxQCKZZEXTa2PPvWu2LIL9ZD3bDYkkz8sV/WQwspnlgqQT9VHZpcgW\nqDZeNLZIDi1Vae2vq6KZSWpfxuRjY2c/KFZUlsWOYmZjYOpFYhhh5bK/zz4vmT4q0obaM7I4khcr\nm9m42LiV6yi31t6442lhxyLRFEIIIQ5GRTJZ0WTPo3xYVi4Avf5HYjMCysgpEs5IMr3HiBlHtmC1\ncSJ5QPEj7CI2q58JJXvMRNHrwyuriuCIcFaEcQYvxoxkog8fMrmxfdtz1EeUZ6VuhUhMK7K5sm5l\nvNFj4Ekm+vApeu5JNIUQQoiDkcllf56JJirbSzRnJXNFDhWyPpF8MsLqnbN9e0QLUhuPFRtUDy1Q\nWdlEx2qd7ZwVXit2mWBGwlkRS0YoUV8oDvMYzj6HPIGx19GHLkyOmYgxbRlpZKjkksVFIjgrm54k\nRmXomhmDRFMIIYQ4GEgGM8lE8piJpneNcpqBWRCyi8aV4lmJ5Yllfz96zGxf0eLW7ljYhaaX/4pd\ns9k6I2LpHUfOkbShPDPhZGJH8srmlYnthvd8sHX3+kDGI5I/NqfZnDNxzKQvGwPzeszqsxIflTMf\nCKDr6DUr0RRCCCEOBhLDaJeMlU0kml4b5j5DtDhm2iHsrqL3sxdRfE84oyPCW2jamF6Zl48X27tm\nRZIpRyIZlVnpqkomI3423xHpy8bulVVEGBE9luwHNEheK0SCiMoiIbXtbB1P9qLYM4KbyWOWq9du\nGwPT1pPEGeGM5kGiKYQQQhwMRjQrx6ws6j+6xzCyILVlIwvhDTbvUUmN6mcfDtjzaBfE1vfmJJrL\nCE/gsrpMeSSaqDwSSi8+qm/LvbxsLkgEvTyi8UfzyIiw196Tjq1t9bU5Kpdbf30OK8SuEmcjGgOS\nzkwgvdddNM6R8z539jU+K5zRYy3RFEIIIQ5GZTds9sjkwNSfgRHOGdkcxZPPSEbRGJgPCSxol8ru\nRqGyKqxMzYim196TTCSXqG61HPVn5wGNjZ3nTNyrj5f3eI++Lvd6Tc0KZwTK2b5HRJJZzc+TRhSD\nEUw2jq1vx18Rzmi8Ek0xzJ133tne9ra33fx505ve1K5fv37z58UXXzx3ikIIIQB7C+ZFEs2NbOdh\nNI89c/fmCclotKvpLZZbm5PHEWZlE0llds6Koa3L5s2UsyLqlSO5Rfmifjcqu3vnoiJeUftqf17b\nSqxMHqNYnri2hr8WG5V57VGeldiV+aBE89VXX23vf//725UrV9pv//Zvt+eff77963/9r9sXvvCF\n9uCDD7aPf/zj7Z577mFCiduIt7zlLe3ee+9tDzzwQLv//vvbXXfd1Z555pn2zDPPtKtXr0o0hRBi\nR2Z+N0dyGAnjSDniHKJp8RZPo7mcc8HuCWd/RIvdLOYKCY12VLI8kDhlsTJx8+pG9aI6Ud2K+GWi\n6+HVQW3769WSifKciT8qdlE5Onp1vLhZHFYmbXnWD1ufPY/mjo1t80TcAUs6fv3Xf709/PDDNwM9\n8cQT7bHHHmtPPfVU++AHP9ieeOIJJoy4zXjLW97SLl++3N71rne1Rx99tH3f931fe+ihh9r999/f\n3va2t507PSGEuK2Z/d3MCKMV0JHrlT8zsbO2fbmdDxYU91REY93uVWKsyCci272Lytg6ttz2a/Nh\nJBONJWoX1Y/uZ2NjYnm5nOo1WelrZd2t3B6rdWfmKssh6ifLhY3FjCWKVcnTIxXNL33pS+13f/d3\n28/8zM/cDPSJT3yiPf7446211h5//PH2W7/1W1kYcRty1113tXvvvbe9+93vbh/4wAfa933f97WH\nH3643X///e3v/b2/d+70hBDitmX2d3N1IXZRf0ZyztqsZkXMan62bmW+VpHFygSy8sPGs/WYdlsd\ne2SkD9X35iGan2wOs1h9Lq2dTjJP0Uc1h60+e0TnTLtKOdM2G3uWc2UeK3lGr/X0q7O/8Au/0H71\nV3+1ff3rX79579lnn22XL19urbV2+fLl9uyzz2ZhxG3Ia6+91l566aV2/fr1du3atfbKK6+0b3zj\nG+3FF19sr7766rnTE0KI25bZ381Xr169uTi4++6729133x0uyPpztLjwFiO2bOTeBvrqF6q7xau0\nu+hU58Crm8nLqfHEq3Jt72cyF5VbaUNHdicS5RsJarUsyqlnz9cbam/7sDGj52jlvi3PjnvD5uld\no7L+2NrrvxZvr70y276HiWWvP/OZz7TPfvaz6VyEovk7v/M77d57723f8z3f037v937PrXPR3rDE\n6Xj55Zfbc88915566ql248aN9ta3vrV97nOfa88880y7fv36udMTQojbkhW/m++///7WWu2rZF79\nnqgdc43KvAVrhLfIixZ+3sJsJSsWt5U5QIvLSK4iiZnNeaQ+OmfueYLnSWLUXyaZ6Dpqn0liVSBR\nfTse5jkz+npD4jLynM9etyslkZE5K6ZRfll9Jl5FNrd7reWCadv39/v4lVittfae97ynPfTQQzev\n/8t/+S/uXIei+Qd/8AftE5/4RPvd3/3d9uKLL7avf/3r7Sd+4ifa5cuX21e+8pV23333tS9/+cvt\n3nvvjcKI25SXXnqpPffcc+3GjRvt2rVr7c4772xf/epX23PPPdf++q//+tzpCSHEbcmq383ZV6TQ\nMRNNr5099669/KqLy2iBxLbr21aJdgv2JlpceqLFxFqVU7U+Eqgsrid91SMjmah+JLeejGZlaFzR\nmHsqr6GLsvtfzaF/ju+xm5kJcFQfyWaf94hsbu23+308psw+X6qxUF13Pm6Qs/6pT32q/dqv/Vr7\n7d/+7faLv/iL7du//dvbv/t3/6498cQT7dq1a+4/OrDqjUpcTN70pje1u+66q73lLW9pd911V7t0\n6VJ7+eWX28svv9xeeuml9sorr5w7RSHEbci5F0IXidHfze9///tba744spLJiKYXx6vjkS1gtrF4\n196CH9X35KE/euNGc8HWrf5ksftyNOdIfDzpYctHf6K598SpIpp7HZnnCiOizNxmj1OUUzQ/Eczr\nLYLpf/T1yjze1ce0j1Ftn/U7U7dStmfbao6PP/64+55e+n80t2Af+chH2oc//OH2G7/xG+3BB//2\nn1AXx+PVV19t3/zmN9s3v/nNc6cihBCHZeR3c7STWdnNrOxqjojmLJcucTsP9l7UrtrPKP2CONtt\nRTsl2aLdCkqUw0q8uGjBH+WRiUsUK1v0o/ZRHHaBbu+hMvbaMvpcHG2XPf/75+Ys9nXR973qdcvE\nqfTl5Rjlbcta4/5ukmlbvT7ZjuYIe71BCSGEOC7a0Zzj0qVL7Xu/93tba/G/UJiVewK5UjTZsXjX\nmawwkrAdmV3FqGzVzifTv3dE8+ONPbuflVV+sjjocYyeB4xYRvMQ3bP5ZverZdHcMHHOgdcves2x\n9bLXKYrTz0fU1tZhH3evryhm5XGbedxXXc8+l3/yJ39yfkdTCCGEELc+mVB695hdTxTb1vGuT8Wl\nS/P/8qWFGcvWrrrjEvXRx9zy7Y+ofiYodtHulUU/1bFF5UzMTCbQebSYRnEZ6agKiSdJ2XWP93hf\n5A/k0GurtdpXeO1zfjQH7xzFrvRlX/Oon61Opa+sLnO9Udm1rO5oSjSFEEKIg8HsQrJyWT2iPPbE\nWzSicybOaP+V+q3h+UELWGaBHsmTV7cij7YPpl4kqWz/mUB7klYRw0w82VgoPzte5joTy3OIZvY8\nz57XI32hPrMPXVA8pnzkvYONEwniCrnMPrDKriN59pBoCiGEEAcl2rFkJXNmVxPlg4gW19WdBrRI\ntQu7U+ItxL0covyyhTUrTV67ynyMzl0mn15sT77Qua2fyeBekhmNMxJlyzl3Lmf7HhXPTDK9ul47\nJGJM/Oy9I7qfiWpWv7X4bzaZ8g1m1xOJ8VYWPT8lmkIIIcQBQYLISGZ0z4uNdlBRTlWYnQHUxquf\nLc5Gc8tiRYs8rz27W4PaZ2KEJIiVzpWizooYGp9X3xu3V86UjUpmdYz2uXpO0bSMPB8tFYn02m3n\nWz62LGrHxEa5bv1Fr9tMNrMxoDF5fWblUV5eLDS+bP4kmkIIIcTByETR3ot2Pr32kXTacy8vD3a3\noFre1/EW87Zsq89S3XVFC8w+HnMvi9+fR6LU10X3kJSuJhNHlC8rml6Z129FMqO4bBsL+8HN7cCs\ncDK7mZn0Mf31jxVqn8kiErmsjY3f5+DF6u95faC6SF6j17xEUwghhDgwaEdzRDLZXU3vOrrPSma0\nmPTaRIs2G2+7jnKPYIS4j50tEtmFHuqnv2YlyKuT9YFkdFRSUb1MJrMyJHhV4cxElZVcNK7WLrZo\nzuxqMq/fqF0UayRGdH9F3ja+95pGZdmOYhTLlmdjzfLSjqYQQgghXkckmFXJzGSyKptRrqMwgol2\nO2byyOSUFUy0a9LDLvKR3GQSlAkQ6qMCkkhP5LIYmUhG8VB/KyUzGrMle23d6lTkLItRPWbtt7KN\nSEhZCYwED8ln1I8l24WM+vbi2Pbofcki0RRCCCEOhieKvTB6daJzWx/dGxXNWbJFYCabluhTf1SX\nLc92N6oC57WpSFckRVYAkZxWc2YlFtXLhC472rZ7SWbUxwbzHLxIsjkrjJmcMa/PFf1lfbeG/w4T\nvXajfqvymc1BlEN27cVB9bP5k2gKIYQQBwOJZn9v9Jw52jxGyBZmbDvvPlpQ9nXYvqNFnFce7WBs\n99EOhicpSPQY6coEE+GVIxkdJZJNVigz0UTHSDK99ln9TDK959BFFU1E9hqJxjDSFompJ2mRxFUF\n175eWxv7m83s2uunJ/vACvXPxmJyaE2iKYQQQhyOTDT7MnQeyeQpRJMFiZq3+MsWn1nOSABRmVce\n7Rqwgob6ZEXKO27n3jWSyEgss7EwYx2VaNs2mhd7L5LGESmNhHmDef1cBNlEr5msbnTPK69KXzV3\ntt+q5I7kwb5HeXFaGxPOaqxobBJNIYQQ4oBkkmnr2TZefabc5rCa6gI22lVgFojMYnLFgtBbvHpk\nQjoqm5E0eX14kuuJaEQmsigOI5AVwbZjGpXMLBdL9nrJnpt7yqeX88r+KnLW149e/5kARuX9eJm8\nUAwkpn3c6D3JXmfPnez9zatbiZUh0RRCCCEEJY3eDgqq4wlndD4DI5dI1LIFWCRTfR3bV09WZhex\nTP+2b2bRZ3OoimZ/zkgnI4aZtFZYLZhentl5tW5r8etgZBfzFLubFdnIRGnlLiaKH0ledb7Q6zMS\nXK++bRcJZyaj2bhmYzF5ekg0hRBCiINR3QmJdipZycykcwXVHYv+nj3frrc8+7ZWFpgFW7Q4Y2Sz\nsqvJzJM9n5HMPlYknFndvp79Ycc0I5RZHTZGNF+2ncV77kSvmaz+OYjkrSqKo/1lYsm+B0R9VcZi\nH3P0PpNdZ+8jtm9bxsbycq0KamsSTSGEEEL8HZ4sRpKZtevLo+OeRLK55WAXjzZvJE+ovq1jy7zF\nZ3aNqOyAenlVxAxJJpLIaN68ulHu7LhWimbWvirlaByMLGavmT0/wGHJxAO9Fr2y/p4nh5X4TJxR\nuR2RTe+1vtXLriPJi+a/GitryyLRFEIIIQ6IJ5F9GWpjj5FknmJXk1lMMgtctPjs8/QkiVnUZfmi\nPvbYzbTj6q9nJROJZSaXSFIjWUU/KKdM+KqCykhmFJt5LYzK5jlEM3oteK+vqthV+xuJgd4XNtB7\nBiOdkdjNCGYknD1efVYgMyGN3oskmkIIIcTBYHdQst3JGcmcWRSPLFKri8oNbxEWyYG3KLTxkAz3\n5Qyjwjkqmtl5fw/JVpQTqoMELosTCSc6Xy2cPeh5w34Ac5FFswp67lZf24zkValIrCebG9F7A7ru\n29n3BLYuM6bofYrJO6rfI9EUQgghDgZakHpiacu8euja64tdVDNkOwvMwi4TSW9RZRd1aOeB2SlA\nOwzeIjMS4gpINPvzGcm0sZF4odyQgCCZZftlpDMrq4gmGvPohy+siEYxVpLJXVYePZejtiP9jr4n\nRDmgMVRy8wTRk0gk00g4vTxsWfU9L5sLD4mmEEIIcUCYRW0knCskc2QHZnTHI7rux2bv2fyYhagV\nQrTrEInjCqFEVEVzO7KS6clfJIkox0g4szJGDrPxonyqErvhfbBjz9HrDtWP4lfLI5jxzMTOZIZp\nFwmmPbd1WvNf54zUbm2ZfFAe0ftQ9CETem9B91BZ9PhGko7ib0g0hRBCiIPhiV5VOL2yWeGsgBZ1\n3qIok83+fj8WdD9bwHn927b9NVpIZuWjRKLZX6+QTK++lw+ST7YsiovGFB2986q89njP9RnRZK6z\n9ntSlcZTE0lp9l6ykb1HZIKa7RBmoofqRrnZ3Jmy6P0JxdiQaAohhBAHxhNFu0vJlnnXkdRmOzSj\n2EWRJ4docZQtwLyYlbqnksmIEdHcjqyE2rieiEaiGM0Bqh8JaZQ/GjfbNnsu2evo+R99+FIRTeaD\nlQrRjtYoTF6Z/EVSONMv6p+Jk72O0XtMFB/FRILJxPbuo1jMeDwkmkIIIcTBiRYK2Q5LJpz2/oxo\nVnYJovOoP2YB5t3LpDKSzY1TyWYmdplQRZLJ1vFkMBJVL18kqbZOlN/I2DPRZAUzqxedZ9d7fIiz\nKo59HewhiEx/G5EsVvv3xNf2g95jvPvZexcrmOx9lGckmdFrUKIphBBCCHfH0pPIqMy7ziSTXRBH\nizxGKrMFmc2hUj4rm+zOwUpsH4xs2XuMZPbtPMnMBJOZCy92JLGeoDJjzObGg33u22vm9cGI6p7M\nPldnxNGTVPQ+gNqxeXiiyua3tbNx+uv+npcP0y6TV7Z+1p8XJ5oPiaYQQghxQNgFXlRvRDgri+0N\nZmEYffIfyZ3XF1Pu3UcLQEY2szLLikU+uo4EczuPJNOTMUYyvbaovSeL3hi9cSJJzMYYzRMSQ+/5\njuSREceqnJ6D6PWKZI9tH92bzRPlasu895qN6D3HXmdyyUgjI4UoL1SficW+90g0hRBCiIPSy5/3\nE9Xz4mTXI4vtiGxxxginx6zEeX2xssngtanG8epGsonKIhnt60RSx8ZH48gEFEku6tf2jcR0A314\n4j3fM3nMxPFWEM0qSO4YwbTy573uoj6RPEZiFn1gFb3n2Gumrid9Kz5Ai+pXY0VINIUQQoiDwS5E\no3oV4fQkc1Q0WbnsY7Gf+m91RiUzWoxGshnl4C2GZyVzI5LNTDC3I3Ovb8+Uo3NGKr1Y0RhZUfba\ne89VRi4jgVwhmii3iJHnUCRyI3iy54mgrV8pY+ui95XsNcwIpjdWtoytb6m+F2bvT7ZfhERTCCGE\nEMMgcYxElN3dich2Prb7fcxsIW0XV9VFtBUVVjbRoi5b/FcXl0ze/fXocTv3RBH1YfvPJBPVR7Ey\nqfXyR/c8vOd0RSyrZex1hNdP9Lig9jPCWRVIJhYjqbZvRja3e63h9wpGMG17VMbkjGJ57aK8svoo\nh76uh0RTCCGEEJDqwjWSS09GbR8zC1YUI1tUoRjVHR4vXkUsEZGkZm36XLJc7flq4UR5IImMJDOq\nz4zRa8OKcGu5IHrnUX3maM+Z6wgv/rmI5NATm0gQR/pFsezjPyKU6Dor894rGEH1yPLK6tsydt4l\nmkIIIcQB8eSPqVutj8r66/5oz3uyBVhfz/bp3d+TrC+083KufBjRjMqsAFbPkWAyY2EENZuHaKw9\nrCieSzTRPUTfx4i0jQreXiBhXSWuUdvqdSaMSHoZefXy9tr296L63hww71cSTSGEEOJgzC4MrXhG\nAsoIZ7SwRgs15pP5UcEclb6tnZUWmy9aUM70nTEjmuw9K3ZVyaxIZ1SXGZ8not4Ye6zwsaLpHVeU\nodxQHWZMFbzXpo0TSVxVUkfro9cYk6cdD5PXyHXfDxI5RjCz564nmNX3zsp7lERTCCGEODirdiQi\n8URl0eK8B+1IoMWYV8aOgW1n8/TaZQs15nwFq0QzqpuJWySQkWBmApi1zdp749iYkUn0nK5IaFav\nhxFQRFWsbL1MAlfL5UicLWeUS/Qek411Vja9HBGecDLz37ft79m4XpnXL8PhRTOaZCGEEEKM4wmn\nVxYt2nuyT+7tAm3kd3pFMjNxGVks7sVK0fTKWMnMJJApj8YQySjbPlu0s8/d6hGds6LplVVeA6Nr\n4Kr02TZM+4qoeu8TqA0rm147G3eFbLI59+WROG9kkhi9/4wI5sZhRfPuu+9u99xzT7vnnnvat37r\nt7YXX3yxXbt27ebPK6+8cu4UhRBCiJNhdxxP9cFrtGj3FlDRImxPUbM5j/Q1IrEjfaE2zI6evUay\nWdl9tPe9HcgoP1ZGo3wq7bMdSvR8vdVF81aH2YVE7ymeoHmvo2gXcuba66PSdz8ur37Ujy1H/Xhl\nKPbGoUXzypUr7R/+w3/YHnzwwfb888+3L3zhC+0LX/hCu379ukRTCCHE4VklnEwMtFC3C6iZT9dX\nMCJ+o7mOCCez08rcZ0QQySOzm9lfozpRXSSX2dgiOe1ZIZmMUFbKbkfR9IQP7dChtkgaGdlsDX/1\nNBO5jej9aUYwWeGrvL9E7Ubk18uz59Ci+Y53vKO9733va4888kh75pln2pvf/OZ2/fr1dvXq1XOn\nJ4QQQtxWeDumnsh6i2m7eDxlzpbZ/tn2aCeXaTOSR2U30SuLJLC/n0kmyiFqF/UT3ffuWeFjxbI/\nR3Vtnag9c/S41URzI5JKJIz9OZJGFDeL4dWNRG/1DmbUn1c3i+2188bBlmX9bhxaNK9cudLe9773\nte///u9vn//859v169fbM8880+68885zpyeEEEIcBrRbdC7B3HJY2Se7Mzmyi1mt2+eDrm1ZJpq2\nnnc/kstsRxPlkeUdjSd7HPrzyu4lI5q2/cgxyzu6N0q2y7gqfqWfaFfUK28N72L2dTY86UPXrHCi\n/pAgZyLuEb0nZO+rlbba0XR44YUX2jPPPNM++9nPtre+9a3t6tWr7emnn27PP/+8vjYrhBBCnJBo\nEZcJwSlyWhULCeRqqa3klN3r70cimZVn7bx6fX2mXyS0kbxaPMFkdzWz+raPilAicc3G4F2vhBHC\nEXn04kc7lV5spj6TW9aX97qu7Gii+qPvEdlurpcHs2OKyqK8Diua3/jGN9qXvvSlduedd7YXXnih\nPf/88+3pp59u/+///b/2N3/zN+dOTwghhLjtyBZZW51+8ZJJyJ5UBCWK4R0jTiWetg9GNCvH7dx7\nDCNZ9K6j9ujxycpsrntL5ohIRruniFOK5giZ9EVtKvJo6zCy2Ro3X97zxvaFyqJ4Ua49WaxMbL3c\nV5X1HFY0X3jhhfalL33p5tdl//qv/7r91V/9lXY0hRBCiL+jsvCajWM/yfdkczs/tXD2rJBNxKl3\nNmdF096rlkeyiM5RzL6MEU9LJHTMzmRFMisi6cmvvY/Ggq5PRSR5bLv+uiqbrb3xK7Ioj6wO+kCi\nL0M7mvacETe2nkcm7WhcdmxsWdTPYUXzG9/4xk3JvOOOO9prr73WXnvttXbjxo322muvnTs9IYQQ\n4qREi5pT9IsWVkjSrFCcU9DYNmjBXI23SkhZ0ezL9jhmktnnEIkoev5E4tlT3b3szyuSmYnk7SKa\nFZgdv6pseu288tbeKIlRPuh5w8SKRBfFQn1H+Xn9RmT1Rt9zDiuam1gKIYQQYh/QYskrQ/KFjlF/\n/XXl5xQguZyRx9G2kdij+8zjEglj9niiNqxkZo+tN75I5hjhzOqja3uORDISVw/v/grZzGTQq8tI\nIOoDvUcwsZjYjJz2/WdjZWNFz0EknFFdr3xkDFE95r3c47CiKYQQQoi/pbKAZGJtMJ/GZwuwTGC8\n+qPiWGk3I6nRmCNpZHcnqnkw91mx7O8hYUTxVkkmGpONHe0mrpJM1I4tQ/V62B3Mmdc4+x7Bik2l\nP1YwUb1K/S13T3h7Ion1Ynlxbfs+bkVGUawKzHvLyAdaEk0hhBDiYKwQy0yGvHpocZYtXlg58dqN\nCudIm2gnrdqPnZeZHc+R/m15JJjeeSSGXrwVkmn79x4HRhoY4RuRUnuPaRvlEOUfUXntz4ijJ3qz\n7UbkMZI97/0JvS8hkbR92Xz7fhFI9KI+s/dg9j3ai+1Ribch0RRCCCEOCruIZBbnqH62qEELQRTP\nE4vterVwriDKaYNZhO6R/0rR9OowYsh+iJDFQs+LPre+DpJLRhQzyYykshK3z83mGtVZKZoVPOGr\nSGbUPovDyGaWF3oPinYSvb56GIFEsW27mR3NKMcoz1kkmkIIIcQBqe4ysDFbixdLW3l1QZPtI3XF\n6AAAIABJREFUXHn3mDIkoSsXXEjOVszLrIRGbZm8o/NMBveSzOzxtVLmvQ4i4axK5shuZrRLme1w\netdsWQX0HlK5P/I+hGSRlc3+Xg8Sueo16mNESPtyG4t93c9+kDXyQeSGRFMIIYQQEGYnYSP79H50\noWTbZgJi4zL9oHbMT5U+Z3ZX12PlTicj2+gxQOWZXLJlo5IZYWXO7miOSGYfC7VBxyyW1w7ds+Nk\n7lWIxCpqE4kaEsQsXiUWElQ0LvZ6uxdJolff69trV+kri12R4Si3qL8eiaYQQghxMKqLOVTWWu1v\niLwFEitLkeR4coGus75GxTGLn+W3wcxHtvsxCivonuDZNugxQe1HJDOK611vMDuafb2ZnUxWNL24\nXh7oXmUHc0Y02fcOVBeJYCVulgsrm5aZHUzvfS0qy6TVa2fb2n5GcoliZzDvQxJNIYQQ4sCwn4wz\ni5fZT/4reWZygcq9WFlfK/Gk1NvVPAcV0dyOI6LZX1eEMxPVTErRTuF2jeRwlWRWhNM7snUsK0Vz\nhEg4V4krEkqvXSSoG5EMZoKV7W7a3PqYXh5MjqivKE8256y+djSFEEII8TqYRQJTL1o0WZHaQGKV\nLXaY3TEkNpGQIilCZRkjdc8tmX0u6NqWMaJp42Sy6JWNSGY0BiSEkXz21/bci+nFsfX2OHp4ZYzc\nVSSQwUph9bjFsGOw7yWeYHqyaeOgsUeCGQlrFDd73c/KbNTWy71St6+fvW9JNIUQQgjxOtBizgMt\n6rYydkHCiBYSlu3IigcjUFEZI4R7iemeeHlkc2HrVEQTHVdIps07k0jvvhXJTDiRmEZyOCOUXnuE\nN84qFfGcldRINrP+ovPW8l1Cez+TXEtWlj03s7hRzl7b6EPCqI+sLoNEUwghhDg40cIk+nTelqMd\nBebTe3Yhw4iKNy4knPYnKq+C+vDiXVTZjERz5ojKIsn02qH6KPeKXNqy7bovi2J4dRlZ9XJFsU4p\nmiMgQWTue7LZWv29yPbFSlokqIxgsgKZwYrriCRmkprllX0AINEUQgghDky04GttzY5mRSSZfPvz\nyg6Zd+3Fz+TKno9yUeSy55Siae9HkjkqpT2RGDJl2S5mJo+RTFZEMsoHcSrRzMSDqY/eP7x6VVn1\n6m59obI+Fw8kmIzg2TpMHih/7z24ErsC+54u0RRCCCEOSiSB1U/nmR3NlXmzx0xevJ0w29brO6oz\nO66ePeavksOsaFbKmPOoHOWbiZ0t88h2HFGc6JjtgEYimUkoyj+7t1ERRvQekckhOrd10bHv246J\n/bCLFb5oPpBgZvPr5cLKrNfOvgezooyo5u8h0RRCCCEOBvoUHNXx7vft0XVPtGCsLoBYuWEkE43N\nxsnkJvqpjidib/FcJZqjZaOSac8jsdtA0ulJoBcL1c/k0uubEVKbo3e05egalTGShOp6Ioja2T6z\ndpFssjl547LvXyiOrdvjSWDldZpJpJdP5b2CEViPFe9HEk0hhBDiYKDFVV+GFnFox6CPh3YTVkkS\nKyzbkZHOPl4kiJFgMvmisops7skeosnUY6U0ehxRvtFuYHTPa5/tNNo2kVhG4mrbZKIZnXvXXr6Z\nIEZU2yJhrMqmxQrmdr6VMTKX3fPysuW2n4rQRcJbEeCtXiSZ2ftNJsHZ4y7RFEIIIQ6GtzhgF0vR\ngiOrZ8tnxDMTku3IyIk97+9F9yNJzeQTjeV2Ek22HhLJqCyr2xr+yizaBbT10P1IIqNdShvLO0f9\nReKIJBXV9xgVzNbeKHVsLNTOk8QtRySoXkyvrI/l3bf9oPa2PipndyBRPqwsV2Heo22/I3lINIUQ\nQogDUvkUvb9vF2Fo4bHXbqaXf0VOvDaewHgCGeXCClk1xsicMQvtLJfsHjP/bD3myDyOG9FOY1+n\nP6I67I5lVs7KaLSbyexYnkM0NzLJY3cqs/jR+0llx9ODfb/KxJApQ/VQnlFuK99fs11QL1+ERFMI\nIYQQN0G7Ca35Cx10jli5IKrsjjHnXnxPOCOp9MqRyHo/ESvmd0Y27X1GMPcQTXTP4skduyOJdhdt\nfNS+v+/V8dqjmPa+7d8rP4do9tj3EUYkK3VRuSdizIdoI/33RAJWkTO2biS0TB/RPIzG8pBoCiGE\nEAeDXaSxn6pn5yvl0uZrz9ndsEhe0K6Z7ZuRTrY+GtfGyBx6j18lBhp3dF4RTHtvVDgtFWmq7mhW\nJBRJY99vJqa2rs2ZqZONkymvEElm9t5j29jcbD0v/+z9y97rqbzOvD69cjSOqC5bFuWEWPVezAi5\nRFMIIYQQ7oJww1swRQJZvT+Tc3SeiaVXd0TKkKCiMnsvaltZZPbYuY7ELBsbc30q0UTHaJfQA8ki\nkkIkkoxQsjJZkUz26I03m49VIMn0pJI9365tzp7wZO9hKOetPJJRGz8qz8TYi5VJLBsnYub9mG0r\n0RRCCCEOiLewQQtBW4epv1oqmTGwO2DoHlvHk8IoL1uWzUsku5kQoNiVxyLqP7pmxdA7rwgnuueB\ndhz7sqgtWz8SzBHJXCGYlbF59zL5WSWnI7LZ51fdDRyRyEj8MsFlX3usXEZ5soy+P1f7lWgKIYQQ\nB4NZxCBhjGQzi7Wa6u7aiGSievaeV5bl7rWNBGpmLvcSzf5eRQwj0azGtCC5ZO4zbWx9JI02DjpH\nbT2JjISyIpszkugJoPehk9fGvl8gqdzK0PsQauv1a8dr38+8+qNtvNzs/WgcDLPvqdHjlFHtV6Ip\nhBBCHAwkh9ECkJVNtAhiFkfV3boR0bTHbDctqpcJJqoTjQ+J5uzistoW5VERTXRe/SAgitUT7VrO\n7E56sdgdy0wwo7Z9G0ZIbf1oXqL7rWF5iyQzi+PVR+fb9ZYnEkZGNvtYduysJCLp9NpFdWy9rG7G\nqCzOvp+wSDSFEEKIg8HuEtj7rGwyjCx0RkUTlWWSiYQSCSaSM1snElUbayWVmJHUjcy7V7f6wUB1\nDJ7MZXVQmSeWXl2vn0z6mJ3KSDRt3SyH7D4jmR5ZeV/He+/Yym1+6P2KaRvlgeqiHFAddkcye89j\npTF6/67CyvEoEk0hhBDigGSLFU8eGdkchWkf7ab158yOWkUybX9IMFEODEheWaq7JJXyqmgy7SvC\nyeS7Ee1g9seobbWfbAfSXkfyiuJEu52onZczOzYLI5GovidpFamyIsfuqDLPmUwS0YdomXSisXh9\nV/K1eY0QjakyZxtRG4mmEEIIcWCyT+oz2fRgPrkfWSRFO4X2PJIVVjL7dpkEZrKKftB4+hishFd3\nRNg6rGj25yNzFR29OIw8ovrRLiW7i5n1Y2Oh2Gg8jGRGgsnuao4QPd88AUSy6b2/ZH1V3os2olyz\n8oqAVfKZFcXtfMvT1vFg3rszKnlLNIUQQoiDgRZ5rb1x4YIWjJWFV1VUs9yj+5lg2mN2z0qhJ6Ao\nD0YuI+n0+oxgZXNP0eyvUf7Z/DNtRyVqZkczk85IVr17mUBWJPPUoonw3ltY2fTq2Lr2XmvxtzJs\nXVQnKr/IkoleD7PjqeaEkGgKIYQQBwQt8jYyOYxEtbLIyRZ6KPfo/szRE0UUv7+ftY3q2/vMWGfI\nYlbFEtVhRLNy9PqMxAoxsqOZxbD3mT5tzlXJvIii2VOVzS3HSDZ7vA/FmPpendEdwD5nBkaKI7x5\nivqOdjz3eG+xSDSFEEKIg+It8rb723V1YbPh7WpYIe37Qu2z/L3rSFQqktm3qciP19b+oPq2TdSX\nhX1s9hBNW47msm9fEUzvuRMJ3QjMbibbFsksK40zkonmZw/RzGSyIpuoftT3RvYBl61vy0ekK5I4\nRCbLI0Ty6r2Xz8B8ANAj0RRCCCEOBto9iASzJ5PI1Xmy5RXB3M4z0UQx7Lknh55Yen1HY63KJkNV\nRlH+zHVF9rMyj8oOYrZLGbVD5UwuqJ/+aGPbeIxkZruaq0QTSeCsbG45Vt5TPFGzufWx0XhQ3Ig9\npJFh9H135v16dGwSTSGEEOJgoJ2AbAGS7XCuFs49RBO18+QyE0tbhuJFY2GlNYoxwujcVq8ZiWTq\nZAv/TCCzNpX4mbxVYqL6s5KZSecKMoFkZNPmxYiQJ6h9GXrOsDGzumwuTFvUpiLFq/ocbRM9rySa\nQgghxMGIPonPPvX26m73V3+SP7rzNiKYSCrtMavvCWbUPhtrJJloV6iKt/iP+mRzQ/UygUaPIyuS\nVeG07ZhdUE/0ol1OlFNUvy/PJJMRzBWiaZ9zWZ1MNrf7fa7o/QnVj/r26qCcK8zuXjLvr5V2p6Iq\n5BJNIYQQ4mCsWKhkn8avWgxVdt4YCfIkMJNLlIfXzovNtPfyYXNYASuQqDyb5+jInHuSx+5CrqSy\noxm1R+NZKZmRfM7ifSjl7UyicySs3uNdETJvR3OlmDExR8XWvm/O5L+HkKIPAaJ+7mACX7t2rf34\nj/94e+ihh9rDDz/c/vAP/7A9//zz7bHHHmvvfve724c+9KF27dq1ueyFEEIIQTH7exnJTV+W7eah\nn75upd2KH69vJgdmLrI+UT1Ubh8PRur2/rnjjjvaHXfcMT337Fxlc4bmpIeRzmhncpRMNr1+oxio\nrCKZzG4sU2+0XZSXd87MLTuXtt2qx5h93qx8bnmxs3sz/TKP6yiUaP7cz/1c++Ef/uH253/+5+1P\n//RP23ve8572xBNPtMcee6w99dRT7YMf/GB74oknphIRQgghBMeK38tIELZrdJyRvlO0rcoiGj/T\nzpsjb55tTFTfi79qLrKfEcEcnTs21ga7+K0silcvqJmFutcPK6IVmUPH2R8mfpafHVc2D2gOT/H4\nVdpGMdk+2T6y/tjcq3VHuHQjafm1r32tfc/3fE/7/Oc//7r773nPe9qnPvWpdvny5faVr3yl/eAP\n/mD7zGc+8/rg4E1XCCGEGGWPT4xvJWZ+L7f2t7+bP/CBD6QL0b6sL7fnUT1b1jPyiTySs+ieJ5xe\nWSR4kUihOJl8ef0yArbH2iqL6c0Lc40kPJq/HkaSbHlWvxJrdbu+XtQGlWVjtXPmHe15BvNaYp7P\n9pr5QKIvi+qx8fZoVxnr9mHO3mPZI3ZW/yMf+Yj7vEp3NP/v//2/7R/8g3/Qfuqnfqp97/d+b/vZ\nn/3Zdv369fbss8+2y5cvt9Zau3z5cnv22WezUEIIIYSYZNXv5WiRuGKR1/dz6sWRN8bRBaOdM2/e\n+mPWBtVH/Z5y8Tk677Pl7Bx5jHxgwcaqtGMlM2qTlc1K5qiAj8TPrtkxV/MfffxGqTz/vBxn+r4V\nSP8xoFdeeaX90R/9UfvoRz/aHn300fbzP//zb/g6DnpDFkIIIcRaVvxevnr16s3zt7/97e3v//2/\nf3PBY9vduPHGf6DinL/zPRHL6iIBtWWe4CAZQvEj6UXtGLn0xrSSLF4279H8VstnGZGovu2eVEUE\nlUUyZsuj3c0ZLl3y/5Vq+16C3luysq18z/cb7/2twq3oPyvm9POf/3x7+umnW2vxHKSieeXKlXbl\nypX26KOPttZa+/Ef//H2y7/8y+2+++5rX/nKV9p9993XvvzlL7d77713KmEhhBBC5Kz4vXzlypXW\n2usXnv2iEC0ImfvMImZGXiuiuZUzIpmVVyXTi4/a2baReKI8V1CRzapoovOLsFD3ZHPljpntI4vN\nlHnXSC49wWTGsgkkc7+/lwmnbRflk70vMURjPeeHaFF/o7mwj+ss73znO9t3fud33oz1yU9+0q2X\nfnX2vvvua+94xzvaU089dTPQe9/73vYjP/Ij7cknn2yttfbkk0+2H/3RH51OWgghhBAxK34vZ9I0\n8jPb/pQ/NtfsekQyI+HM5BT1v/ccR8+X0fnN2nt9bFTEjpXC2Z3MGQHN6lV2O9GOZpSjzXemnOkf\nXa+cF1tv1WNTeR6t+BBiRayZHPaC+n80/+N//I/t3/7bf9tefvnl9p3f+Z3tYx/7WHv11Vfbhz/8\n4fYbv/Eb7cEHH2wf//jH985VCCGEEG3N7+VLl/z/B485nhNPyJj6ex2380hKGeH04lREdk/QmL06\n3jXTHsEsviMZsHGidqt2LLN6ld1M1N67RqLY58eMeXut2+v+Pqqznfex7WNt+7T1vXwyZt6bbFvv\n2ubp9RXlgOb5VmBmbinRfOSRR9r/+T//5w330TapEEIIIfZj9vfyyKKhX2ycUzy9/rLduOiY1WGE\nk5FMZscvGgOStFPM/4hoovpRjIuwI3OuHJidM+8+c+0JZ9YvghFKTzCtlFrO9SHWRfjwbAV7jWM2\nLiWaQgghhLh9qOwQZJ/2o3soJts/ArXN7meiw0hiVi9rz8RGO5pRu2j8MzC7lFn/jNi39vrn27lZ\n9fXLkX7ZvOw9VAe1Yfv0HhNvN7OP5e1QRs/PWZmpvv/0SDL3jSvRFEIIIQ4Gu+jzFv/Z18eYuDNk\nMZAAeXJjr1lJRMdZyYzGxAryKjKRZEWzL8sei4sgmQhWPEcE1bav5BP1613bPtj+vPeB7CuwlQ+0\nKqB+R+vdSpxKlle9X0s0hRBCiIMxK4jnkszWuNwzEctksyKGjHBWYmU7mjZPNMZZ9hRNe+8iCyai\nKoTZj9emEj/q19YbEc3W8E6mjVXZXbS72mweTPzbQSx7bsUxSTSFEEKIg4G+sjiyW4l2QEfaj+Sf\nlY+cRxJo70V1WMnMRBEJJtt+lFWyifI7xaJ5dGeRjb0nI3KaiWsmm71M9q9lRgwr0rjnY7/nV0lb\nuz12RiNWzp9EUwghhDgYSCxHdypHF2AzCxpmB827znY4I9G0x6xsRDKZ3Uzb1rteRZQDyqvS/lbn\nnLuxkUQj4fTKojF47wvR6/3cMnYr7vox7DEu9Liv7EeiKYQQQhyQmV1MxN5/m+XByI+9H0kcEkHU\nfkYyUdwoN29MXrvW1i36KzuuUc6erNyKX5u1MDuOTIwV/Wdl2e7mhrez2Zeh3EefayMfcnncbpJ5\nbnGfRaIphNgdb5FyOy0yhLjViHYnsgWft7tR3Q1d/el85SuZjMwhifTKs53Oal1GStFPX9fO8cx8\nZ6LplUVCbXfCb1eq4jkqqTZGFt8797CyiWLOyGXfF1uXqX+rcqpxnmrnV6IphNiVS5cutXvuuefm\nz7d+67e2r33ta+3atWs3f273xYYQF42qGF50RkTT1qvsOqJ6rGTO7IKysod2P0dghTWaL1tv9B+k\nWc2ef8N5LrLxoF3N/n2B2Um7nd5DWjv/7uHtNp+tSTSFEDuzieaD/7+9swvZ5Trr97039kCkfrSY\nhJomqSW7yU7bJCUiFBQ07BakqbWtgoW2iOhBEVR67mGT4oGt4FHxIFgweiRFatFQBKWNULaJQSNJ\na964aZMcNNnB2tKP3ed/8GfiZOX++N33WjPPx/wueHlmZt3rXmvmmXmfdb1r5nlvuUVuvvlmufnm\nm+WZZ56RZ555Rs7OzuSll146uQ95Qo4BTTatW2m1ARA6KFpj8JQVzekVFUmr3IofKZnz9q0Z0LbM\nI/teVI6ttyxymHeynJpwIrfyRrKpxc45FSnat2CeMhRNQsiinDt3Tn7qp35KbrnlFnn7298ud955\npzz22GNy7tw5eemll+S///u/991FQjYLcruaJaJeXCbnCKqiWXm1ylCx1OqhIuptQ/Y9G4dKpbYt\n+x7vS/LWFMx9i6wmntr+tzPO07Z9sdZM3z6F8xRnM0UomoSQhZlmNG+++Wa566675Bd+4Rdelsxn\nnnnmJH+xEnLoRPKIPqd5KIOjfYnmtJydvZwvZyQzqpsRvRGzn9Fxz85krj2rqN2+u3T7I744aHRf\npuW5YO5LtjSW7Iv2u2zN32unPptK0SSELMput5OXXnpJrly5Io8//ricP39eHn/8cbly5QpvmyVk\nT5zaoGYJ0ayUZYUTldK2/55QorK5pmha315q5Vvrc6EVqzW+pMg6pvv4LNTEyjrv1uqP9ceVJduc\nv7bLS7PP470GFE1CyKLsdjt58cUX5ezsTEREXnrpJTk7O5OzszN58cUXKZqE7AFtgKl9GcixDIBG\niuaImJGSaQ2622Wvb95xqGDlt3Ii8ra04Hntiqwjevvax7YPE9r1782S74u1+rBvyT5FKJqEkEXZ\n7XZy9erVl7/455lnnpGrV6/Kiy++yG+cJWRPaLc0WnJ5DMK5lGgi8VkprUomum+Zmanq+xodK4tD\n/n2/9mzq0iAzp+017/0BYe2ZxjU5tf05JCiahJBFmURz+uKf6YPthz/84cl9yx8hxwIiBMc08Bot\nmlF5Rjazkjlvw1qPZFKL9Y5FhUjQ5xzqbObUtsjpCKZI7hZlTzaX+kPFobJv4Ty14ylC0SSErMAP\nf/hDERG5du3anntCCBF59UyGRa9wot9aO6JtVDYRYUTjKqKpLaOxUbwns9GxyIDMaCJyicYeM2sf\nE08yW8H0YpY+h+a5kRynOJOqsdZ+rnUcKZqEEELIBkEGnXOyz3BWJVP7FkZ0UGTN7lnbekVzWu4R\nzqg8Est23WvHIjvojI5T++yfFntKchldB2iOHrm02rOuQet69M5tS4BGyFGmrvaHlVOU0FPYL4om\nIYQQsjGyAxdPEjWhbNuozIy2dUbKJiKRS4qmV+bJpLXd2+YdF+8YIXHecRXRnwc8Nfa5X5rMe2VT\nX6Nr0zvfp3XrfNm3GB2zlHkssV9rSDpFkxBCCNkY0ayGReUbaSuxyBeUeGRkMyOWUQwinF4dRDLb\nfYgkc6RsRmKp/cFh33gyNiL30vvpvSfWbLFVhl6/1nmOnH9W2dJCY/V/dN5TFVmRZWZQKZqEEELI\nxtAGEkv8e5MROTKiZNWL1lEx1JYR0Wy3ocJp9cUauCPrHsjxRSReKz8U8dwHyHGt3mLsiXT1D0ro\nH1S0eug5lJXTU5c8hGPcf4omIYQQsjG02Q9LLkd9Ay0iGvPBrHYLLlpfq1cRTXSbJ5momKI5LcFs\n982TY4sekffKTkkyIwm0/oiTyZ+5VrzrBHkm08utLVf+4IG2hcYj8nmqcnps8k3RJIQQQjZGO1hu\nJTP7BUFL97FSb5RoarEZ0bTyZfNEA3rteEX90uKrRAJ2THjHIfq3IT37HtXXjnEknJUv5bLOf+QP