2d convolution

{
 "metadata": {
  "name": "2d Convolution"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "%load_ext octavemagic",
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "octave window = [1 0 1; 0 1 0 ;1 0 1]",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "text": "window =\n\n        1        0        1\n        0        1        0\n        1        0        1\n"
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "octave image = [1 1 1 0 0 ; 0 1 1 1 0; 0 0 1 1 1; 0 0 1 1 0; 0 1 1 0 0]",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "text": "image =\n\n        1        1        1        0        0\n        0        1        1        1        0\n        0        0        1        1        1\n        0        0        1        1        0\n        0        1        1        0        0\n"
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "Now we convolve the image with the 3x3 window using `conv2`:"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "octave conv2(image, window);",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 8,
       "text": "array([[ 1.,  1.,  2.,  1.,  1.,  0.,  0.],\n       [ 0.,  2.,  2.,  3.,  1.,  1.,  0.],\n       [ 1.,  1.,  4.,  3.,  4.,  1.,  1.],\n       [ 0.,  1.,  2.,  4.,  3.,  3.,  0.],\n       [ 0.,  1.,  2.,  3.,  4.,  1.,  1.],\n       [ 0.,  0.,  2.,  2.,  1.,  1.,  0.],\n       [ 0.,  1.,  1.,  1.,  1.,  0.,  0.]])"
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "Suppose the image dimension is n1xn1, and the windown dimension is n2xn2. The default shape is 'full' which results n1 + n2 - 1 dimension, but we want 'valid' which results n1 - n2 + 1 dimension."
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "octave conv2(image, window, SHAPE='valid');",
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 9,
       "text": "array([[ 4.,  3.,  4.],\n       [ 2.,  4.,  3.],\n       [ 2.,  3.,  4.]])"
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": "![sf](http://deeplearning.stanford.edu/wiki/images/6/6c/Convolution_schematic.gif)"
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": "",
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}