{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np\n", "from skimage import color\n", "from skimage import io\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def plot_flag(flag):\n", " plt.imshow(flag, cmap=plt.cm.gray, vmin=0, vmax=1)\n", " plt.axis(\"off\")\n", " plt.show()\n", " \n", "def plot_compressed_flags(flag):\n", " # compute SVD\n", " [U, S, V] = np.linalg.svd(flag)\n", " \n", " # truncate the SVD to k singular values \n", " for k in range(1, 7): \n", " compressed_flag = np.dot(np.dot(U[:, 0:k], np.diag(S[0:k])), V[0:k, :])\n", " plt.subplot(3, 2, k)\n", " plt.imshow(compressed_flag, cmap=plt.cm.gray, vmin=0, vmax=1)\n", " plt.axis(\"off\")\n", " plt.title(\"rank = \" + str(k))\n", " plt.subplots_adjust(left=None, bottom=None, right=None, top=1.5, wspace=.05, hspace=.05)\n", " plt.show()" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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AwMBAnDhxAg8ePEDv3r2xbt06i41FLA0TREREYMiQIZg7dy4KCwuxfv16REVF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\ndBMAAAAASUVORK5CYII=\n", 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XWPV6vUgmk2WJXOTCodBJy7J4A5bi6KnGPq0wKXnLsiy43W643W521dD5D6lU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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Lets try this compression with the American flag \n", "\n", "usa = color.rgb2gray(io.imread('USA.png'))\n", "plot_flag(usa)\n", "plot_compressed_flags(usa)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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kGTOnycWLFxNvS+Pu9Xqxwj8cDtHr9dxwtt/vO+FnDnWn00Gn08FwODwi/PK5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\nUyiVSmi1WoHJKXo4TKljXR6m03Fb1u6XQ+9yuYynnnoqIMC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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# The Canadian flag has a maple leaf that is high rank\n", "# so the compressed approximation improves as the \n", "# number of singular vectors increases. \n", "\n", "canada = color.rgb2gray(io.imread('Canada.png'))\n", "plot_flag(canada)\n", "plot_compressed_flags(canada)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# The German flag has rank 1, so it can be reconstructed perfectly \n", "\n", "germany = color.rgb2gray(io.imread('Germany.png'))\n", "plot_flag(germany)\n", "plot_compressed_flags(germany)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# The Norwegian flag has rank 3, so it can be perfectly\n", "# reconstructed by any SVD approximation with rank\n", "# at least 3.\n", "\n", "norway = color.rgb2gray(io.imread('Norway.png'))\n", "plot_flag(norway)\n", "plot_compressed_flags(norway)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Rtzt4r2YymXD8+HE89dRTqKurg8Fg6HQ2QGJiIsLCwmRz1KDFYkFJSUmXh8sQ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\n", 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rHrqEA5CMGei+ZZlmKizW2oSypJMRQkqMj8x5z0XlKPS1QJTXIiLzsswhspfv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\ni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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# The Mozambican flag has guns and books and stuff. It's pretty cool.\n", "# But the complex crest, along with the triangle that does not follow\n", "# the horizontal or verical axes, make this flag difficult to compress\n", "# using the SVD. \n", "mozambique = color.rgb2gray(io.imread('Mozambique.png'))\n", "plot_flag(mozambique)\n", "plot_compressed_flags(mozambique)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python [Root]", "language": "python", "name": "Python [Root]" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 0 }