{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "#Principal Components Analysis (PCA) of natural images" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The idea is that each subimage will be used as a statistical sample. We compute the outer product of each, and the average all samples to get an estimate of the autocovariance matrix." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt # matplotlib provides plot functions similar to MATLAB\n", "import numpy as np\n", "from skimage import color, filter # skimage is an image processing library" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAQcAAAEACAYAAAC+rrMfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzsvWlsXed1NvrsM88jeUgeShQnkZIoUrKswRoaW/GQOG4z\n", "FEmarygCFAVaoP2ADn++/Gpwi/65Fyj6r8XFxQX65xa3o9smTWzLsWPZcmRTkiVGoyWK83h45nnc\n", 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"plt.imshow(im, 'gray')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##Break a large image into a series of 16x16 subimages" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Crop patches from image\n", "patchSize = 16; nDim = patchSize ** 2;\n", "w = im.shape[0]; h = im.shape[1];\n", "nx = im.shape[0] / patchSize; ny = im.shape[1] / patchSize\n", "nSamples = nx * ny\n", "\n", "patches = np.zeros((nDim, nSamples)) # column vectors\n", "[X, Y] = np.meshgrid(np.arange(0, w, patchSize), np.arange(0, h, patchSize))\n", "X = X.flatten(); Y = Y.flatten()\n", "for i in range(X.size):\n", " x = X[i]\n", " y = Y[i]\n", " patch = im[x:x+patchSize, y:y+patchSize]\n", " patch = patch - patch.mean()\n", " patches[:,i] = patch.flatten().T" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##Calculate autocovariance matrix" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAQcAAAEACAYAAAC+rrMfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzsvWmMbdl13/fbZ7r33HmoujW/eejXczdbTbLZbJEiZSlk\n", "bFqQY0kUYAiIEMSC5G9CjCRAlHwyksCC/cGxBYvOYCiUFKElhZrMQWyqB5I9kD2/od+rV++9modb\n", "ded77hnyYe1992uHSLoRNZ4V1AYKVXXvOfvsvfZea6/hv9ZRWZZx3I7bcTtu/35z7vUAjttxO27/\n", "YbZj4XDcjttx+5HtWDgct+N23H5kOxYOx+24Hbcf2Y6Fw3E7bsftR7Zj4XDcjttx+5HtIxEOSqmf\n", "VkpdVkpdU0r9Fx/FM47bcTtuH21Tf904B6WUC1wBPg+sAy8Dv5Bl2bt/rQ86bsftuH2k7aPQHJ4E\n", "3suy7GaWZRPgq8CXPoLnHLfjdtw+wvZRCIcl4PZd/9/Rnx2343bc/ga1j0I4HOOxj9tx+/9B8z6C\n", "PteBlbv+X0G0h2lTSh0LkON23O5Ry7JMfZDrPgrh8ApwXil1CtgAfg74hX//oq0XZgiLA964dD9/\n", "HvwU1zlDlwrfnXyc6LCAl5/g5iN6O3VGqyVYU/zKL/6P/BivcJpVrnOWVU6xzRxXucg7yf3srS6h\n", "woh0Ow9tBQp4Cz71j77Bw7xBjMseMxzQZJ0l1tvLpArGuxW448IO0Af2gJtw4p9dpukesPPf/haD\n", 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"plt.suptitle('Iteration')\n", "for i in range(nIter):\n", " plt.subplot(4,4,i+1)\n", " for j in range(nSamples):\n", " x = X[:,j]\n", " y = np.dot(W, x)\n", " # W: (16, 256), y: (16, 1), x: (256, 1)\n", " # inc = learningRate * (np.outer(y, x.T) - W * np.repeat(y * y,256).reshape(16,256))\n", " inc = learningRate * (np.outer(y, x.T) - W * np.tile((y * y)[:,np.newaxis],(1,256)))\n", " W += inc\n", " plt.imshow(W[0,:].reshape((patchSize, patchSize)), 'gray')\n", " plt.axis('off')\n", "\n", "\n", "plt.figure()\n", "plt.suptitle('Visualize weight matrix')\n", "for i in range(16):\n", " plt.subplot(4,4,i+1)\n", " plt.imshow(W[i,:].reshape((patchSize, patchSize)), 'gray')\n", " plt.axis('off')" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.8" } }, "nbformat": 4, "nbformat_minor": 0 }