\nHtp6tr0sSH7r5xRYYj9GHR+KJiGEELIxPLGszoJ48Wv+X84RounFo1LoteGJpteWt671ed720qJ5\nKvTK4hLttjKpbfOEc+S/CsoIZpvjEM+9Uznnl9qP3rwUTUIIIWRjWIMH5Ntl15TGCj2iiSxXRXNe\nJ8qr5deWvXpeW1rfou0RS33ZDtKGJWnz7ZasjfpmXLSud31ZMRXBRG6DR/6fZrsenYuocCJlkZx6\n/c2A/K7ovXYq+3Qo9PSXokkIIYRskIw09srlmrNEFdFs17Uc1gA6I5vaIN1qt3e5zY8el2i7xvyP\nEBm0NubClH220cplxVUkExFFry5yayzy70oygmn1N4pDzs12G7LetpHpRxQ3SlSj+tV2tPZ6c2k5\nDwWKJiGEELIxeiTiEAczE96sAyJYkSTOl7OC2b5qOawyb2CfkUxvXzWWlE0vtiKtPbTtefs9YsYz\nktVIwK31dnnErezIeZ4VTk2oIkns+b1j5UZ+JyzJqGuvrRf9jMbLSdEkhBBCNsZ8YIAMRkf/m5J5\nGyPzeeXooNIaNLdlva/WQDqSTiTWk9hoH63jMV+33rdD+RKg7Lk66vZZhEiw2/5YZdr6Ere1Z8/t\nadlbb/MvIVwo2vmd+TlG1uw3RZMQQgjZGEsMSvfx7GZ2gIrI5gjRtPJ427RyRDK9wW8kAVXRnDNa\nyloR8+TLil/6OUurrgdyZ0B2RnMeZ/0f3N5nq6M/VLSv3vkVnavIebyE9I2sG/1OysSfAhRNQggh\nZGOgg+KRoP9zsBdtgFopj0QQLUOFU9selbex3j56dT2sY5S5RVakJqSamHlf7rM2rehFcdHzp9Y+\naULZLqNU6iDn9vSKnqPz3FZ/rD+QeP3slc4RWBI9Xx+Rt4e1jhFFkxBCCNkY1oxJu33aFolFNHjd\nx783aZez5RmJ9OIj0bRetXgrp9dGlLcimtb/XtXqZr7cRzv/rJioPQSkvQzWsYy++dZq3xLK6N8R\njZrN1PrYK5mRcLZllrS1P7305PNEOSpD20NENdv/bGwFiiYhhBCyMQ5FCpdCky2k3FpHRDOKQ0TT\ni0Xi0Ly9oimi3woa3cLqiWBWErU+Rs8+tvQ+I4zMrkYiGR2PrGx69Fzb6LWASqbXj4yItuVejgxZ\noe0V3srxQOsjbXs/PVA0CSGEkA3SO4DwZkv2/Q210YBzlGhay4g4ZgbqWv5MXlQyrWM1YvawbQN5\nrhI9f6LbVpd8jtQSaqtvWpm2n9ascSSbo2cztX6PkkxPajzRicq05VFEOSNpi2RZy7VEP0fljNqh\naBJCCCEbwxqczkEHuG2def59kRmAerKFDq6j+Giwbb1G4tojmcg+t+u9z1lqZVbeHkGs9jkjtta1\nobUZiad3K21GNpckcy1kJdNqZ74Nkc5IeLPi5x2LHgmccni5s/XWInvcKJqEEELIxrAGCMig9Rhu\nrUVmDBC5GiGdPZKJimaUI9u2dizaW2UzeOebFT9qtjTTt8wzpOgX+3h5W4ls807r8zasOvPtS1yj\nmWvBO3fnMfPtVh2tH57keHmj/euRzgrofo4QW6TNah2vnKJJCCGEbIzMoHTEbEpVHCpkZgMiwUTL\nkfiKaHplyEBei0VlWNuPzDfN9ohpFq1/6IDam33UYtty7wt8PLRjZF1b0R0Hmf5WyVwL0Xlsncta\nvqhP1vlqnfuIvHmxVr1RIoiQOUYj6lXriFA0CSGEkE2SHbhmJTMzgF8KVCzbdW3gG5Uj4ufFZwbq\nUX8iyYzktCUrmD1oORChamPXvM1XK0clsBXKNle7nP3G2VF4f4Dokcx5Lis+Er1I8pDyCp5wZqS2\nFyTHqHaQfZpD0SSEEEI2BjoIzlD5Fsw1sKQxWs9Kpxc3QjizZYhYWvUQkNtBK8/sZr59oB4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Ucs5+VRXLt/SwtnVjw9quJYaUuEokkIIYRsjvkgqiKbhz4Y7hXN3nUrZ1s2QjTnudD6rVRZ+4R8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\nuSqb87LK8ryPUX8y0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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "imrow(image,morphology.distance_transform_edt(1-image))" ] }, { "cell_type": "markdown", "id": "de283ad2", "metadata": {}, "source": [ "This is closely related to the Voronoi diagram in computational geometry.\n", "In fact, we can see this connection more closely by performing a *feature transform*.\n", "Here, not the distance, but the coordinates of the source pixel, are returned.\n", "\n" ] }, { "cell_type": "code", "execution_count": 29, "id": "c73c5b88", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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wLKN5nGOHw6ENWB8/fqw8z+2bm/PmWR2tjuPQ0QrgmUzIura2pu3t7XOPj9en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\neyjZIDLZ1CoMQ+VyOXmed6iPD2SBkBUAAACZSWa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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "ix = morphology.distance_transform_edt(1-image,return_indices=1,return_distances=0)\n", "imrow(image,ix[0],ix[1])" ] }, { "cell_type": "markdown", "id": "021a8b25", "metadata": {}, "source": [ "If we just want the Voronoi region corresponding to the source pixel at (64,64), we can ask for it as follows.\n", "\n" ] }, { "cell_type": "code", "execution_count": 30, "id": "4d4d8c94", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Q6dOnCU0AAIAx4PF4lEqlVK/X1el01Gq1VCwWVSwWCU2HEJoYa+FwWOVyWdPT01pcXNSb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\nvqhLly7pO9/5jg4cOKD9+/f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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "imrow(image,(ix[0]==64)*(ix[1]==64))" ] }, { "cell_type": "markdown", "id": "70ac8106", "metadata": {}, "source": [ "The Euclidean distance transform is closely related to binary morphological operations\n", "with circular structuring elements: the latter are simply a thresholding of the former.