{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Image registration" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A common problem when working with collections of images is registering or aligning them, relative to a reference. The [`thunder-registration`](https://github.com/thunder-project/thunder-registration) package implements a set of registration algorithms all exposed through a common API. These algorithms support parallelization through Spark, but can also be run locally on [`numpy`](https://github.com/numpy/numpy) arrays. Here, we generate example data for performing registration, apply a registration algorithm, and validate the results." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Setup imports" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import seaborn as sns\n", "import matplotlib.pyplot as plt\n", "from showit import image, tile\n", "sns.set_style('darkgrid')\n", "sns.set_context('notebook')" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import thunder as td" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Generating data\n", "---------------" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will use a toy example dataset test registration algorithms. These data do not actually have any motion, so to test the algorithms, we will induce fake motion. First we'll load and inspect the data." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "Images\n", "mode: local\n", "dtype: int16\n", "shape: (20, 64, 64)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "data = td.images.fromexample('mouse')\n", "data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are 500 images (corresponding to 500 time points), and the data are two-dimensional, so we'll want to generate 500 random shifts in x and y. We'll use smoothing functions from scipy to make sure the drift varies slowly over time, which will be easier to look at." ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from numpy import random\n", "from scipy.ndimage.filters import gaussian_filter\n", "t = 20\n", "dx = gaussian_filter(random.randn(t), 1.5) * 10\n", "dy = gaussian_filter(random.randn(t), 1.5) * 10" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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j74GiKPSbrQxYbFisNqw2Oza7HbuieOS/19FkDHmYNfQ0ktN4mlj/0WSGpasd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\nyERERDLAQiYiIpIBFjIREZEM/B90mwnV3KmTaAAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(dx);\n", "plt.plot(dy);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's use these drifts to shift the data. We'll use the `apply` method on our data, which applies an arbitrary function to each record; in this case, the function is to shift by an amount given by the corresponding entry in our list of shifts." ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from scipy.ndimage import shift\n", "shifted = data.map(lambda (k, v): shift(v, (dx[k], dy[k]), mode='nearest', order=0), with_keys=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Look at the first entry of both the original images and the shifted images, and their difference" ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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C1GXQr3ht3kfRr5JOhH3jWKnPSfXy0t5BjWOrt2UMSnVTeD9Ku+BYeP40Nup/\nGH+536caOKwx185F8mOOlevKeU5apL3cW/hPi4iIiIiITI0PLSIiIiIiMjU+tIiIiIiIyNRMoWmx\nHsM2o3oMVctqMsxUj6FqszUZ1lmPoWrumgxL6jFUzVuTgXPKfnNO2eYctr+nXzGG0NaZI00/fPHF\nF7v2k08+2bWTrXMOmRvM77f2QB0HayB85zvf6drMjefvWbuK+oaUs80YR9q5ZMxgjOC1k/6RufT0\nE+ZYM/7T5tgfxrxHH3106zP1iYztI21P1U4NRKo98bWvfa1r0ya/8Y1vdG36A9ttHOC+x/g3qmdS\nlTV66yLlxNN+Ukxp9QVcP/oJ/Y5+Rlv8hV/4ha79wAMPdG1qUDg2xjDGaa4J4zy1E/Tr9vzU7r72\n2mtdm3of2irjG7Vp7AvnkjGK0NfSnkTf4r1FGyd4X8Tvct54L8E254ptxlPuRbwe545tnp/QB37t\n135t6/Nf/uVfdsfefPPNYV9pk+laSU+5Cv9pERERERGRqfGhRUREREREpsaHFhERERERmZopNS3W\nY9iGeapLajLMVI9h1fXWWZNhnfUYquauybCkHkPVvDUZaK8jP6/amevLvPo2jjDvl7aZcq5H566q\nevzxx7s27YkaGtoP55g52q22gr+lDoN+y74wZzrZMm2fvsS5pC23Y+N3GQOYQ01Nwq233tq1uU48\nzvMx35uaFfrKSLvW1omq2qmjo80wJiRd0/PPP9+16Q9cR9ZrYv/4/Tbe0/4Yn0b6h1XnvlJwzPQ7\n2lPSxaWaVe0a0DYZNzlnqSbFxz/+8a79G7/xG12bmqSvfvWrXZv3Brw+/ZTtixcvdm1qNw4fPrz1\nmWOldox+x3MxnrIvjFFJQ8gYx7kmnCtqdEb3IuwLz8VrM7YT7pepzgttnHGDNsy5oS9yf6dvtzo/\n6t441qSjGumOq3aOPelnq/ynRUREREREJseHFhERERERmZop0sN8tenu3+dfhUtebzrTq02rNvt6\n03W+2rRq7tebLnm1adU8rzflmNnmX830ZcYF2m/7fb4KPf2lznPx++wr14dpSFx/2jpfd8rUkfZv\n9Mcee6w7xvRAjvVP//RPuzb9mnHhqquu6tqMK7RdrhPto+0PbY3pW/Qjpp3w1eMpnYEpUoxhTJlh\nHOGryl955ZVdr8WUGV6La840OsYsplZwnbgO3PsYX7l3tDbFc9Efbrnllq7N1+czrW6/WJq6yvVu\n04hSqjZkjSqdAAAgAElEQVTnjClI7Avj1+c///muzT2D9w7026985Stdm/bYpo5X7bQ/po22pNfq\nMva2qdpVO+eC16at0tY5VsYU2idT+RiP+Xu22/jO/ZF9p82wzdRuxhDODdeNMZIximtBO6Hd8d6F\n42l9l/sc14nzzH2QNnzy5MmuzdT1VH6hyn9aRERERERkcnxoERERERGRqfGhRUREREREpmYKTYuv\nNt1m9GrTVb8fvd50plebrvr+Ol9vus5Xm1bN/XrTJa82rZrn9aYcI3Nxk8aFjPQQ1GXwWsytTX7M\nvONz5851beoJuEacc+pQeP02Z5wxjDnPfD02j/Na9Hv6Cu2Bc0lb5+tM27lOr+ukToD6Gh6nLXPe\n6HeM560msGqnPog22M4lNYNcU8Yv6iPZt/vvv394nH7I+M11Y7wcQXumxorrtvS1r1eKpKdKcP1H\nrwnmHsAx8jhjCjUxXA/uh61eqiq/bpZ9Z1zgXNFvGcfbNjUqSffIvjCeppIEjAPcT/l7zgV9gb7C\nsfPepl3LpIujn3Mv59joxzw/tWa0M85teu0w43Wy0zYuMWaNdKKrzsV7Pq7b9+K//tMiIiIiIiJT\n40OLiIiIiIhMjQ8tIiIiIiIyNfuiabEewzZL6jFULavJMFM9hqrN1mRYZz2GVX2dqSbDknoMq841\nS00Grgl9j3GA/aZvtbV2aDvf/OY3h32hrRLGCfaNOdOptg3X8Ld+67e6dusbzF1nXjH1Ubw254K5\n9Q8++GDX5rpQi8Tjo7HSz5j/zTXnmtK2mS/OvjMu0K+5bozn7E97PWpU2Df2hfEw1exi/Ob3GS+5\nb3Jd+fv2+7Rnnps29dRTT3VtarquFOnegdA2OWb6CuN2+/vbb7+9O8b55X7JOMv1JvQT7sdcf9rH\nJz/5ya597Nixrk1dB/fAO+64o2u3+zv9hLDWCGMAx879kn7PeJlqo1Bzw7HSj2nPr776atdutW28\nj0maPdoc7STdY7L+HMdCOJfsH+2KNs/+tu1UL4d9o96G9y0PPfRQ12btoK9//euV8J8WERERERGZ\nGh9aRERERERkanxoERERERGRqdkXTYv1GLZZUo+hallNhpnqMVRttibDOusxVM1dk2FJPYaqeWsy\ncL2pvaB98DjzoNs1ZAxiHnHSaSR9AfueNFDUP9D3RmOh3/FczOfmuWm79HOen31P+efMa25zrF97\n7bXuGG2NMYnrxHV45plnujbjO3UJZ86c6drUITBGce7aeMy6WIwpqQbYRz7yka7NPPtU14N95/nZ\nP8a4Ng4w/nDe6fO0EX5/XdBPacuck3Rvwf21nRPaAmMCr83557UZI7ie3F+p/6KOhGtC3Qb9knGB\n2sT2/PTxpTpktmnLqSYcf891T/cOqc4a+3PkyJGtz4xBvOfjvQGvTT0k54rrTN+hTXLvT1pk7uep\nLlt7Pc570i5RVzrSHVftnPe93Lv4T4uIiIiIiEyNDy0iIiIiIjI1PrSIiIiIiMjU7IumhViPYZtR\nPYaqZTUZZqrHULXZmgzrrMdQNXdNhiX1GKrmqcnAOWc/k6aJa8TzPfvss1ufOd+0bebuMubwOH/P\n8//qr/5q12ZNhV//9V/v2lxD6h3avGfW/El1AWiLnEfmcNN3qFFhX5MftznUjF/M73755Ze7Nm2V\nOdDsO0k1i2688cbhceabt75y8803d8eon6G+hvPGvYD2/txzzw