{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as pt" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/usr/lib/python3/dist-packages/PIL/Image.py:1513: ResourceWarning: unclosed file <_io.BufferedReader name='andreas.jpeg'>\n", " self.load()\n" ] }, { "data": { "text/plain": [ "(500, 500, 3)" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from PIL import Image\n", "\n", "with Image.open(\"andreas.jpeg\").resize((500,500)) as img:\n", " rgb_img = np.array(img)\n", "rgb_img.shape" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "img = np.sum(rgb_img, axis=-1)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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38gFmzVsymL+mWiQ+uuMtCF18Dl6bTBCXyMZ7El9oNBr4+7//e9y/fx+JRALNZhO9Xg+L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\n9a53hfdHJmNu52qPHTMYm5ubO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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "u, sigma, vt = np.linalg.svd(img)\n", "sigma\n", "\n", "pt.plot(sigma)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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DD55/Yb1pecybn/FwjA0yG3oxtfizTjMH74FLltfVwQ1POB3LzNc8fzHifA5k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\nRmwnusOWy3A8WLfahnx0cmodFCR49ya3K5fH7yRFBMC8eGM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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "compressed_img = (\n", " sigma[0] * np.outer(u[:, 0], vt[0])\n", " )\n", "\n", "pt.imshow(compressed_img, cmap=\"gray\")" ] }, { "cell_type": "code", "execution_count": 37, "metadata": { "collapsed": false }, "outputs": [], "source": [] } ], "metadata": {}, "nbformat": 4, "nbformat_minor": 0 }