\n", "\n" ] }, { "cell_type": "code", "execution_count": 25, "id": "41e68723", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "imrow(morphology.distance_transform_edt(1-image)<10)" ] }, { "cell_type": "markdown", "id": "c62b8695", "metadata": {}, "source": [ "# Brushfire Algorithm" ] }, { "cell_type": "markdown", "id": "9a69f8ee", "metadata": {}, "source": [ "Let's look at how the brushfire algorithm is implemented. \n", "\n", "We start with some useful variables and coordinate arrays.\n", "\n" ] }, { "cell_type": "code", "execution_count": 126, "id": "734ce4ec", "metadata": { "collapsed": false }, "outputs": [], "source": [ "h,w = image.shape\n", "ys,vs = mgrid[:h,:w]" ] }, { "cell_type": "markdown", "id": "c8c0fc5c", "metadata": {}, "source": [ "During the algorithm, we keep track of the source of each pixel (the closest \"on\" pixel) in the `sources` array.\n", "\n", "We also keep track of the shortest distance to a particular point so far in the `dists` array (initialized to a large value).\n", "\n" ] }, { "cell_type": "code", "execution_count": 127, "id": "a597c857", "metadata": { "collapsed": false }, "outputs": [], "source": [ "sources = 9999999*ones((h,w,2))\n", "dists = 9999999*ones((h,w))" ] }, { "cell_type": "markdown", "id": "a8b3dda9", "metadata": {}, "source": [ "At the location of the source pixels, the `sources` is the coordinates of the pixel itself and the distance is zero.\n", "\n" ] }, { "cell_type": "code", "execution_count": 128, "id": "74ed9d7a", "metadata": { "collapsed": false }, "outputs": [], "source": [ "for u,v in zip(ys[image>0],xs[image>0]):\n", " sources[u,v,0] = u\n", " sources[u,v,1] = v\n", " dists[u,v] = 0" ] }, { "cell_type": "markdown", "id": "61eb6732", "metadata": {}, "source": [ "We build a little iterator to find the neighbors of a current pixel.\n", "\n" ] }, { "cell_type": "code", "execution_count": 129, "id": "47d9c8de", "metadata": { "collapsed": false }, "outputs": [], "source": [ "def neighbors(p):\n", " for i in range(-1,2):\n", " for j in range(-1,2):\n", " q = array([i,j])+p\n", " if i==0 and j==0: continue\n", " if amin(q)<0: continue\n", " if q[0]>=h: continue\n", " if q[1]>=w: continue\n", " yield q " ] }, { "cell_type": "markdown", "id": "b1f3abf5", "metadata": {}, "source": [ "We also need a FIFO queue.\n", "\n" ] }, { "cell_type": "code", "execution_count": 130, "id": "9af91422", "metadata": { "collapsed": false }, "outputs": [], "source": [ "class FIFO:\n", " def __init__(self):\n", " self.left = []\n", " self.right = []\n", " def __len__(self):\n", " return len(self.left)+len(self.right)\n", " def push(self,x):\n", " self.left.append(x)\n", " def pop(self):\n", " if len(self.right)<1:\n", " while(len(self.left)>0): self.right.append(self.left.pop())\n", " return self.right.pop()" ] }, { "cell_type": "markdown", "id": "b9e45b0d", "metadata": {}, "source": [ "We initialize the FIFO queue with the initial pixels in the source array.\n", "\n", "This says that the neighbors of these pixels need to be updated.\n", "\n" ] }, { "cell_type": "code", "execution_count": 131, "id": "b781c5a4", "metadata": { "collapsed": false }, "outputs": [], "source": [ "fifo = FIFO()\n", "for p in zip(ys[image>0],xs[image>0]):\n", " fifo.push(p)" ] }, { "cell_type": "markdown", "id": "e7de1f5d", "metadata": {}, "source": [ "The main loop of the algorithm takes a pixel from the queue of pixels whose neighbors need to be updated, and then checks whether we have found a shorter path to any neighbors than we previously knew about. If yes, we update its info and add the new pixel to the queue.