3PR80i+0odH/cS2ngLNQe0Ic4T\nbepKQT/jnsNYxzhPPQF9g7barim/y/XimHkvwN/T9tv4VFV1/Pjxrv0rv/IrXZv7OfWvTzzxxLA/\nyVdaDdRIP1q1M/by3IyHhPGUcN24R7HN/tIOGAdoR20cYH24pBmkxoS+w7GyRhttmPV2eH7ehzEO\n0e6oP+P52rEzRqV7ccZn2gltkPdRe9HC+U+LiIiIiIhMjQ8tIiIiIiIyNT60iIiIiIjI1EyhabEe\nw+7n5zvAl9RkmKkeQ9VmazKssx5D1dw1GZbUY6iapyZDevc/fSvVUGL+bWs/9FvCOED9FX/POeBY\nqKU7ffp016Zvck34+/b8SZPCPH1CzQrn8aMf/WjXZv74n/zJn3Rtzh3rCrTrQg0Lv8t5pd1zb6BN\nsL4R/YoaFvrxiRMnujbnuo051BZduHCha3PNGT+TJpDxl/bNueTxj3/848Pvt3PFcdLn6ZvM009j\n+V7hfp32b/oh2+n8rf2l+nK0VR7nfQvnkJrPUc2Yqp1rQr+k3oDX4+9pX+336We0HeppqLd64IEH\nujbtI+nw6Nf8fdoLqCuhHVDL3I6P92Bnz57t2lynVB+Hc8O9hNq0NLZUX49xgNfjur/wwgtbn5Nu\nlOtGG6cPcCw8vhctnP+0iIiIiIjI1PjQIiIiIiIiU+NDi4iIiIiITM2+aFqsx7DNknoMVctqMsxU\nj6FqszUZ1lmPoWrumgyXU4+hav9qMtC3mAucNC/0BR5vf0+NCv042TahvVBLwZoLtH2en7ZN+2jX\nhPPP9WGeMXOceW3GV+ZIc6yMkazjc9NNN3Xt+++/f9ffcixcp1tvvbVrJ+0RbYIx7p577una9DPO\nHeemzXdnvGOMeOihh7o2bYQxizGC60D7Zm469wrOHa/fxt+0R7MvtFfO25UixQC2GVNoX0kT0+o+\n+F3GReoiUr4//ZB7TFtvrmrnHvO7v/u7XZu+RFtlDKFOhbbfzgXnhedm/Ez16rh/Jd0k54p2QC0c\n1yLViaHdtPcejNVJx8z4y+O8r0p+zbnj3PP7hJoc7qvs76VLl7Y+cx1435Q02Tw3fSb55yr8p0VE\nRERERKbGhxYREREREZkaH1pERERERGRqptC0WI9h99/z/JdTk2E/6zFUbbYmwzrrMVTNXZNhST2G\nqnlqMiytuZC0HLSB1teYi5vqN3AOqPtJdQRYJ4jff/jhh7v2Zz7zma595MiRrv3FL35x6zPXk/Ue\nUn0kzvvjjz/etZkTTY1KqnnEuW2vd99993XHaFuMCUl/w75R30U/fvLJJ7v2XXfd1bUZA8+dO9e1\n2/pK9DP27fDhwzWC9ko/ZKynf1AXQBs8depU12ZMaWMO96nkL4xXtKlNwX5xDThnI91bVW/bvBfg\nb3lualhG567a6TfcH0+ePNm1n3766a7N/Z2amKSFaGu8Ve20pxbWeOP+xvjG/bbVTaz6PeeGmlB+\nn21+f3SPWLXTz9u5+fCHPzw8N32Dfec8sq+8D+PcMCbSDunn3JsYl6gtph20c8H7JpI0KYwjaQ/f\nS9zwnxYREREREZkaH1pERERERGRqfGgREREREZGp2RdNi/UYtllSj6FqWU2GmeoxrPr9OmsyrLMe\nQ9XcNRmW1GOomqcmA/uRcnfZT84JfaMdR/otbZ/rzzjC2je0L36fc8bf09ZJGzM5L8y55tiY88ya\nQJwb2iqvx3Wjpoq+1J6fufHMLT9//nzXZgxrNSVVO2sgUCdCm+K8c90Z0+g7f/M3f7P1mTo35vGf\nPXu2a//93/991+aa83zsC48/8MADXZsx8Pd///eH12v9I9kfbWxdOrfLJWlc6Iccd+tn9GFqUJKm\nhfc5hH7J9XvhhRe6NueYvpRiFPcw0v6e5+Z6816D1+JeT60ZfYP3PfRj3ldxrJxr6vyS5qWNUYx/\nXHf2hdogxgHGLK4z4y/vJahJ4fmoYaTelm3eR/3cz/3c1meuO22GdkAfoB2wzXsL7pur8J8WERER\nERGZGh9aRERERERkanxoERERERGRqZlC02I9hm1G9RiqltVkmKkeQ9VmazKssx5D1dw1GZbUY6ia\npyZD0rolXQh9g7R6BmobOMaUf8715rWpUeK7/jlWvpv/y1/+ctdmHGhrFrEv1IG8+eabXZu2zHm9\n9tpru3aaiwMHDuzat6pxvjpjAG2R+du0TZ6b88p1Za485y7NJde1zQdnvnbSFnGs/D1tivnl1Nfw\nOOMnNYYvvfRS125jEv2DNsA9mX3n3rMpUg0KxsKk52vtKWlpCW2Rc0otAe2FewJtk1oH1mVhjY0n\nnniia7P/1IO1c8P15n0RYwzHxv2Ofs/9juvCmETdJu2TOhTeKzBG0X7bex32letEP6Mfch05V+m+\nijbL7zOmMUZy7Fx3xqF27ngt+hfhfQrngr+nXSUtXZX/tIiIiIiIyOT40CIiIiIiIlPjQ4uIiIiI\niEzNvmharMewzZJ6DFXLajLMVI+harM1GdZZj6Fq7poMS+oxrDpO9qsmQ8qjZ34sx8F+tbm/tGXm\nDVOnQegrKV+d+eW0j1THgOdrr8eY9cYbb3Rt6q+YM82Yxd+//fbbXZvrQj+nnzLmtmNl7E7zSJ0H\nc+GpDeK1ua5s07ZZ04D9bWMU9YWpDhV9muvC73MdGN8Zo6ijoi6AufCt/9xxxx3dMWoI/uiP/qhr\n0wZoU1eKdO/A2EaSzpNz2q5h0rtyvbkfsq+EtkcdCOeY9UDSWHg+xjy223sb9i3Vn2Nspm6Cez81\nJklHx7Ew1tOXCMfK77fnSxpq3uNxnXhfc/LkyeH3eT7qa7l3MMYxDnFst99+e9fmvVGr22MsJ7w2\n9w7ep/C+i+uWagdV+U+LiIiIiIhMjg8tIiIiIiIyNT60iIiIiIjI1ExRp8V6DNuM6jGs6s+oJsNM\n9RiqNluTYZ31GKrmrsmwpB5D1bw1GXhe5lEnaD+t/afaULRVfp9zwjbtj7oTwvPT/kjbvzvvvLM7\ndvfdd3ftZ555pmvT1phnTFtmzOJx2hvjDONGe5zzRFtkfjZ1ebwWc+s579SF8PqcG2oWef42hjIe\n8rf0w5tvvnn4/VtuuaVrM1+cmhjW7eDcPfXUU12bMa2NgdQLUpOV6qGsi3TvkOI824zL1C+012NM\noK0mTSfvY6g54flom+wbx97WaKuqOn36dNembTPmjHQd3M9oO9So0D5Yq4SaEq5Din+0N/oOtW5c\nO/rS6D6R+x3Xhfsp4yX1iZwbxhTaCeMz+5O0SbQb3utwPEePHt36zPuMdI/IfZB7cPLXpPuq8p8W\nERERERGZHB9aRERERERkanxoERERERGRqdkXTQuxHsPu5+P1ltRkmKkeQ9VmazKssx5D1dw1GZbU\nY6iatyYD7Y/57ITjGsUNjuHhhx/u2tQQsU1oH8zV5foxV5j2xpxt5k1/+9vf3vqc6uQwh5n538yR\nZn55q5NbBX2LNYt+6qd+qmu3MZXj4ppTB8K+sFbFz/7sz3ZtzuO3vvWtGsF1YDxnbn5rR8xFH323\naue8Mx7TZjivjDnUrHBdUoxrr8d95oknnujajF/0zXXVbuJ+nuquMCaMdJCrvt+2aXv0Yc43r0Wd\nBq9Fe2AMIfw990PW+qKvJY1Oe6+U6tXxt2mvp06jjWdVO32FcG6451Ffxv5wLXkv064l/ZpzQT/n\nvpN0HlwXxl/GxKQzSffTvI/ifVsbB2jTvCejjR87dqxrU7dHXSrnItl8lf+0iIiIiIjI5PjQIiIi\nIiIiU+NDi4iIiIiITM0UmhbrMewO+7ekJsNM9RiqNluTYZ31GKrmrsmwpB5D1bw1Geir9HPm4lKv\nRntp8+yZh3zixImuzePM3eWcMIefcYLnY4xLNRTom609cz1TDSCeO+nkmA9OWB/i9ttv79r0xfZ6\nzK/+yZ/8ya7NeeO8cmzUZ9GW2RfGmJMnT3ZtxijqBNr8c8YY+jjPlepOsfYFjzNG/d3f/V3Xfv75\n57s2/Zx5/W3/aG/UdHEs69K1LYW2zfx++m2qDdbGFI6ZWgSei99njGDfkk6ENeC4/lzPpAmkHox7\nXHtvwt9ynjg2zgVjNfvGPYr3Ejwf7ZO+QntkDOO9DTUt7fior0l6GcZDrivnjmPlXBHui0knwnvM\ne+65p2vz3qO1O8ZLrgP1N1wHzhXXjX1NutUq/2kREREREZHJ8aFFRERERESmxocWERERERGZmik0\nLdZj2GZUj6FqWU2GmeoxVG22JsM66zFUzV2TYUk9hqp5azLQN0Y1FFb1i3M2OsYYkvLLmVecfI19\npZ6B2gzmlzPPuc3ZZn520tcwZtE++Ht+n9oNaiVoL/SNdmw89/Hjx4d9p16GOqbf+73f69rM1+Y8\nct0ItWi0ydZuuIa0Adonr82Ywb2Gx+nHPJ7W9ciRI1277T9z2ZkXz7FQe0n/WBf0K8J+pDZp/Z4+\nST0WtQWck1R7hHsK29QHcOyMUbweNa1sMwa2cYXrnTQntB/GKH6fY6U2gr5y9OjRrs04wnsJ/p76\n3E984hNdu40rSfdE30haJ9oc55b3RTwf5yrZGeMz+0NNZBvjqEFh/Et1jrjuyYaTP1f5T4uIiIiI\niEyODy0iIiIiIjI1PrSIiIiIiMjUTKFpsR7DNqN6DFXLajLMVI+harM1GdZZj6Fq7poMS+oxVL13\najLQ79lmLjDXrM3Hpd/wXKmmQtLdjXR2VTtjHPPlmcdM22/Pn3QaPM6aCOwb88O53vfdd1/Xpu1+\n9rOf7dq0n8cee2zrM3VqzLOnJpD529RvcSxJF0Xuvfferk3dHPPXW/0Xaz1wnhkzOHauU6oZxnhM\ne+dcMoZQ79PG66Spol6R195LvYXvhaV616S/Szn6rZ/Rp9O9QuobY06qCcc14PpS40RtGWMK+8/+\ntH7L+Jfua3ifQr999tlnuzZr0ND+eC/B49SkUteRao/xfIcPH976fPr06e4Yx8a9mPPMmMI4wHVg\njKFNUtPCsfD83OsYl6g7aa/PdU012nicfWU85z64Fy2c/7SIiIiIiMjU+NAiIiIiIiJTM0V6mK82\n3Wb0atOqZa83nenVpqvOv87Xm67z1aZVc7/edMmrTavmfb0p14DrT3tiCsMonYzryflNKVKME/yb\nO71enOkQtA/6AlP42r/dR+mxVeNXma76PftOvz927FjXZpom056YntjaE8fFNWOMYQoWX7POlCmm\nsXAuDh061LUZv5lWOkqXYOpDer0n1ym9mpSpFvQPXp/+wBQZvub185///NbnU6dOdcdo77QRxiNe\ne1OklK0Uq2h/7fc5B6l8Aa/F9WYcpa0z/SulutE+GMMI54Yxp41pHDv3V+4h9GuOhTAGMV7yFctc\nJ6Zs8d6FcYBzzXTxNh2N88L4yfRYtgnXnetAO2Kbc53Se7l26VXX7X3cd77zne7YI4880rUZ4zg2\nzjt9gr9P6WdV/tMiIiIiIiKT40OLiIiIiIhMjQ8tIiIiIiIyNVNoWoivNt39/EtebzrTq02rNvt6\n03W+2rRq7tebLnm1adV75/WmtK+RrqdqrI1LWjaOkXEj6e54PsL1pR/zelyjdm54jL+l7aTvM+/4\n4MGDXZv6H+Y9/+Zv/mbXHumBqLNg/PvWt77VtalBoe6N60Ab4etLGV+ZO8+ca85lm7vPa3Mema9N\nG6EmkH2hfXPv4FgYTzm3f/AHf9C1W7+nf1CXxH2T52bs3hSMGWxzP046kfY4NSO0rfRK5HTvkeyH\n108xKJVjYIyjrbd7CueN12JM4Lm4B9G+qJUgjAPcb7nn0R4ZX2mfvBdq9WVJO0k/5H0Tf0+9GOeO\n56PdcOwsXZH0R2xzrlp4n8R55lzwPof3Uexb0q2uwn9aRERERERkanxoERERERGRqfGhRURERERE\npmYKTYv1GLYZ1WNY1b9RTYaZ6jFUbbYmwzrrMVTNXZNhST2GqnlrMqR3tvM4xz3K8WZeMOH75alR\non1wDtL76qnnYv46+8640voyc9V5Lvo94foy/zzF3zNnzgzPxxjYxoWkj+K1OI9f+cpXujbngmNP\n9ZZoQxw7dX1tf/ld9pWxnn500003dW3aELVFrNfAsbE/tClq1VqbZN+5Lly3VLNkU9D22WY+P+H+\n3o6TMTzpPBgzOCc8zj2EcZh7AuecY0u1UWgfXNPW93jfxGul/enuu+/u2tRtsM3rcS6Shobxnfcq\nvB/gfVm7lrw2+8p1YG2+NM/UGNIu6Nf0Tf6ec8O5oB0zDrX3ZZw3alxefPHFrs2YwvjLsXFu93Iv\n4T8tIiIiIiIyNT60iIiIiIjI1PjQIiIiIiIiUzOFpsV6DNuM6jGsOj6qyTBTPYaqzdZkWGc9hlXX\nnqkmw5J6DFXz1mRI+ejMFWb+7c///M937SeffHLr87lz57pjHGOKG/SlpJ2gL3Js9POR3oDXS7Wi\nqMPg2Gj77BvXl+/qp9aNMY/r1J6P+d+pbtbf/u3fdu277rqra3PsH/zgB7s24z1jHK/PfPCf+Imf\n6NqtFo4aPMJz055pQ+wr54q57VwX7ptcZ65LOxfUazAecY1pUzz3ukj3DvRT+hFz8qnnauMyNSWc\ng2T3XH/2jXsC/TrVdeHYk04u6XHb8fDcHBuPs520utyvqX3g/kdb5txw/7355pu7NnV2pF2bFCM4\nr7zHI0mTTd/jXDJO0O5uu+22rs04wLmhD7XjoU2eOHFi+NtUS4hxJNVcXIX/tIiIiIiIyNT40CIi\nIiIiIlPjQ4uIiIiIiEzNFJoW6zFsM6r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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "im1 = data[0].toarray()\n", "im2 = shifted[0].toarray()\n", "tile([im1, im2, im1-im2], clim=[(0,300), (0,300), (-300,300)], grid=(1,3), size=14);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It's also useful to look at the mean of the raw images and the shifted images, the mean of the shifted images should be much more blurry!" ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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59rjau+t91byaJlFOU9Sqn7Xmazxr3dV7n87bei/1bZum2FX/p+v9a1/72rJe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\nANtwgAEAALbx/wAU30HhqtXhLAAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "tile([data.mean(), shifted.mean()], size=14);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Registration\n", "------------" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To run registration, first we create a registration method by importing the algorithm `CrossCorr`" ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from registration import CrossCorr\n", "algorithm = CrossCorr()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This method computes a cross-correlation between every image and a reference. First, we'll compute a reference using the mean of the images." ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "collapsed": false }, "outputs": [], "source": [ "reference = shifted.mean().toarray()" ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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VnumWhN+Kv5wkSeNYnCRJ41icJEnjWJwkSeNYnCRJ44zsrZcm47rjUwqFjkXp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\n+ZqSpwAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "image(reference);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we use the registration method `reg` and fit it to the shifted data, returning a fitted `RegistrationModel`" ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "collapsed": false }, "outputs": [], "source": [ "model = algorithm.fit(shifted, reference=reference)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Inspect the model" ] }, { "cell_type": "code", "execution_count": 47, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "RegistrationModel\n", "length: 20\n", "algorithm: CrossCorr" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The model is a dictionary mapping tuple indices to transformations. You can inspect them:" ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "Displacement(delta=[-4, -2])" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model.transformations[(0,)]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can also convert the full collection of transformations into an array, which is useful for plotting. Here we'll plot the estimated transformations relative to the ground truth (as dashed lines), they should be fairly similar." ] }, { "cell_type": "code", "execution_count": 49, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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0o4+9bW8pCsn8/aqNdcuiWHJKW3j3QBnT4wMuOTVqTYmRvvz89jRe31nE4dx6\nsktaWL84ljlJwcP6ner0BjRa/ZDPps+UtPDq52fpUWu/9e9p8QFDJuTp8QHEhHoR5ONiM7Md44nt\n/XWOEburDmCQDVwbsdiq+9FeSm5ZK7XNvcxKDLK5ZCyYTlZxM21dGpamheHs+N+v+4rIJZxsyOSL\n87u5KmiaUXfJe07X0NjWx5LpYZecErQ2Py9nVsyK4KMj5/n0eAU3L7x4+tMWxIR68eu709mdUcOH\nR8r592dncXNxYOp3mps0tvWxP7v2W3e7nT0DJEb78qNbpl50XFdnFR6uDkQEuePj6Yyvx+Dz3dCA\noR8Debo54inOB1YjErIZdGg6OV53Cn9nX9KDLv6S2ILPT1QCsHJmhJUjEcwpu6QFgEXTQ7/17z7O\n3twSdwMT3IONSsadPRo+PnoedxcHbphv27u9LZ85kSO5dezOqGZB6gSChihOsgVKhYLlMycyY3Ig\nB3PqSI25+A62p1/Lrozqr14v4ePhRFy4NxFBQ7dBjQ/35vf3zTJr3ILpiIRsBnsqD6KT9SyLXDSq\n53PmUlzdQUlNJykxfoTZ4PPjoegNBspqu6xe9GJv7luVwLol8fi5XTydOTd0ptHH/fhoBf0Dem5f\nFmPzy0mcHJTcsjiOFz/M5+29pfxgXYq1Q7osPy/nIQuoAML83fnlHen4eTrh4eZos4VqgnFsby51\nDJgelMrM4DRmBqdZO5QhfXmqCoCVs+zn7vj59/L4y7Zsi+/kY+8UConJkb4mPWb/gI5jBQ34ejqx\nYKpl+1UbK31SAJMnenOmtIX88lZrh2M0J0cl0RM88XJ3Esl4DBIJ2QyivSK4I2E9KoVtTkDcuXwy\nty+Lt6u7zbnJIegNMu/sL7N2KONextkmNAN65iWH2M2GCZIksWFpPJIE22ygz7UgDMU+vk2CSXm6\nObLITHvhmkvapADiwwfvcAoq2qwdzrh2OLceCZhno8uILiU80J2FU0Opb+1jX2aNtcMRhIuIhCzY\nBUmS2LAkDgl4e28JBoPtLOYfCzo0nbxT/BE9A5d/JFDX0ktpbScJkT74m2HHKHO7cUE0bs4qPjp6\n/uumF4JgK0RCFuxGRLAHc5NDqGnuJbO42drh2CSDLPP09uyv6wSGK7spjwM1R9lddeCyrzuSWw8w\nZJ9ie+Du4sCa+dGoNXrePyQefwi2RSRkEylsLaJD02ntMMa8m66O5v7rE0ifZFtdoWxFZlEzhRXt\nVDV2j+iKWb99AAAgAElEQVR98ybMxNvJi4M1Ry/5d6zTGziaX4+bs2rIxv72YuG0CYT6u3E4p57K\nhpH9ngTBnERCNgG1rp//FGzlL6efR2/QWzucIR3Nq6egos2m+rYaw9vdiVmJw+tgNN4YDDIfHi5H\nIUmsnjeytcEOSgdWRi5Fa9DxZcW+IV+TU9pCd5+W2UnBI9rP19YoFQo2LI1DBrbsKbb774Qwdtjv\nt8qGHKo5Rp9OzfzQ2Ta57lit0bFtTwkvf1yAVieqS8eqE4UN1Lf2MS8l2KjmF7NC0vF38eNI3Ula\n1BcXzh3+arp6QYp9Tld/U0KkL9PjAyit6eTk2UZrhyMIgEjIo6bRD7Cv+jAuKheuDptj7XCGdOBM\nLX0aHdekh4v+tGOUTm/goyPnUSklrp9jXOcspULJqqhlyLJMcXvpt37W1tVPXnkrUSGedtNM5krW\nL45FpVTwzv4yNAO2ObMljC+2uVDWjhyuPU6PtpeVkUttcptFrU7PrlPVODsqWfyd9oljhSzL434K\nu7tPi4+HMynR/vh5Gf93mBaUSoRnGIGu335GfDSvHlke3G5vrAjwdmH5zHA+PVbJZycqL9kdSxAs\nRdwhj4LeoGdf1WGclU4sCp9n7XCGdCy/gc7eARZNC8V1iN1g7Jksy+w8WcVftmWP+2VQPh5OPLFx\nGuuXjG7zBIWkuCgZG2SZw7n1ODoomDnFCnvtmdF1syLx8XBi58kqmjvU1g5HGOdEQh4FpULJY9Pu\nZ9OUm3F1sM2G9Ufy6lEpJa6ZEW7tUExOkiSqmro5V9XB0fx6a4djdZIkoVKa/itdVNlOS2c/MyYH\n2uT2haPh5Kjk5oUx6PQGduwrvfIbBMGMREIepSC3QKYH2m6z+h+vn8YPb07F293J2qGYxbqrY3BU\nKXj/YDlqjc7a4YxJhy6sPR4DxVxDmZkQRGyYF5nFzZwVXeAEKxIJeYxzclQyxcSbC9gSX09nls+c\nSGfvAF+crLR2OGNOb7+WzOJGgn1diQvzsnY4ZiFJEpuWxiMBW/eWoDeIlQiCdYiELNi9FTMj8HZ3\nZOfJalo6x89zQLVGR6cZ2z/qDDqey3gNRcwp5iWP7bXfEcEezE8Noba5lwPZddYORxinjErIOp2O\nn/70p2zatIlbbrmFffuGbiQgCJbg5Khk3cIYYkM90evHT3HX7oxqnnjpGGcr281yfKWkpKmzG6VX\nG0ET+8wyhi25aUEMLk4qPjxcTo9aa+1whHHIqIT88ccf4+Pjw5YtW3jllVf47W9/a+q4bJbeoOfd\n4o+p62mwdijCN8xODOYnG6YR5GubxXWm1qPW8mVGFY4qJVEhHmYZo7Kxm+7ywTXNe+v2jvmOVp5u\njtwwN5Lefh0fHCq3djjCOGRUQl6xYgWPPfYYAAaDAZVqbFVeXk5mUw77a45wsOaotUO5pB37Szle\n0IBhjJ9Av0mSpDE9pfpdX56qQq3Rs3JWBM6O5vn+Hc6pR+7zIsplEpXd1eS2FJplHFuyOC2MYF9X\nDpypHXE/cEEYLaO+yS4ug9uu9fT08Nhjj/HDH/7QpEHZKoNsYGfFPhSSgmURi6wdzpDqWnrZebKK\n6AmezEoY/ZrRo3n1fHLsuFlabioVEhuXxjM1zt/kxx7LunoH2H26Gi93RxaZqdmLRqvnRGEj3u6O\nbEi6jj9mFPNp+Zck+09BIY3d0hOVcrDP9TM7cti2p4Sfbpw2ri70BOsy+tK6vr6eRx55hNtuu42V\nK1cO6z0BAeaZWrOUY1WZNPY1sShqDpMnRlg7nCFt2VsCwK3LJhMY6DmqY3X2aNi+t4QBnWFU3Z8u\npbldzZY9xcxPC8d5jK1vNaePjuUzoDVwz6pJhE3wHtZ7Rvrd23e6GrVGx6p5cUyNjuOatvk4qhzx\n8XXBUeVoTNh2Y3GAB0fyG8gobKS4vpt5qdbvcGfv505heIw6C7a0tHDvvffyq1/9ilmzZg37fc3N\n9jsFZJAN7Mj9FAmJBUHzbPK/pa2rnwOZNYT4uRId5DbqGF/feY7efh333ZDE7CmBJoryv94/VMan\nxyp5/dMCk7ctbO/WsDujmnULY1AoxtYdTlqcHx1daqbF+A3rMw4I8Bjx38LnRwafoabFDo5xQ8Qq\nADrbNYBmxDHbm5vmRZF1rol/fZhHZIAbTlbsAW/M5yfYhpFeSBk197R582a6urp44YUXuP3227nj\njjsYGDDf8gtb0NDbRLO6hfSgaQS62uYU685TVegNMitnRaAY5TRbZUM3h87UMcHfjZVzjdus4ErM\n2bbwg0Pl7DxVxcdHz5v0uLYgLMCdO5dPNtsWiI1tfRRVdzB5ojeBRuwaNRYE+bqybEY4rV0adp6s\nsnY4wjhh1B3yL37xC37xi1+YOhabNsE9mN/M/l8Msm3uCmOQZYqqOvD1dGLmKJ8dy7LM1j3FyMCG\nJXFmaccI/21b+PInhezYV8r3b0o22bHXL4nlbGU7nxytYFK495hujmJqF7ZZnJ86NjtzDdeqOZEc\ny2/gixOVzEsOMctjG0H4prFbnWEGXk4e+DgP75mdpSkkiV/fNYOfbJg26gR66mwTJTWdTIvzJzHK\nvInMXG0L3ZwdeHBNIgqFxOZPCunsGfvTrKagNxg4ml+Pi5OKtPiAK79hDHNxUrFuYQwDOgM79os+\n14L5iYQ8higUklEb03+TZkDPjv2lqJQS6xePbueg4TBn28KYCV6sWxhDV+8AL39SOO53hBqOvLI2\nOnsGmJUYdNm9s4vby9Dox/ZjKoDZScFEhXiSca6JoirzNGARhAtEQha+5fMTlbR3a7j2qokWe35o\nzraFy2aEMy3On0kTbXNmY7j2ZdXQ2G7+blmHcwd//wsus5HE8boMnsvezIHqI2aPx9oUksTGa+IA\n2LqnRFzUCWYlErLwtZYONTtPVeHt7sh1sy27rMtcbQslSeL7NyWzem6U3VZbVzf18NauYl7+2LyN\nOTp6NOSUtjIxyJ2I4EtXh04NTMJN5cruqoN0aDrNGpMtiJngxdykYKqbejiUI/pcC+YjEvJllLSX\n8Vz2y1R311o7FIvYsb8Urc7AzQtjzdb96VLM2bZwtBXn1vbh4cHfxw3zIs06zrH8we5uV9pm0UXl\nwqroZah1al7N34LeYJuFjqa0dmEMTo5K3j9UTm+/6HMtmIdIyJfxRcVeittL0Rlsd5/d7JJmPj9R\nOeq7yrOV7ZwuaiYm1JNZiaPv8GWMb7YtrG7qsUoMtuZ8fRfZJS3EhnqRHO1ntnFkWeZwTh0OKsWw\nPv/5obOZFpBMWWcFH5fvNFtctsLb3YnVcyLpUWv56PDYW0on2AaRkC+hvLOSovZSJvvEEeVlm125\nYHDHn3cPlNGvMf6iQW8wsG1PMQAbl8ZbrVXghbaFsgzb9hSbdTODAa193NV98NXd8Y0Los36uRRX\nd9DYriZtUgBuzg5XfL0kSWyacjOBLv7kt5wdFwVeS9PDCfRxYV9WLbXN4oJRMD2RkC/hi4o9AKyI\nWmrlSC6traufoqoO4sO88Pd2Mfo4B8/UUdPcy7zkEKJCRtduc7SSo/1IjfHjXFUHmUXNZhnjbEUb\nT2w+TnF1h1mObyotnWrOVbYzJcKHKRE+Zh3r67XHV5iu/iYXlTMPp97LT9IfwUk5tttpAjioFNy6\nOA6DLLNtb8mY3/1KsDyRkIdQ2VVNYWsRcd7RxHqbp0uVKZwobERmcGmGsXrUWj44VI6zo5K1V5u2\nfaWxbl0Sh1Ih8fa+UrPcyapUCrp7tWz+uICuPtu9s/P3cuGpB2Zz27J4s47T16/j9LkmAr1dRlyN\nHuDqh7Nq/DTMSI31IynKl8KKdrJLWqwdjjDGiIQ8hD6tGmelMysibffuWJZljuc3oFJKpE82vs/0\nh4fL6e3XsXpuFF7uTiaM0Hj/bVvYb5a2hXFh3ty4IIr2bg3/+rTQprep9PV0JsTPzaxjnDrbyIDO\nwLyUELsvgDM3SZLYsHTwgnH73hK0Ovt49CHYB5GQhzDFL57fzH6CSb7mb4xhrNqWXmpbekmN9R/W\nM7+h1DT1sD+7liBfV5amh5k4wtFZNScSLzdHPj9RSWtnv8mPv2JWBEnRvuSXt437XsWHcuqQJJib\nHGLtUOxCiJ8bS9LCaOns58tT1dYORxhDREK+BHdH896VjFaovxu/vmsG18+JNOr9X/erlmHDkliz\n9as21jfbFr5zwPRtCxWSxPdWJeDt7siHh8tp7x6frTWrm3qoaOgmOdoPH4/Rz5AM6AfYdu49anvq\nTRCd7Vo9NxIPVwc+O145bv92BNOzrbOwMGySJBER7MHEIOP2Sc0sauZcVQcpMX6kxNjm7lUX2hae\nOmuetoWero48eEMSP7plqkmSkSlYulDo8FeNLhaYaCOJso4KjtSd5F95b6LWmX5mw1a4Ojuw9uoY\nNFq9WS4YhfFJJORxaECr5+19pSgVErcuibN2OJdkibaF8eHeTDZzBfNIZBY187cdZ6hv7TX7WFqd\nnuMFDXi6OZISY5o1zlP84lkycQFN6ha2nHt3TFciz0sOISLIgxMFjZTWjP2OZYL5WbYdk436tPxL\n3BzcWBg212prcC1p56kqWrv6WX7VRIJ9L9+vOr/lLBnnMlFrrFeNHJTWQ2O3ht8fOT1mt8BzUKhY\nHLaAD4800tDaZ5G/w6ziFnr7dSyfOdGkjyxuiF5BRWcV2U25HPCKZFH4PJMd25YoFIMXjH98K4u3\ndhfxs03TLd7hzpbIssyhnDq7qz6XGOx5bwtbtI7fv56vFLQW8UXFXvxd/JgdMgNnlW1MXZpLW1c/\nnx+vxNPNkevnRl7ydbIss7/6MO+XfoaMle9ylKD0hgZdMw2t1g3FnHKbz9JvSGJO8vQrXiiZwoWN\nJOanmLaYS6lQck/SJp469Rzvl35KtFcEEZ7hJh3DVsSFeTM3OZijeQ08tSWLx9al2szjD0sabC5U\nwr4s+2wzHGcje6aP64TcoenkjcLtqCQl9yZtsotkXNXYjYNKYfRSmB37SxnQGdi0LBoXp6E/fr1B\nz7slH3Oo9jhejh48seBhnLXGPas2lV2nqvjgcDmLpoVyy2LzTrOfq2wjPNADNxfjqteNUdRaxuac\nN3GMzcF7gj+yPNmsd8nNHWoKK9qJC/Myy7Iqbycv7k7cyImG0wS7WacVq6XcuXwySoWCQzl1/O6N\n0zy2LsXo2g57pNbo2PxxAbllrYQFuPHITcl4udn+ufRrEjhdZqtRSxq3CdkgG3i9YDs92l7Wxa1m\noodtLfu5lHcPlpFf3safH5w94u5cxdUdnDrbRFSIxyWXuPTr+vl3wRYKW4sIdQ/hoZS7ifULp7m5\n2xThG235jGiO5jZzMKuJxVMjCA1wN8s4Zyvb+fuOQlJj/Xl0bbLFHmF01HvRXzgTz6Qz7K3bS6/c\nyYZJN6FSmOcresSIzlwjNck31qaXDpqKSqngzuWTCPJ14Z39ZfxxSxYP3ZBos8WSptTW1c9z7+ZS\n3dRDUrQvD92QdMkLfeHKxm1R167KAxR3lJHin8jCsLnWDmdYOns0FJxvIyrEc8TJ2GCQ2br7v/2q\nh2oA0d7fwd+yXqSwtYgE30n8aPpD+Djbxj7CDioFty4xf9vCSV8VeZ0pbWFXhuXWmOr1BjwUfvxw\n6veZ6BHKifrT/DPnVfq0apOPZTDIHMmrx9lRyYxRNJUR/kuSJFbMjODhNUkYDDLPvZvLvqwaa4dl\nVpUN3fzujdNUN/WwcFooj61LEcl4lMZtQk4PSiU1IInbptxsN4VcJ882Icsw24jdmA7l1lHV1MPs\nxGBiQr0u+nlVdw1/Of08tT31zAudxYMpd9lcS8TUGD+Sos3btlChkLj/+gQ83Rx590AZZXWWqZ5d\nND2Mpx+ew0Q/f/5n+kOk+CdS3F7KXzP/SYu6zaRjFVS00d6tYWZCEE6OtjFVN1akTw7kpxun4eHi\nwFu7itm+1zyrA6ztTGkLT23JorNngFsWxXL7sniUinGbTkxm3P4G/V38uD/5DtwczF88YyrHCxpQ\nSBJXJYwsIff2a3n/YDlODkrWLYy56Od5LYU8k/USXQPd3BS7ilvjb0SpsL0TtSRJbFhi/raFXu5O\n3H99AgaDzEsfFphk/1u9wUBRVTvb95awP3vowpcLlc5OSkfuS76dxeHzaehr4i+n/8H5TtN1EzuU\nc6GYy3zT1Zei0Q/QNWDdxx/mFjPBi1/ckU6Inyu7Mqr55wd5aAbGTovNPaer+cd7uciyzMM3JrN8\n5kS7uamxdeM2IdubupZeKhu6SYr2xdN1ZDvrfHTkPD1qLavmRFxUAXqg+iibc19HlmW+l3w7SyYu\nsOkvl6XaFiZE+nL93Eh0egMtHcY1uBjQ6skqbubfnxbyw38c5U9bs9mVUc2JgoYrvlchKVgbdz3r\n49fQq+3jueyXyG7KMyqOb+rqG+BMSQthAW5EhVi28KhX28dfTv+DV/LeQG8YOwlqKAHeLvzi9jSm\nRPiQXdLCU1uz6Oix745eBsNgd7+te0rwcHXkiU3TSZsUYO2wxhTlk08++aSlBuuz4Z11bJ3eIOOo\nUpI2KYCgESyJqW3p5T+fnSPA24X7rk9EqRhMtgbZwLslH/N5xW48HN15dOp9TPYdunrZzc3Jpj67\n6AleHMmt42xlB3OTQ8z23Co+3Ju5KSEE+Rg3i1Lf1seftmZT3dSDq7OKWYnB3LggmtVzo77+HK4k\nwjOciR5hnGnOJ6MxG0eFA9FeESO6aPrm53cgu5a88jaumx055KMLc3JQqCjrOE9hWxEa/QAJfpMs\nOr6lOaiUzEwIor1HQ15ZKxnnmkiI8MXTbWQX1Lbw/esf0PHihwUcy28g1N+Nn26cRqi/eQorxxK3\nEVabj5uE3KnpwknpaNN3f5fj7KhiSoTPiJKxLMu88mkhTe1q7rluyteVyf06Df8ueItTDVmEuAXx\n2LQHCXG/9DS4LZwQvslBpcDV2YHMoma6+gZIm2SewiRJkoa1HKK5Q42rk+qivy0PVwccHZTctCCG\nWxbHMjXWnyAf12En4wsCXQNI9JtMfutZzjTn0znQTYLvJBTS8Ca4Lnx+sizz2s4i1Bod31uVgKOF\nl3pIksQU33hymgvIbz1LqFvwmF8SpVBITI31x0GlIKu4heMFDUQEeRA4gos8a3//2rs1/O3tHIqq\nO0iM9OGHt0y1mZ3hbN1IE/K4mLLu06r5a+Y/+Vf+Wxhkg7XDsZgzpS0UnG8jMcqXqbGDSzA6NJ08\nm/UieS1nmewTx+NpD+PnYjutI4fLmm0LDbJMeV0X7x0s4//96yRPvHScupaLW11KksTKWRFET/Ac\n9baGYR4T+En6I4S7T+Bo3UleyHkVtW5kFdhldV3UtfQyLS4Adwuusf4mZ5Uz30u6DUeFA2+efYem\nvmarxGFJkiRx3exIHrwhEZ1e5tl3cjlwxj4aaFQ39fC7N05T2djNgtQQHrs5FVdnUUltLmM+Icuy\nzJZz79La306IW9Cw7yrsnVZn4O29g/2qNyyJQ5Ikarrr+Mvp56nuqWPuhKt4OPUeXFQjWz5lKy60\nLQTYsqfYYnsaf3Gykh//8yi/e+M0nx2vpKlDzdRYf/QWqKT1dvLif6Y/RJLfFM61l/DXzBdoVQ9/\n0w1TbyRhrAnuwWyYvJZ+fT8ZjWesGoslXTUliJ9umIars4o3dhaxY3+pTe/FnVfeyh/eyqS9W8PN\nC2O4c/lkm9sVbqwZ85c6h2uPc6Y5j1jvKFZELrF2OBazK6OKpg4116SHM8HfjYLWc/w7/y00+gHW\nxKxk6cSr7Xb6/oK4MG9mJQRxorCRo7n1zLdAohnQGtDqDMxNCmZqXABJUb4WXTrkrHLigZQ7ea/k\nEw7UHOXpzOd5MOWuK7amVGt0nDrbhJ+nM1MirT8jclXwdHydfYjxirR2KBYVG+bFL+9I49l3ctl5\nsormDjX3WeHxwZXsz65ly65ilEqJh9ckkS7Wq1vEmL7cqe6u473ST3FzcOXuxI02uZTnSvoHdCNu\ngtHereHTY5V4uDpww7xIDtUc56Xc1zDIBu5Nuo1rIhbafTK+YN3CGBwdFLx3sIy+fp3Zx7v2qnCe\n/cE87l2VQNqkAKus41VICm6Ov4F1cavpHujhmayXyGnOv+x7Ms41odHqmZcSMurpc1OJ9Y4aM3+H\nIxHo48ov7khj8kRvMoua+fO2bDp7baNGwyDLvL2vhDe/LMLNRcVPN0wTydiCxnRC3l25H51Bxx1T\n1uPtZNmKUlN55ZNCfvmvk/Soh78W9t0DZWi0etbMj+SL6p28XfwBbipXHpv2INMDU8wYreX5ejpz\n3exIuvq0fHLsvNnHc3ZU2UwDhEXh83gg5U4kSeKVvDfZV3Xokhdvh3PrkBh89i5Yn5uzAz9aP5U5\nScGU13Xx+zdOUztEHYIlabR6Xvggny9PVRPi58ov70i3eCX+eGcbZxYzuT1hPfcn30mS/xRrh2KU\nHrWW3LJWlArFsItwymo7OV7QQHiwM8XKfeyrPkywayA/Tn+EKK+JZo7YOpZfFY6/lzN7TtdYZB9h\nW5Lsn8APpz+Ip6M775V+yo7iDy9a41vd2E1ZbReJUb5jdvtKe6RSKrj3uimsmR9FS2c/f3gzk8IK\n03ZlG67OHg1/3ppFVnEzkyd68/Pb0wgYYXteYfTGdEJ2UKhIDUi0dhhGyzjXhN4gMztpeEtDDPLg\nwn0cNCjiTpLbUkC8TyyPpz2Mv4v1txYzFweVkvWL49AbZLbvLbV2OBY30SOMn6Q/Sqh7CIdqj/NS\n3mv06/7bzGTXyUoAizxjH42G3kbeL/3UbH3KbZEkSayeG8V91yeg1el5ZkfO18V3llLTPFhJfb6+\nm7nJwfxo/VTcnK1ThT/eGZWQZVnm17/+Nbfeeit33HEH1dWWa8I/nhzPb0ACZiUED+v1R/Pqqeio\nwzP1FE2aemaFpPP91HtwtaP2oMaaHu/PlAgf8spbySm1rw3STcHH2ZsfTX+IBL9JFLYW8besF2nv\n70CnN7DvdDXuLg5fL32zVR+UfsbeqkPsqz5s7VAsbnZiMD++dRrOjkr+88U53jtYZpEK7ILzbfzx\nrUxauzTctCCae1ZOEZXUVmTUb37Pnj0MDAywfft2Hn/8cf74xz+aOq5xr6lDTWltJ5MjfIa14bla\no+Od0ydwSjiJVtHL9dHLuW3yzWbbvs/WSJLExqVxKKTBPtc6/fhZb36Bs8qZB5PvYn7obGp76vnL\n6efZU1BAV+8Ac5KCcVDZ9ol24+Sb8XT04MOyzylqG38zHfHh3vzyjnQCfVz47Hglmz8qYEBrvhaj\nB8/U8syOHLQ6mQdWJ7JqTuS4LLKzJZJsxPzQU089RUpKCitXrgRgwYIFHDp06IrvM/eeukfrTjIt\nIAVXh9E9+2jqa+FUQxZ62Xr9dtu7NeSVtxId4klY4JVb1OVXNlIrn0UpKbgrcT1pQVNNFktAgIfV\n90Meri27i9mbWcPaq6O5bnaktcOxClmW2V99mPdLPwNZyUBDGFenhOI+wh7oV+Lr7MPcCVeZdG1/\nSXsZ/zjzL5QKJT+Yeh9RXhEmO7a96FFr+cd7uZTUdBIV4kl6QpDJO3W1dfVzvKARdxcHHl2bTFyY\nbWyzOtYEBIysX7xRt089PT14ePx3IJVKhcFgQHGF6tORBjcSx6pOs/XcexR3lfDT+Q8ZfZyCpmKe\nznyJXjPsQzti3lCohsLK4b1c0jvyiyWPkBw8dE/q0TDnZ2dK31uTzOmiJt47WI67uzNrF8WOy6v+\ntX4rKCwdoNCwB4eQCo41V5hlnJLuEh6bdQ/ODqYpFgsImIrK9Xv87dgrvJj3H/6+8jd4OI2vnskB\nwJ8enc/f3z7Dgawaztd3mWWc0AA3fvW9WUwQPalthlEJ2d3dnd7e/1azDicZg/nukJv7Wnkp4y0c\nlY6sDF9m9Dgn6geTOsAt8WsI97DtIpgLyuu62L63hKunTCJYGWzy37M93SED/OiWqTz7Tg6vf1bI\n+Zp2bls2aVw9F+vr1/HCh3kUVigIC7mOu9dFIpt4q0qDLPPF+T1k1uXxi91P82DKXSZbWhjlFMPt\nU25Ba9DS3yXTj/387ZnS7dfEsWjqBFxcnejo6DPtwSWYGOiOgyzb1Xfb3ljkDnn69Ons37+f5cuX\nc+bMGeLj4405jEloDTpeLXiLfr2GO6asJ8ht5IvYZVnms/O7+aJiDy4qF+5PvoN4n4v3DbZVJzNK\nMPT4MD3GPi4gzC080J1f3pHO39/N5VBOPa2d/Ty0Jnlc9OBt6VTz7Du51LX0MjXWnwdWJxIW6m2W\nk+7Dqfewveh9jtVn8PTpf/JQ6t2EuptmnfNVwdNNchx7JkkS4YHuX10Qi6rn8cCo24ZrrrkGR0dH\nbr31Vp566in+93//19RxDdtHZZ9T1V3LrOB0Zoakjfj9WoOO1wq38UXFHvydfflx2vftKhkD5Ja1\n4OSoJF48B/qaj4cTP9s0namx/hRUtPPHtzJp6bSBxxBmdL6+i9+9kUldSy/XpIfzyE3JZu0kplQo\n2Th5HTfErKBd08HfMl+goLXIbOMJwlhn1C2DJEn85je/MXUsIybLMrIsE+wayC2T1oz4/T0Dvbyc\n9zplnRVEeUbwQMqdeDja1/OUxrY+GtvVTIvzt/kqWktzclTyyE3JbN9Xwp7TNfzujUweW5dCVIin\ntUMzucyiZl75pACt3sCma+JZkhZmkXElSWJZxCL8Xfx4vXA7L+X+h1vib2B+6GyLjC8IY4ndnMH7\ntH0XbZ0oSRI3x9/AT9IfxUk5sgrSpr5mns58nrLOCtICU3ls2v02kYy37y3hvYNlaHXDW7aTW9YK\nQKqNrzG1FoVCYuPSeDYujaO7b4A/bckis2jsbPknyzI7T1bxwgd5SJLEo2tTLJaMv2l6YAqPTXsA\nV5UL24s+4P2ST02+1WllVzXPZb9Mr9bEz1MFwUbYbEJu7+8goyGb7UUf8PuTf+Onh39DfW/jkK91\nVjdsk+IAACAASURBVI1sE+jSjvM8ffqfNKtbuTZiMXclbsBBaf1nNH39OvZn15JV3IxKObzK4Nzy\nwYScHO1nztDs3tL0cB5dm4IkSbzwQR47T1bZfUcovcHAm7uK2bG/FC93x6+n6K0l2iuCn6Q/QpBr\nIHurD/Gv/LcY0JtuuU5mUw7F7aX8M+ff3+pEJghjhU0m5H/lv8Uvj/2B1wq3cbj2OM3qVuK8o9Ea\nhr/BwqWcasjiH9kvo9b3s2nyzayOWW4zeyRnFjeh1RmYlRg8rKU6mgE9RVXtTAx0H1bzkPFuaqw/\nP9s0HS93R3bsL+XNXcXoDfbZQESt0fHcu7kcyK79uogtItj6S9P8Xfz4cdrDxHvHkNOcz7NZm+nU\nmKagbE3MSmYGp1HZVc1Lua+ZNNkLgi2wStmp1qCjqqsGdwfXIauiIz3DMRj0RHtHEuMVxUSP0FFv\nnSjLMl9U7OGz87txUTnzvaTbmexr+vW6o3E8vwGAWQnD611dWNmGTi+THCPujocrItiDX96R/nUy\na+lU89ANSbg42U8FdltXP8++k0NNcy8pMX48sDrRpuJ3dXDl+1PvZdu59znRcJq/nP4HD6fewwT3\n4bWAvRSFpGDT5HVo9AOcac7jlbw3uT/lThzGSTc6YexTPvnkk09aYqCsujwOVBzn8/O7eafkI47W\nnUShUJDgN+mi10Z7RZIWNJVor0h8nL1GfQerNeh469w7HKg5ip+zDz+Y9oDN7XzU1tXPtj0lxIV5\nce1Vw4ttd0Y1FQ3d3LwwFl9P8+3i4+bmZPJOQdbk4qRiVkIQNc095JW3kVvWQmqsv00ltUupaOji\nz9uyae7oZ/H0UO5dNeWKm9tb4/NTSApS/BNQKpTktBSQ0ZDNRM9QAlxGd/GokBSkBiRS1V3D2bZi\nYr2iCHAd2xekY+37N564uY1s5tJiZ6CnDr8AgIREmHsIMd5RJPmZf1vEXm0fr+S9QUlHORGe4TyY\ncheejtaf2vuuwop2ZGB20vDuImRZJqesFTdnFdETxl7VsLm5OKl4dG0y2/aUsC+rlt++cZrH1qUQ\nGWy7v8vskmY2f1yAVmtgw5I4lqaH2XQXMkmSWB65BH9nX948u4MXcl7l1vgbmRs6c1THVSlU3Jd0\nB6Ud5Uzxs14PBEEwNYsl5JsSVjDBIZRIr4m4qCyzJ2tzXysv5P6bpr4WpgYkc2fCehxHWI1tKfNS\nQogL98JzmP2Ga5t7ae/WMCshCIXCdk/KtkypULDpmngCfVx5e28JT23J4oHViUyLC7B2aN8iyzJ7\nTtewfW8JDg4KHrkpmWnxthXj5aQHT8Pb2ZuX815na9F7NKtbR1274ah0GHJ2TRDsmcWqmW5NXs0U\nv3iLJeOyjgqeznyepr4Wrpm4kHuTNtlsMr4gyMd12NOmOWWDWwyK58ejI0kSy2YMNtEAeP69PHZn\n2M52onqDga27S9i2twRPN0ee2DjdrpLxBbHeUfw47RECXfzZXXWAV/O3MKAffZGmIIwltlFebGKZ\njWf4+5mX6dOp2TDpJtbErrSZSmpTyStrRUIsdzKVafEBPLFxOp5ujmzbW8IWG6jA7h/Q8Y/38tib\nVUNogBu/vCPdrpuaBLr683j694n1jiK7OY/nsjfTPdBj0jE6NebZiEEQLGFMZSlZltlZsY9XC7ai\nkpQ8nHIP80JnWTssk+vt///t3Xl4U2X6//F3kibd95WWbnShhdIWWkFAFBCEsooiLoiKqLjgjs58\ndUb5zrj9lNFxEEYBRwVXxIVFRQVXEBFKaQsUulOgdN/3pMnvD9SvOpQ2adIk7f26Lq5LuHKe82lj\nevec8zz3oyX/dANDQjxwc7b++un+InKQB3+5IZUQf1d2HTzFqg+yaevQWSVLbWM7z7x5kKyCaoZH\n+vDI9Sn4evbN3SVLclO7siz5Vi4IHEVxQwnPHXiJsi76CxirsP4Ef/txJTtLvjXLeEL0tX5TkHU/\nz6TeVrgDb0cvHky5q99O+DhSVIPeYCBRro7NztfTiUeuT2F4pA9ZBdU88+ZBahvb+zRDSXkjT2w4\nQElFExOTg7l3fqJdzADvKbXSgRuHXc2MyKlUt9WwMn01x2vyez2uh8YdJwdHPsr/hO9O7TVDUiH6\nVr8oyC3aVlZn/ocfzxwgzH0wD6Uu6/Wax76y93AZRWcajOoalZl/tjtXYpS0y7QEZ0cH7p2fyMTk\nYEoqms4Wx/K+2aIuM7+Kp988SF1jOwsmRbNoWv/cOlKhUDAzcio3DruGjk4tL2WuZ2/p/l6N6efs\nwz3Jt+KuduO93I/YdybdTGmF6Bt2/0mvaq3hH+mrya3NJ9FvOPeNuh1PR/t4ztbe0cmGL47z748P\n9/gYvcFAdmE1nm4awgKt33u7v3JQKVk0bSgLJkVT19jO028eJDO/yqLn3JV+in99kIXBYODOeQlM\nHxNm08uazGF00CjuTr4VJ5Xj2TtcBTt61QM70DWAu0feiouDMxtzNpFRkW3GtEJYll3fByuqL+Hl\nrNdo0jYzOXQC86Jn2tXkrYy8Sto7OpmaGtrjH7xFZxpoatUyIXFQv/9hbW0KhYLpY8Lw83Ri3faj\n/OuDLOaOjyTQx8Xs58o9WcfXGafxcFFzz/ykAbW2PMZ7CMtT7mJN1mvsOPEVla3VLIpfYHJ/+RC3\nQdyVvITVh16lU2+dOQBCmMJuC/LBiiw2HH0Xnb6Tq2Mv5+LB46wdyWh7j5ydzDJ2eM9aZcLZ2dUA\nibLcqc+kxgXg7eHIqs1ZfLy7yGLnCfZz5b75ifh5OVvsHLYq0DWAh1KW8Ur2G6RXZFLbXsdtI0zf\nDjXCI4z/HftnXNQD73sp7JfdFWSDwcDOkm/5uOBTHFUabk9cRIKf5Tt+mVt9cwdHimqIHOTOIF/X\nHh+XWVCNSqlgWISPBdOJP4oK9uTxxaPJKqhCb4FNotQqJaNi/XFxsruPpNm4aVy5J/lW3jz2PgfK\nD7EyfTV3Ji4+Z7/7npBiLOyNXX36O/WdvJf7EXtKf8LL0ZM7Ehcz2D3Y2rFMsu9oOXqDgQuH93zy\nWX1TOyfKGokP9+5Xs27thbe7I5ckh1g7Rr+mVqm5cdg1+Dn7sqN4FyvTV3PbiBuI8Y6ydjQhLM5u\nfqq36lpZn/0mx2rzCHUL5vakxXg5elo7lslGxweg1xsYE9/z29W/7H0st6tFf6ZUKJk9ZBp+zr68\nfWwzqw6tZ2HcfMYMSun12CWNp/DUeOLpaHv97IWwixlQ1a21/CN9Dcdq80jwjee+UXfYdTEG8HJz\nZPqYMDxce97OU54fi4Fk7KBUliXdgkalYUPOe3xS+IVRywP/qLSpjOfT17D+8EZ0MtlL2CCbL8gn\nGk7yXPoqzjSXM3HweJYm3oiTg3FbWvUHuk49R4pr8PdyIsgCs3yFsEVDfaJZnnInvk4+fFq8kzeO\nvofWxGI6yDWQRL/hFNYX837eVjMnFaL3bLogH6o8zAsHX6apo5n5MXO4KnauXS1rMqf8U/W0tneS\nOMRPljuJASXINZCHUpcR6RHG/vKDrMpYR5O22ehxFAoFC+OvIsRtELtP/8ju0z9aIK0QprPJ6mYw\nGNhV8h3rszeiUChYmngjk0IvsnYsq8r65XZ1tNyuFgOPu8aNe0YuZWRAIgX1RfzjwGoqWoxv1OKo\n0nDbiBtxdXBhU+4WCuuLzR9WCBPZXEE+O5P6Yz7M346Hxp0HRt3BCL9h1o5lNmU1LehNeA6WVViN\nxkHJ0FAvC6QSwvZpVGpuHn4dl4VPoqK1ipXpL5FfZ/y6cD9nH25OWIhaqaaxw/grbSEsxaYKcquu\njZezXuf703sJcRvEQ6nLCHXvP8tMtDo9T7xxgKc3Gtdjt6quldKqZuLDvdGoVRZKJ4TtUyqUzI1K\nY2HcfFp1bazKWMuBsgyjx4nzieHv4/6HJP/hFkgphGlsZtlTbVsd/856jdNNZxjuG8fNw6/DycH+\nt5v7rc9+PEFLu47YMOOucmW5kxC/Ny54ND5O3qzL3shrR9+hsrWG6RGTjZpfIY1DhK2xiSvkksZT\nPHdgFaebznBxyFiWjrix3xXjE2WNbPuhGG93R2ZeGGHUsb88Px4hBVmIX8X5xPBgyp34OHmzvehz\nNuZskuVMwq5ZvSBnVx3lhfR/09DRxJXRs1gQezkqZf+6LavV6Vn/yVE69QYWz4gzqj1ih7aTnBO1\nhPi54ucpv9EL8VvBbkEsT1lGuHso+8rSWX3oVVq0LSaPp+3UmjGdEMaxakH++uRuXsl6AwNw64hF\nTA67uF8u6fkpp5zTlc1MHBlCQqRxV7nHSurQ6vRydSxEFzwd3blv1FKS/BPIrStgZfoaqlqrjR7n\nh9L9/O+Pz1HbVmeBlEJ0zyoFWW/Qsyl3C5vztuKuceP+UbeT5J9gjSh9YlxCELfNHsaCScb3480q\nOLu0I0kKshBd0qg03JJwPZeGXUx5SwXPHXiJwvoTRo3R0dlBbXsda7M30CFXysIK+rwgt+naeSXr\nDb49tYdg159vN3mE9nWMPqVQKLhweBBOGuPm0BkMBrIKqnF2dCAqxL5bhQphaUqFkiuiZ3HN0Hm0\n6Fp5MeMV0ssze3z8JYPHcWFQKiWNp3j3+Ie9atMphClMmmXd1NTE8uXLaW5uRqvV8uc//5nk5ORu\nj6trr+flzNc42VRKvE8sSxIW4uwgz0W7cqa6har6NlLjAnBQWf1xvxB2YULIWHydfHj18Jv858hb\nVLfWMDV8YrePwxQKBdcMnceZ5nL2laUT6h4y4BsSib5l0k/51157jXHjxrFx40aefvpp/va3v3V7\nTHHtKZ478BInm0oZHzyGOxIXSzHuxq/duYbI7WohjDHMdygPpNyJt6MXWwo/4+1jm+nUd3Z7nFql\n5tYRi3DXuPFZ0U5ada19kFaIs0y6Ql68eDEazdldinQ6HY6O3W/28NhXK2nTtTMveiaXhvbPyVu/\naOvQ0dCiJcCrd79w/PL8WCZ0CWG8X5oLvZz1Gj+c2U91Wy23JCzqdv2xt5MXS0fchLODk1w0iD7V\n7RXy5s2bmT179u/+FBcXo9FoqKys5OGHH+bBBx/s9kSdBj23JCxiStgl/boYA2z6uoDHX/2JgtP1\nJo/R2q4j71Q9EUHueBqxRaMQ4v94Onpw36g7SPQbzvHafNYd3tijZ8ORnmEEuQb0QUIh/o/CYOLM\nhePHj7N8+XL+9Kc/cdFF3T9nKawpYYhPmCmnsisZxyt4bO1ewoPceeH+S1A7mLamek9WKc+8sZ9r\nLxvKddPizJxSiIFFr9fz/3b/m4wzh7l/3C2MDU2xdiQh/otJt6zz8/O57777+Oc//8nQoUN7dMwQ\nnzAqKxtNOZ3daGnT8cI7B1EpFdw0PY66WtMbFOzOOAVAVJC71b9v/v7WzyBMJ+/fWXPCZ5BVlsPr\n6ZsJU0egUdnHnSd5/+yXv7+7Ua83aVLX888/T0dHB08++SSLFi3irrvuMmWYfuedXbnUNrYza1wE\n4UHGvRG/pTcYyC6oxt1FTcQg08cRQvyfABc/JodOoLa9ji9LvjXqWIPBwDen9nCsJs9C6YQw8Qp5\nzZo15s5h96rqWtl3tILwQHdmjg3v1Vgny5uob+5gXEIQyn7+vF2IvjQ9YjL7ytL58sQ3jB2Uio+T\nd4+Oq2yt5qO87TiqHHn4gnvwc/axcFIxEMniVjPx83Lm8cUXcOvsYb1eM5z58+xq2d1JCPNycnBi\nblQaWr2Wj/M/7fFxAS5+LBh6Oc26FtZmv0F7Z4cFU4qBSgqyGYX4uRLs59rrcbILqlEqFCREym/h\nQpjb6KBRhHuEkl6RSV5tYY+PGx88hgkhYznddIY3czZJJy9hdn1WkJ/4zz4qejHJaaBoaOmgsLSB\n6MGeuDiprR1HiH5HqVByVcxcAN7P24LeoO/xsfNjZhPlGcHBiiy+Ovm9pSKKAarPCvK+I2X89dWf\n2LanCK2u5x+AgeZIYQ0G5Ha1EJYU6RnGmKAUTjedYU/pTz0+zkHpwC0jFjHMZyiJfsMtmFAMRH1W\nkB++PhUXRwc++r6IFa/9xPGS2r46tUUYDAZyT5p/mzZ5fixE35gblYajSsO2wh1G7aHsoXHnruQl\n+LvIZ1SYV58V5AkjQ3jy1jFMGhVCWXULL2zKpLHFfidG7D1SxjNvHeSTvcVmG7NTr+dIUQ0+Ho6E\nmOFZtBCia56OHqRFTKFZ28InRV9aO44Qpi17MpWLk5pFlw1lfMIgzlQ34+5iHwvz/6imoY23vszD\nUaNidHyg2cYtON1Ac5uOC+IC+n17USFswcTQi9hTuo/vTu9lfPAYgt2CrB1JDGBWmWU9JNiD8SMG\nWePUvWYwGHj9s2O0tuu4enI0/r3cQOK3sgt/3t0pys9sYwohuqZWOnBlzGz0Bj0f5G0zeea0wWCg\noUO6aYnesallTwaDge+zSmnXdr9NmrV8l1nK4aIaEiJ9uCQp2KxjZ+ZX46BSEh/es2YFQojeS/CN\nZ5jPUI7V5pFVdcTo4w0GA+sOb+TZ/atkfbLoFZsqyIfyqnjt02P8df2+X/cCtiV6g4FvD5Xi7OjA\nTWlxZr2tXNPQxqnKJuLCvHDUmLYhhRDCeAqFgitjZqNUKPkgbzvaTq3Rxw9yCaC2vY4dxbsslFIM\nBDZVkIdF+JA2Jozaxnb++X4maz7Kprax3dqxfqVUKPjTwlE8cHUSPh5OZh076+fb1bL3sRB9L8g1\ngImDx1PdVsMuE9YXXxYxGW9HL3aVfEd5S6UFEoqBwKYKsqNGxVWTonn8pguIDvHkwPFKHl33I4Wl\nDdaO9itHtYqoYE+zj5td8MvzYynIQlhDWsQU3NSufH7iK+rajdvL3FGl4cqY2XQaOnk/d4t08RIm\nsamC/IvBAW78+fpR3Dh9KCF+roQGuFk7kkVpdXqOFtcS6ONCoLeLteMIMSC5qJ2ZEzWdjs4Oo/pc\n/yLZP4E47xhyanI5XJ1jgYSiv7PJggxnbw9fkhzCI4tSUDvYbEyzyD1ZR7u2kyS5OhbCqsYOuoBQ\n9xD2l2dQWF9s1LEKhYKrYucyK/Iy4rxjLBNQ9Gs2X+m6mjhV39TeJ7eFjhTV0Nahs+g5funOJc+P\nhbCu3/W5zjWuzzWcfRadFjkFtUr60Avj2XxBPpe2Dh1/33CAf76fRWFpA81tWosU59OVTby4OZPn\nN2VatPhnF1TjqFERO9jLYucQQvRMlFcEqYHJlDSe5sczB6wdRwwgfdqpy1xa2zsJ8nEhu7D612Ya\nThoVCUN8ufPyhP96vV5vAMXZ2+A9pevUs/6THHSdBmaMCbdY56zymhbKa1sZGePX72/NC2EvLo+a\nQVblEbYW7GBkwAicHczXAEiIrthlQfZ2d+TBq5NJP15JTkktNfVtVDe0oVadu2gePVHDi+9n4e3u\niJ+nEz4eTvh6OBEZ7EFy9Lm7Yn269wQnyhoZPyKI5BjLdc76Zb11Uhc5hBB9z9vJi2kRk9lW+Dmf\nFe3iiphZ1o4kBgC7LMhw9tlyalwAqXEB3b5WpVAQEeROVUMbx0r+b4em0fEB5yzI2YXVfLy7CG93\nR669NNasuf/o1/XHQ+T5sRC25NLQi/mhdD9fn9rN+ODRBLp2/7PmjzIrj/DNqT3cmbhYniuLbtlt\nQTZGfIQPj0b4AGeXGNU2tlFd34aT47m//PKaFhQKWDwjDhcny32L2jp0HC+pJSzADW93R4udRwhh\nPLVKzRUxs1iXvYHN+du4K2mJ0WPk1xWSW5vPzpLvSIu81AIpRX8yIAryb6kdlAR4uxBwnvW+4xKC\nGBnjj6+nebtx/VHOiVp0nQaZXS2EjUryG85Q72iOVh/ncFUOCX7xRh0/I3IqB8oP8fmJrxgdNApf\nZ+lTL7oms4jOwcVJbfFiDL95fiy7OwlhkxQKBfNj5vzc53obOr1xSyCdHZyYFz0TrV7LB/nbLJRS\n9BdSkK3EYDCQVVCNq5MDQ4I9rB1HCNGFYLcgJoSMpaK1iq9P7jb6+AsCRxLlGUFm5WGOVh+3QELR\nX0hBtpJTlc3UNraTMMQXpdIyS6qEEOYxK3IqrmoXdhTvor7duH2PFQoFC2IvJ9AlAAflgHtKKIwg\nBdlKsn7uziWbSQhh+1zULsyKnEZbZztbCz4z+vjB7sH8ZcwDxHpHWSCd6C+kIFtJVkE1CiAh0sfa\nUYQQPXBRyBhC3AbxY9kBihtKjD5eqZAft+L85P8QK2hu05J/up4hIR64u2isHUcI0QNn+1zPAeD9\n3K1G97kWojtSkK3gcGENBgMkSjMQIexKjHcUIwMSKW4oYX9ZhrXjiH5GCrIV/LLcKVGWOwlhd+ZF\nzUStdODjgk9p07WZNEZ7Zwc7S76lU99p5nTCnklB7mN6vYHswmo83TSEBbpZO44Qwki+zt5MDZtI\nQ0cjO4q/MmmMz4p28lH+J3x9yvhlVKL/6lVBLigoIDU1lY6ODnPl6feKyhpoatWSOMTXYjtICSEs\na2r4RLwdvfj65PdUtFQZffyU8EtwdXDh06IvqW9vsEBCYY9MLshNTU08++yzODpKD2ZjZOX/crta\nnh8LYa80Kg3zomeiM3TyoQkduNzUrsyJmk57Zwcf5X9igYTCHplckB977DEeeOABnJws32KyP8kq\nrEalVDAsQpY7CWHPRgUkEuM1hOyqHJM6cI0LHk2Y+2D2l2eQV1togYTC3nRbkDdv3szs2bN/92fp\n0qVMnDiRoUOHYjAYenSinT8Zv26vvzlV2cSJskZiQ71w7mKnKSGEffilz7UCBZvzthk9QUupULIg\n9nIUKDhSfcxCKYU9URh6WlF/Y9q0aQQGBmIwGMjMzCQpKYmNGzee95jZD27hyknR3DBj2IBsFZmd\nX8WTr/9Ec6uWBxemMHHUYGtHEkKYwboDb/NlwffckDyfWUON32LxZH0poZ7BFkgm7I1JBfm3Jk+e\nzOeff45aff7Nt5c+vZPSqmZSh/pzy6xhaNSq3pzWruzJPsPrn539DfimtDjGjxhk5UTG8fd3p7LS\nuP69wnbI+2dZTR3NrPjxWQwGAyvGPoy7xryrJ+T9s1/+/u5Gvb7Xy54UCkWPbls/d8/FxIZ6ceB4\nJc++k0FDc/+fmW0wGPjou0Je/SQHR7WKB69OtrtiLIQ4PzeNK7MiL6Ots41thTusHUfYsV4X5F27\ndqHRdN/+0cNVw4NXJzN2eCCFpQ08seEAp6uae3t6m6XV6Vm37SjbfijG38uJR29IIS5cNicXoj+a\nEHIhg1wD+aF0PyWNp6wdR9ipPm0MonZQcsusYcy9KJKq+jae2phOTnFNX0boE40tHax8N4Mfj5YT\nFeLBozekMsjX1dqxhBAWolKqmB8zBwMG3s/d2uPJrudS2VItfbIHqD7v1KVQKJh7USS3zhpGh7aT\n5zdl8n1WaV/HsJjymhae3JhO3ql6RscH8PC1I/GQDSSE6PfifGJI8htOYX0x6eWHTBrjYEUWf9+3\nkt2n95k5nbAHVmudOTYhiOXXJOOkUfHap8f48LsC9L2bX2Z1uSfreGLDASpqW5k5Npzb5gxH7TBw\nJq8JMdBdETMLB6UDHxV8Snun8fNkojwjUSvVbCvcQVNH/32kZytq2+r4+qTttC+1ai/roWHePHpD\nKgHezmz/4QRrtx5Bq7PPZut7j5Sx8t0M2jo6WZwWx5WXRKGU1phCDCh+zr5cGnoxde31fHHia6OP\n93R0Z+aQqbToWtla+JkFEorf8nL0pLa9jvLmCmtHAWxgc4kgHxceXZRC9GBPfsqp4Ll3DtHQYj8z\nsA0GA1t3F7Fu21HUDiruX5DEhCRZUyjEQHVZ+CQ8NR7sLPmWqlbj58hcEjKOYNcgfijdz4mGkxZI\nKH6hUCi4InoWga4B1o4C2EBBBnB30fDQNcmMGRZI/ul6ntqQzplq279do9XpWb89h493F+Hn6cQj\ni1KkJaYQA5yTgyOXR89Ap9fxUf52o49XKVUsiJ2LAYP0uR5gbKIgA6gdVNw2exizxkVQUdfKUxvT\nOV5Sa+1YXWpq1fL8e4fYe6SMIcFnZ1KH+MlMaiEEXBA4kiGe4RyqPMzxmnyjj4/xjuKqmLncMOxq\nC6QbuGx9/2mbKcjw8+2Di4dw84x42jo6WfnuIX44fMbasf5LRW3L2V8YTtaROtSfh68diaerzKQW\nQpylUCi4Kmbuz32ut5pUCCaGjsfHSXoXmMvBiiye/Ol56trrrR2lSzZVkH9xUeIgHliQhKNadfaW\n8PeFvVrXZ075p+p5YkM6ZTUtpF0Yxu2XJwyoNqBCiJ4J8xjM2EGplDaX8X3pj9aOM6D9VHaQ/xx+\ni/r2Bmrb6qwdp0s2WZAB4iN8eGRRCn6eTmzdU8z67UfR6qy7WP6nnHKefSeDljYdN04fylUTo2Um\ntRCiS3Oi0nBSOfFJ4Rc0aW1/Xkx/9EPpfjYcfQ8nByfuHnkrkZ7h1o7UJZstyADBfq785YZUooI9\n2HuknH+8m0FTq7bPcxgMBrb/UMzLW47goFJw34JELkkO6fMcQgj74q5xY0bkFFp0rWwv/KJXYxkM\nBtp07WZKNjB8d2ovbx17Hxe1M/eOvI0IjzBrRzovmy7IcLYH9kPXjiQ1LoDcU/U8ueEA5bUtfXZ+\nXaf+58Ylhfh6OPLIohQSIn377PxCCPt2yeBxBLr4s/v0j5xqNK0rYYu2lVWH1vHG0Xdt5vGdPajv\naMBd7cZ9I28n1N32L6JsviADaNQqbp87nJljwymvbeXJDenknrT8c4CWNi0vbMpkd/YZIoLcefSG\nVAb7m3drNSFE/+agdODKn/tcb84zrc+1k4MjeoOerKojHKzItEDK/mlW5GU8MuZ+gt2CrB2lR+yi\nIAMoFQquvCSKm9LiaG3X/bx5Q5nFzldZ18qTG9PJOVHLyBg//nTdKLzcHC12PiFE/zXcdygJvvHk\n1RWSUZlt9PFKhZLr4uajVqrZlLuFxo4mC6TsfxQKBR4a4/YktiYHawcw1sVJwfh6OrHmo2zWSIRE\nPwAAE6lJREFUbj3KweOVOGnM/2VkFVTR0KJl2ujQs5O3lDJ5SwhhuitjZpFTk8uHedtJ8I1DozJu\nqWSAix9zhkzjg/ztvJ+7hZsTFloo6cCh7dSys+Q7hvnGEu4Rau049leQAYZH+PDI9Sm8uDmLA8cr\nLXIOlVLBostimTRqsEXGF0IMLAEu/kwOncCXJd/wZcm3zIycavQYE0Mv4mBFFukVmYytvoB431gL\nJLU/BoOBT4t3MiYoBT/nnnVLbOxoYm32GxTWn0Cr10pB7o0Qfzeeuu1CahotM+vQxdEBN2e1RcYW\nQgxM0yMms68snS9PfMPYQalGN/5QKpQsjL+K7MqjxHpHWSilfdEb9Lx7/CP2lO6jpOEUdyQt7vaY\n8uYK1mS9RlVrNamByaRFTumDpN2z24IM4KBSEuDlbO0YQgjRI04OTsyNSmNjziY+yv+EJQnXGz3G\nINdABrkGWiCd/dEb9LyZ8z77ytIZ7BbMovgF3R6TV1vA2uwNtOhaSYuYwszIqShspJ+E3UzqEkKI\n/mB00CjCPUI5WJFFXm2htePYrU59J68feYd9ZemEu4dy78jbcNOcfz+BfWfSWXVoPe2dHdwQfzWz\nhlxmM8UYpCALIUSfUiqUXBUzF4D387agN1i3A6G9yq46SnpFJkM8I7h75K24qF26fK3BYGB74Rds\nyHkPjUrDsuRbGDMopQ/T9oxd37IWQgh7FOkZxpigFPaVpbOn9CcmhFzYq/E6OrVoVANrzktywAgW\nxS8g2X8ETg5dL0nV6nW8lfM++8sz8HPy4Y6kmwmykf2P/0iukIUQwgrmRqXhqNKwrXAHLVrTuw/m\nVOfy+N5nyKstMGM6+3DhoNTzFuMmbTOrMtaxvzyDSI9wlqcus9liDFKQhRDCKjwdPZgecSnN2hY+\nKfrS5HFc1M40djTx5rHNdHR2mDGhfatoqeQfB1ZTUF/EqIBE7hl5G+4a2+60KAVZCCGsZFLoBPyd\nffnu9F5Km0zrPBjuEcqlYRdT1VrNtsLPzZzQNrTqWqlsqe7x6/Prilh5YDUVrVVcFj6JxcOvs4tb\n+lKQhRDCStRKB66MmY3eoOeDvG0mbxwxM/IyApz9+PrkbgrrT5g5pXW1aFtZlbGef2a8TF17fbev\n31+WwaqMtbR2trEw7irmRqWhVNhHqbOPlEII0U8l+MYT7xPLsdo8sqqOmDSGRqVmYfxVALx1bHO/\nmbndrG1h1aG1nGg8SZx3zHn7UhsMBj4r2snrR99BrVJzV9ISxgVf0Idpe08KshBCWJFCoWB+zByU\nCiUf5G1H22nanu/RXpHMGTKda2Ln2c0V4fmcnZC1lpLG04wbdAEL4+d3+XXp9Do25mxie9EX+Dp5\n82DKXcT5xPRx4t6z/3dNCCHsXJBrABMHj6e6rYZdJ783eZzLIiYR4z3EjMmsQ9up5V8ZaznZVMr4\n4DFcG3dll8W4RdvCS4fWn20Q4hHK8tRldtvJTAqyEELYgLSIKbipXfn8xFc9elban6lVai4IHMmE\nkLFcM7TrK/6q1mpWpq8mr66QZP8R3DdyqV1tt/hHUpCFEMIGuKidmRM1nY7ODj7O/9TacaxuavhE\nro69vMtiXFhfzHMHXqK8pZKpYRNZkrDQ6C0tbY0UZCGEsBFjB11AqHsI+8szKKwvNsuYOr3OLONY\nQ1d9ptPLD/FixlpadK1cO/QKLo+e0S+em5v0Fej1ep588kmuu+465s+fz7fffmvuXEIIMeD8rs91\nbu/6XOsNejbnbuWFgy/Tqe80V0SL6OlyL4PBwOfFX/GfI2/joFBxZ+LNXNTLtqO2xKSCvGXLFjo7\nO3n77bdZvXo1J070r3VvQghhLVFeEaQGJlPSeJofzxwweRylQkmTtoXihhK+6sVEMUurbavjhYMv\nU9Zccd7Xdeo7eevYZrYW7sDb0YsHU+4i3je2j1L2DZMK8u7duwkICGDp0qU89thjTJo0ydy5hBBi\nwLo8agYapZqtBTto7jC9z/X82Nm4q934pOgLylsqzZjQPGraavnnwZcpqC8iq7LrNditujZWZ77K\n3jP7CXMP4aHUZQS7BfVh0r6hMHRzr2Dz5s288cYbv/s3Hx8fQkJCeOqpp9i/fz8vvvgib775pkWD\nCiHEQPLh0c94N3sr4V6D+fOEO/F18TZpnB9PHuT5H9YR5xfFiskP2Myz1srmav736xeoaK7mymEz\nWJAwq8tnxmsPvM3Ogu9JDUningsXn3dDCXvWbUE+lwceeIC0tDSmTp0KwEUXXcTu3bu7Pa6ystH4\nhMLq/P3d5b2zY/L+2adOfSebcj9md+k+PDUe3JG0mFD3EJPGWpe9kUOV2VwdO4+LB481c1LjVbXW\n8GLGK9S01TIzciozIqd2+dqTjaX8v/0vEujizyOj70elVPVh0t7x9zduCZZJvyqlpKT8OpHr2LFj\nBAcHmzKMEEKILqiUKq4ZegXXJ11BQ0cjzx/8N4erckwa6+qhlzM+eDSjAhLNnNI0ubUF1LTVMnvI\ntPMWY4PBwPu5WzBgYH7sHLsqxqYw6Qq5o6ODFStWUFBwdv/NFStWEB8f3+1x8lu6fZIrLPsm7599\n8/d358sjP/D60XfR6XVcFTuXSwaPs3asXjvRcJJwj9Dzvia9/BD/OfI2iX7DWZp4Yx8lMx9jr5Ad\nTDmJRqPhqaeeMuVQIYQQRkoOGMF9Tp68nPk6m3I/prK1iiuiZ9nM82BTdFeMOzo7+Cj/UxwUKq6I\nntVHqazLft9NIYQYQCI8wngodRlBroF8fXI3a7M30N7ZYe1YFvPFiW+oba9jctjF+Lv4WjtOn5CC\nLIQQdsLX2YcHR91JnHcM2VVHeeHgv03ue32o8jCrMtbxefFXFNWXWKx5SGlTGaebzhh1THVrLTtL\nvsFT48G08MkWyWWLTLplLYQQwjpc1M7cmXQz7x7/kB/O7GflgdXckbSYELdBRo1zqrGUY7V5HKvN\nA8BJ5Ui0VyQTQy8i3sc8DTdON53hXxlrAXj8wodxUTv36LiP8rej1eu4PHpGv13idC5yhSyEEHZG\npVRxXdx85kalUdtex/PpazhSfdyoMWYNuYxnLnqMm4cv5KLgMXg4unO4+hgtWtMbkfzWqcZS/pWx\nliZtM7OGTOtxMc6tLSCjMptIjzBSA5PNksVeyBWyEELYIYVCwWXhk/Bz9uWNo+/yctZrLIidy4SQ\nnq8zdte4kRKYREpgEgB17fU4qZzO+drXjryN3qAn1juaWO8oApz9umzkcbLxNKsy1tGia+W6uCsZ\nHzymR3k69Z1sztsKwFWxc+160poppCALIYQdGxWQiJejJ69kvc67xz+isqXa5N2PvBw9z/nvBoOB\nksZTVLRUcbAi69fXxnhFMT92Nm5q119f26Jt+bUYL4ybz9jgC3p8/j2lP3G66QwXDkrtdhZ2f6Ra\nsWLFir46WUtL/50R2J+5ujrKe2fH5P2zbz15/7ydvBgZMIKcmjyyq49yprmMEX7xZmukoVAouCRk\nHKlBIxnkGoRGpaaytZqy5nJmREz5XfFXq9Q4OTgxKiCRC4NTe3yOZm0L67I3oFIouW3ETf3i2bGr\nq3Ffg0mNQUwlzQnskzSWsG/y/tk3Y96/Fm0L67I3kltXQLh7KEsTb8LT0bjmFD1lMBioba/Dx8m0\nHtt/tCn3Y7499QPzomcyJewSs4xpbX3SOlMIIYTtcVG7cFfyEi4MSuVE40lWpr9EaVOZRc6lUCjM\nVoxLm8r4/vSPBLj4MXHweLOMaY+kIAshRD/ioHTg+virmD1kGjVttfwjfQ3HavKsHatLBoOB9/O2\nojfouTJ6Ng7KgTu1SQqyEEL0MwqFgukRl7J42LXo9FpWZ77KntJ91o51TpmVh8mtzWe4bxwJft3v\nidCfSUEWQoh+KjVoJHePvA1nByfePvYBWwo+Q2/QWzvWrzo6tXyYvx2VQsWVMbOtHcfqpCALIUQ/