{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Convolutions" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Load neccessary python modules\n", "from skimage import io, color, filter,transform # skimage is an image processing library\n", "import matplotlib.pyplot as plt # matplotlib provides plot functions similar to MATLAB\n", "import numpy as np # numpy provides efficient matrix implementation in python\n", "from scipy import signal # scipy provides scientific computing functions\n", "from IPython.html.widgets.interaction import interact \n", "# interact function can create an interactive interface to allow user to manipulate parameters and see the result, \n", "# similar to \"Manipulate\" in Mathematica\n", "\n", "%matplotlib inline \n", "# configuration of matplotlib" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "$r(x,y)=\\int l(x',y') k(x-x',y-y')dx'dy' = l*r$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Prepare data\n", "Create a disk image and load a natural image for the visualization of convolution" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAPwAAAD7CAYAAABOrvnfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAB+1JREFUeJzt3T2IXFUchvH3NcHCIIgoq0hEiwhaaZNGJClEYmO0UaxS\n", "iFiotVZqaaOVYGMiKcRgE02l2Vil04BoisQPcCEJYSOo2Eb5W+xFh2Qyunfv1+z7/CDszCS7czbZ\n", "J+fOzLlzXFUCkOGmsQcAYDgEDwQheCAIwQNBCB4IQvBAkJ19fWHbvN4HjKSqPO/23oLH9LVdg2HP\n", "/VnCEmh9SG/7gO3ztn+0/VqXgwLQD7f5X972DknfS3pc0iVJX0t6vqrOzfwZDuknjhl++7rRIX3b\n", "GX6vpJ+qaq2qrko6Julg28EBGEbb4O+RdGHm+sXmNgAT1jZ4DteBJdQ2+EuSds9c362NWR7AhLUN\n", "/oykPbbvs32zpOcknehuWAD60Op1+Kr60/Yrkr6QtEPS4dln6AFMU6uX5f7XF+ZlucnjZbntq+uX\n", "5QAsIZbW9mw7voXYlL8njj4WY4YHghA8EITggSAEDwQheCAIwQNBCB4IQvBAEIIHghA8EITggSAE\n", 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"kkoyVDLGkkoqqSRD/w/kv21EEsUO7AAAAABJRU5ErkJggg==\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Make a disk image, testdisk can be used to visualize the effect of the various spatial filters on the convolution output\n", "imageSize = 17;\n", "r = (imageSize-1)/2; cx = cy = imageSize/2; \n", "[X, Y] = np.meshgrid(np.arange(imageSize), np.arange(imageSize))\n", "diskImg = (X-cx)**2 + (Y-cy)**2 <= r**2\n", "\n", "# Load a natural image\n", "im = io.imread('../data/convolution/cat.png');\n", "grayIm = color.rgb2grey(im)\n", "\n", "\n", "\n", "# Show disk image and natural image\n", "plt.figure(); io.imshow(diskImg)\n", "plt.figure(); io.imshow(grayIm)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##Blur an image with a simple square kernel, Blur the disk image" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": [ 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"filteredIm = signal.convolve2d(diskImg, f)\n", "io.imshow(filteredIm)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "##Make a square kernel of size 2*r+1, and use it to blur the natural image" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAT8AAAEACAYAAADFinHTAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJzsvU2IbVl6JbZORNwbEe/lq6rMVGaq9FsalAQlGuRJTTxQ\n", "D4RpaJDwREITN1YbDI0t03igkgf+mQh3gzWwwcZ/atTGLUtgWsgDYUkGQU/ktgwGg7obi+pCVeqq\n", "TBVSIWW+F//Hg/fWiXXXXd8++96IyLiZ735wued3/++11/d9e+8zjOOIvexlL3t53eTgsROwl73s\n", "ZS+PIXvw28te9vJayh789rKXvbyWsge/vexlL6+l7MFvL3vZy2spe/Dby1728lrKg4DfMAx/YxiG\n", "fz4Mw/83DMMvPEQce9nLXvZyFxnue57fMAyHAP4FgJ8A8KcA/i8APzuO4z+714j2spe97OUO8hDM\n", 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"f = fHorizontal\n", "plt.figure(); io.imshow(signal.convolve2d(diskImg, f))\n", "plt.figure(); io.imshow(signal.convolve2d(grayIm, f))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#Exercise" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Read in and display a quantized picture of Claude Shannon. Devise a simple low-pass (blur) filter to remove the high spatial frequencies. Find the optimal size of the blur kernel by inspection." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Load a picture of Claude Shannon\n", "im = io.imread('../data/convolution/shannon64x64.jpg');\n", "shannonIm = color.rgb2grey(im)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAPwAAAD7CAYAAABOrvnfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAEnBJREFUeJzt3X9slfW9B/D3mxZbC9giQWwF0kJAHFEc7lJAl+kuRjSL\n", "Lnoj6pYxTfaP997h8MfAqTcxhpiNMfGqf+jUSKbOXCSGRecVnBl3IZEfAkOgtCLQllKoDgoVCy18\n", "7h/n0FV2Tn98+nwfZN/3K2lyznmez/N9+uPd55znOd/zoZlBROIw6GzvgIikR4EXiYgCLxIRBV4k\n", "Igq8SEQUeJGIFIbaMEld7xM5S8yMuR4PFngA2LVrV87Hly5dinnz5uVctm/fPtdYe/fuzbtsxYoV\n", "uPXWW3Mue/PNN13jVVdX5122evVqzJo1K+eyOXPmuMYjc/7+AABPPfUU7rvvvpzLFixY4Bpv0aJF\n", 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"metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAP0AAAD+CAYAAADxoQNSAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", "AAALEgAACxIB0t1+/AAAIABJREFUeJztnVuMpddV5/+rq7rd3e7u6ovtbiduxYmEo4w1ITYaw5Aw\n", "iaMEBYQCT0CkQVaEeGKGAFIUwxsPCJgXQDPiZSaJPBZiBoVJ5Ag02AkBzWikEA82cdppHGZiyY7j\n", "djt9qSrH7b5tHuqc4/9Zff6rVn3nUtV86ye1eu9zvsv+LrvOWnvdrLWGoij6w67tHkBRFIulJn1R\n", "9Iya9EXRM2rSF0XPqElfFD2jJn1R9IypJr2ZfcTMTpvZt8zsU7MaVFEU88O62unNbAnAPwD4EIDv\n", "APgagI+11r45u+EVRTFrpvmlfwDAP7bWnm+tXQHw3wD89GyGVRTFvFieYt+3AniB+i8C+GHewMzK\n", "3a8otonWmk36fJpJn57Qu3btwtLSEpaWlrC8vIw9e/aMfX/LLbeM2rt37x61ebtIDbl27drE7Ybt\n", "Cxcu4PDhw2P7XL16deL+169f39KxgY3rY7i/vLyMtbU1HDx4EMvLy6l9lpaWJrYj+Hp8e3V1FYcO\n", "HbrhOwWP0/f5+fDnZhPfrxFnz57F7bffPnad/l4zV65c2bQ9qT8JfgbA+DWoe83PHRh/3pcvX57Y\n", 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"qQAAAABJRU5ErkJggg==\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "qshannonIm2=transform.resize(qshannonIm, (64, 64), order=0)\n", "\n", "def SquareKernel(r):\n", " w = 2*r + 1\n", " return np.ones((w,w)) / (w**2)\n", "\n", "\n", "def AdjustKernelRadius(r):\n", " fim = signal.convolve2d(qshannonIm2, SquareKernel(r))\n", " io.imshow(fim)\n", "interact(AdjustKernelRadius, r=(.1,5))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "###Circular gaussian filter" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Use gaussian_filter from skimage.filter" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": [ "iVBORw0KGgoAAAANSUhEUgAAAP0AAAD+CAYAAADxoQNSAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\n", 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"N3E0B+AJAJsmJMvt6NmtT6M3yA6g51mYqDwAfhbAf/Tl+BaA+/p/n8p9cXLdCWDvtGRBz45+uv/z\n", "7cF3dYrfl59Db5L1PwH8HXqTe43Joth7ITqGIvKE6Bga9EJ0DA16ITqGBr0QHUODXoiOoUEvRMfQ\n", "oBeiY/w3FA60uEveDTsAAAAASUVORK5CYII=\n" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from skimage.filter import gabor_kernel, gaussian_filter\n", "\n", "def GaussKernel(r):\n", " return np.real(gabor_kernel(0.1,sigma_x=r,sigma_y=r))\n", "\n", "\n", "def AdjustKernelRadius(r):\n", " io.imshow(gaussian_filter(qshannonIm2, r, output=None, mode='nearest', cval=0, multichannel=None))\n", "interact(AdjustKernelRadius, r=(.1,5))" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [] } ], "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 }