\n", "\n" ] }, { "cell_type": "code", "execution_count": 132, "id": "c923fd0a", "metadata": { "collapsed": false }, "outputs": [], "source": [ "while len(fifo)>0:\n", " p = fifo.pop()\n", " source = sources[p[0],p[1]]\n", " for q in neighbors(p):\n", " ndist = norm(q-source)\n", " if ndist" ] }, "execution_count": 133, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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erWoMquCPooGsHHpmpuPIUPk5gp8kY91oCJQh9hR582isG0/m8bGv+Jkt40Ga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\ndK8Az9JwnFR9rC+VeaNkZ3VF96gPVX9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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "imshow(dists)" ] }, { "cell_type": "markdown", "id": "6a3341fb", "metadata": {}, "source": [ "Some comments on this algorithm:\n", "\n", "- this is a serial implementation, the way you would write it in C\n", "- you can write faster array-based implementations\n", "- there are some faster algorithms for implementing distance transform\n", "\n", "The algorithm assumes that all pixels within a Voronoi cell are path connected to the source; this assumption is not true for a few pixels. There are fixes for this that make the algorithm a little more complicated." ] }, { "cell_type": "markdown", "id": "cec8e695", "metadata": {}, "source": [ "# Other Applications" ] }, { "cell_type": "markdown", "id": "c6ec0742", "metadata": {}, "source": [ "Euclidean distance transformations have many uses outside strict image processing.\n", "For example, here is a simple application to robot navigation.\n", "\n", "Assume we have a circular robot platform and we want to see where that\n", "platform can navigate on a floorplan." ] }, { "cell_type": "markdown", "id": "d1d91f32", "metadata": {}, "source": [ "We start by reading in the floorplan as an image.\n", "\n" ] }, { "cell_type": "code", "execution_count": 45, "id": "d962cd8e", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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6dAiXLl1i3y/u1asXHj58CODb5fSYmBjExsbydf+ZEELEjcQW4u/mzp2LgwcP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\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "floorplan = mean(imread(\"floorplan.png\"),axis=2)\n", "floorplan = (floorplan>amax(floorplan)/2.0)\n", "imrow(floorplan)" ] }, { "cell_type": "markdown", "id": "6c934454", "metadata": {}, "source": [ "Now the distance transform gives us the distance of each floor pixel from some obstacle. A circular robot platform of radius 15 pixels cannot navigate closer than 15 pixels to any obstacle. As we can see from the thresholded image, a robot can navigate every room of the exhibit, but it cannot get behind the structure in the bottom left.\n", "\n" ] }, { "cell_type": "code", "execution_count": 46, "id": "092edfb4", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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DjHU4Mg9WQ+GbvH/pC3Z9dKiw7LMe4PZa/amd7yxIO3jX16W0k2+EWEK0UUQo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\n3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EUTu5EyfJVFkVs1Vg55NZ0TxbbHf01izCSO5P9eHFE+F/U5lpQANUUM6P2WDqhEu81B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\nc4xvksjpouQDAABAt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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "dt = morphology.distance_transform_edt(floorplan)\n", "imrow(dt,dt>15)" ] }, { "cell_type": "markdown", "id": "1b45b09a", "metadata": {}, "source": [ "Of course, we could have obtained the same result with a morphological operation,\n", "using the footprint of the robot as the mask.\n", "However, the distance transform actually gives us the locally best\n", "place to navigate in order to stay as far away from the walls as possible\n", "(the *medial axis transform*).\n", "\n", "Such computations are often carried out using polygonal approximations in\n", "computational geometry.\n", "The resulting computational geometry algorithms can become quite complex\n", "and spend a lot of resources on computing sub-pixel effects.\n", "On the other hand, they are resolution independent and can\n", "cope more easily with rotations." ] } ], "metadata": {}, "nbformat": 4, "nbformat_minor": 5 }