\nFu0VyfKUZQQ4+/HFia/5z5G36ejUWjsWALtKvqO6rZaJoeMJdPG3dhyrk4IshBD9XICLHw+m3kW0\nVyQZFVn8K+MVGjuarJqptq2OL058hbvGjbSIKVbNYiukIAshxADgpnZlWfKtXBA4iqKGEp478BJl\nzeVWy/Nxwad06LXMHZKGs8O5u4MNNFKQhRBigFArHbhx2NXMiJxKdVsNK9PXkFub3+c58uuKOFB+\niHD3UMYMSunz89sqKchCCDGAKBQKZkZO5cZh19DR2cGqQ+vZe+ZAn51fb9CzOXcLAFfFzhlw/arP\nR74TQggxAI0OGsXdybfgpHLkzZxNbCv8nL5o3Li3dD8nm0oZHTSKSM9wi5/PnkhBFkKIASrGO4rl\nKXfh5+zLjuJdvH70HbQWnIHdom1la+EONCoNc6PSLHYeeyUFWQghBrBA1wAeSlnGEM8IDpQf4l+H\n1tHU0WyRc31WvJMmbTPTwyd3ubPUQCYFWQghBjg3jSv3JN9KSkAShfXFPJf+EuUtlWY9R1lzOd+c\n2oOfkw+TQyeYdez+QgqyEEII1Co1Nw2/lukRl1LVWs3KAy+RV1tolrENBgOb87ahN+i5ImY2apXa\nLOP2N1KQhRBCAKBUKJk9ZBrXxy+grbOdVYfWse9Meq/HPVydQ05NLnHeMST6DTND0v5JCrIQQojf\nGTsolWVJt6BRadiQ8x6fFH5h8gxsrV7H5rxtKBVK5sfOQaFQmDlt/yEFWQghxH8Z6hPN8pQ78XXy\n4dPinbxx9D20ep3R43x98nuqWqu5JGQcg1wDLZC0/5CCLIQQ4pyCXAN5KHUZkR5h7C8/yKqMdTRp\nez4Du769gR3Fu3BTuzIjcqoFk/YPUpCFEEJ0yV3jxj0jlzIyIJGC+iL+cWA1FS1VPTp2S8FntHd2\nMHvINFzUzhZOav+kIAshhDgvjUrNzcOv47LwSVS0VrEy/SXy64rOe0xRfQn7ytIJdQtmXPDoPkpq\n36QgCyGE6JZSoWRuVBrXxV1Jq66NVRlrOVCWcc7X6g163v+5X/X82LnSr7qH5LskhBCix8YHj+HO\npJtxUKp57eg7fFa0679mYO8rO8iJxpOkBCQR7RVppaT2x6SC3NTUxK233srChQu5+eabqa6uNncu\nIYQQNireJ5YHU+7Ex8mb7UWfszFnE7qfZ2C36trYUvApaqWaedEzrZzUvphUkD/88EOGDh3KW2+9\nRVpaGuvXrzd3LiGEEDYs2C2I5SnLCHcPZV9ZOi8dWk+LtoUdxbto7GhiWvgkvJ28rB3TrphUkGNj\nY2lqagLOXi2r1dIGTQghBhpPR3fuG7WUJP8E8uoKee7AS3x9cje+Tt5cGnaJtePZHYfuXrB582be\neOON3/3bY489xp49e5g5cyb19fW8/fbbFgsohBDCdmlUGm5JuJ6PCz5lV8l3AMyLnoVG+lUbTWEw\noR/a3XffzYQJE1iwYAHHjx/noYceYuvWrZbIJ4QQQgwIJt2y9vT0xM3NDQAfHx+amy2zd6YQQggx\nUJh0hVxRUcFf/vIXWlpa0Ol03HvvvYwdO9YS+YQQQogBwaSCLIQQQgjzksYgQgghhA2QgiyEEELY\nACnIQgghhA2QgiyEEELYgG4bg/SGwWBgxYoVHD9+HI1Gw5NPPkloaKglTynM7Iorrvh1idvgwYN5\n6qmnrJxIdCczM5OVK1eyceNGSkpK+POf/4xSqSQmJobHH3/c2vFEN377/uXk5LB06VIiIiIAuPba\na0lLS7NuQHFOOp2ORx55hNOnT6PVarn99tuJjo426vNn0YK8c+dOOjo6ePfdd8nMzOTpp59mzZo1\nljylMKOOjg4ANmzYYOUkoqfWr1/Pli1bcHV1BeDpp5/mgQceIDU1lccff5ydO3cyZcoUK6cUXfnj\n+3f48GFuvvlmbrrpJusGE93aunUr3t7ePPvsszQ0NDB37lzi4uKM+vxZ9JZ1eno6EyZMACApKYnD\nhw9b8nTCzI4dO0ZLSwtLlizhpptuIjMz09qRRDfCw8NZvXr1r38/cuQIqampAFx88cXs3bvXWtFE\nD5zr/fvmm2+4/vrrefTRR2lpabFiOnE+aWlp3HvvvQB0dnaiUqk4evSoUZ8/ixbkpqYm3N3df/27\ng4MDer3ekqcUZuTk5MSSJUt49dVXWbFiBcuXL5f3z8ZNnToVlUr1699/22bA1dWVxsZGa8QSPfTH\n9y8pKYmHH36YN998k9DQUFatWmXFdOJ8nJ2dcXFxoampiXvvvZf777/f6M+fRQuym5vb79pq6vV6\nlEqZR2YvIiIimDNnzq//7eXlRWVlpZVTCWP89vPW3NyMh4eHFdMIY02ZMoVhw4YBZ4v1sWPHrJxI\nnM+ZM2e48cYbmTdvHjNnzjT682fR6jhq1Ci+/fZbAA4dOkRsbKwlTyfM7IMPPuCZZ54BoLy8nObm\nZvz9/a2cShhj2LBh7N+/H4DvvvuOlJQUKycSxliyZAnZ2dkA7N27l+HDh1s5kehKVVUVS5Ys4aGH\nHmLevHkAxMfHG/X5s+ikrqlTp7Jnzx6uueYa4OwEE2E/5s+fz//8z/9w3XXXoVQqeeqpp+QOh535\n05/+xF//+le0Wi1RUVFMnz7d2pGEEVasWMHf//531Go1/v7+/O1vf7N2JNGFV155hYaGBtasWcPq\n1atRKBQ8+uijPPHEEz3+/EkvayGEEMIGyOWOEEIIYQOkIAshhBA2QAqyEEIIYQOkIAshhBA2QAqy\nEEIIYQOkIAshhBA2QAqyEEIIYQP+P0A0qvP1+V47AAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "clrs = sns.color_palette('deep')\n", "plt.plot(model.toarray()[:,0], color=clrs[0])\n", "plt.plot(dx, '--', color=clrs[0])\n", "plt.plot(model.toarray()[:,1], color=clrs[1])\n", "plt.plot(dy, '--', color=clrs[1]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that, while following a similar pattern as the ground truth, the estimates are not correct. That's because we didn't use the true reference to estimate the displacements, but rather the mean of the displaced data, which biases the estimated displacements. To see that we get the exact displacements back, let's compute a reference from the original, unshifted data." ] }, { "cell_type": "code", "execution_count": 50, "metadata": { "collapsed": false }, "outputs": [], "source": [ "reference = data.mean().toarray()\n", "model = algorithm.fit(shifted, reference=reference)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now the estimates should be exact (up to rounding error)! But note that this is sort of cheating, because in general we don't know the reference exactly." ] }, { "cell_type": "code", "execution_count": 51, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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xMnopni7uvJf3EVGeEayIWqx0eJecyKmnpcPEqjnR3DopjPqWXjzdBt4Scyy7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\nylUXJ3ZobiFE9zMoKJlEv3h2VxWQW7mH5MAkALIq8vj28FZ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shRBCdA8eBnduH3QDI8KG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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(model.toarray()[:,0], color=clrs[0])\n", "plt.plot(dx, '--', color=clrs[0])\n", "plt.plot(model.toarray()[:,1], color=clrs[1])\n", "plt.plot(dy, '--', color=clrs[1]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can now use our model to `transform` a set of images, which applies the estimated transformations. The API design makes it easy to apply the transformations to the dataset we used to estimate the transformations, or a different one. We'll use the model we just estimates, which used the true reference, because it will be easy to see that it did the right thing." ] }, { "cell_type": "code", "execution_count": 53, "metadata": { "collapsed": false }, "outputs": [], "source": [ "corrected = model.transform(shifted)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's again look at the first image from the orignal and corrected, and their difference. Whereas before they were different, now they should be the same, except for minor near the boundaries (where the image has been replaced with its nearest neighbors)." ] }, { "cell_type": "code", "execution_count": 54, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "im1 = data[0].toarray()\n", "im2 = corrected[0].toarray()\n", "tile([im1, im2, im1-im2], clim=[(0,300), (0,300), (-300,300)], grid=(1,3), size=14);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As a final check on the registation, we can compare the mean of the shifted data, and the mean of the regsitered data. The latter should be much sharper." ] }, { "cell_type": "code", "execution_count": 55, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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GpCmkNK/oW0Lz4ejoKLqe7k/tof4nNN/S1EFKC6T1nqaZ+RcYSZIkSW14gJEk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\nwwOMJEmSpDY8wEiSJElqY+4pZJTKQak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