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iPython notebook - M-array
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| { | |
| "metadata": { | |
| "name": "", | |
| "signature": "sha256:c68d2246484ccb315fea66290636daab228875c9ded925465c12672f05098102" | |
| }, | |
| "nbformat": 3, | |
| "nbformat_minor": 0, | |
| "worksheets": [ | |
| { | |
| "cells": [ | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "# Introduction\n", | |
| "The algorithm is described in this paper, section 4.3 :\n", | |
| "http://www.vs.inf.ethz.ch/edu/SS2005/DS/papers/projected/salvi-coded-light.pdf\n", | |
| "\n", | |
| "We will tend to use the same notations as in the paper.\n", | |
| "\n", | |
| "The elance job requires the matrix to be of size $641\\times481$ and to be invariant for a rotation of $\\pi$ radians.\n", | |
| "\n", | |
| "It suggests stitching $4$ $230\\times240$ arrays together with an extra cross in the middle. I assume there is a typo (inversion of '3' and '2' in 230) here and the suggestion is actually to stitch $4$ $320\\times240$ matrices.\n", | |
| "\n", | |
| "If the typo was instead to have a $461 \\times 481$ matrix in the end (inversion of '4' and '6'), it should not be too hard to change the parameters anayway.\n", | |
| "\n", | |
| "# Parameters\n", | |
| "## Theory\n", | |
| "The text of the paper do not make he relationships between the matrix parameters as easy to grasp as they could be.\n", | |
| "\n", | |
| "The final matrix has a size of $r\\times v$.\n", | |
| "\n", | |
| "The window size (the size of the submatrices that are all (except for the null one) present in the M-array) is $k_1\\times k_2$.\n", | |
| "\n", | |
| "To fill the window, we need a random sequence of length $n = 2^{k_1k_2} - 1$\n", | |
| "\n", | |
| "From then we define sub parameters $n_1$ and $n_2$ as $n_1 =2^{k_1} - 1$ and $n_2 = \\frac{n}{n_1}$.\n", | |
| "\n", | |
| "The $n_1 \\times n_2$ random matrix is padded on the right with $k_1 - 1$ columns and on the bottom with $k_2 - 1$ lines.\n", | |
| "\n", | |
| "Therefore finally : \n", | |
| "$$r = n_1 + k_1 - 1\\\\\n", | |
| "r = 2^{k_1} - 1 + k_1 - 1\\\\\n", | |
| "r = 2^{k_1} + k_1 - 2$$\n", | |
| "and \n", | |
| "$$v = n_2 + k_2 - 1\\\\\n", | |
| "v = \\frac{n}{n_1} + k_2 - 1\\\\\n", | |
| "v = \\frac{2^{k_1k_2} - 1}{2^{k_1} - 1} + k_2 -1$$.\n", | |
| "\n", | |
| "It is interesting to notice that there is a one-to-one relationship between input parameter $k_1$ and matrix size $r$. The number of columns $v$ depends on both $k_1$ and $k_2$, though." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "collapsed": false, | |
| "input": [ | |
| "def matrix_size(k1, k2):\n", | |
| " r = pow(2, k1) + k1 - 2\n", | |
| " n = pow(2, k1*k2) - 1\n", | |
| " n1 = pow(2, k1) - 1\n", | |
| " assert(n % n1 == 0) # Check that n_2 is an integer\n", | |
| " n2 = n/n1\n", | |
| " v = n2 + k2 - 1\n", | |
| " return r, v, n, n1, n2\n", | |
| "matrix_size(2, 2) # Should return 4, 6, 15, 3, 5 if OK with paper" | |
| ], | |
| "language": "python", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "metadata": {}, | |
| "output_type": "pyout", | |
| "prompt_number": 2, | |
| "text": [ | |
| "(4, 6.0, 15, 3, 5.0)" | |
| ] | |
| } | |
| ], | |
| "prompt_number": 2 | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Finding parameters for required size\n", | |
| "\n", | |
| "We would be happy to find a $r$ or $v$ of either $230$, $240$ or $320$. We will list all posible $r$ for increasing values of $k_1$." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "collapsed": false, | |
| "input": [ | |
| "[matrix_size(x, 1)[0] for x in range(1, 10)]" | |
| ], | |
| "language": "python", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "metadata": {}, | |
| "output_type": "pyout", | |
| "prompt_number": 3, | |
| "text": [ | |
| "[1, 4, 9, 18, 35, 68, 133, 262, 519]" | |
| ] | |
| } | |
| ], | |
| "prompt_number": 3 | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "It looks like it is not possible to create a matrix of exactly the required size. We will create a larger matrix that we will then truncate." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "collapsed": false, | |
| "input": [ | |
| "r = 320 # 4 to test like in the paper\n", | |
| "v = 240 # 6 to test like in the paper\n", | |
| "k1 = 1\n", | |
| "k2 = 2\n", | |
| "while matrix_size(k1,k2)[0] < r:\n", | |
| " k1+=1\n", | |
| "while matrix_size(k1,k2)[1] < v:\n", | |
| " k2+=1\n", | |
| "k1,k2,matrix_size(k1,k2)" | |
| ], | |
| "language": "python", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "metadata": {}, | |
| "output_type": "pyout", | |
| "prompt_number": 4, | |
| "text": [ | |
| "(9, 2, (519, 514.0, 262143, 511, 513.0))" | |
| ] | |
| } | |
| ], | |
| "prompt_number": 4 | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "# Actually creating the matrix\n", | |
| "## Same matrix as in the paper" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "collapsed": false, | |
| "input": [ | |
| "def m_array(k1, k2):\n", | |
| " big_r, big_v, n, n1, n2 = matrix_size(k1,k2)\n", | |
| " if k1 == 2 and k2 == 2: #Assume testing like in the paper\n", | |
| " random_sequence = list('010011000101111')\n", | |
| " else:\n", | |
| " random_sequence = list(map(int,rand(n)<0.5)) \n", | |
| " M = zeros((n1, n2))\n", | |
| " i=0\n", | |
| " j=0\n", | |
| " while random_sequence:\n", | |
| " M[i,j] = random_sequence.pop(0)\n", | |
| " i = i+1 if i+1 < n1 else 0\n", | |
| " j = j+1 if j+1 < n2 else 0\n", | |
| " M = hstack([M, M[:,:k2-1]])\n", | |
| " M = vstack([M, M[:k1-1]])\n", | |
| " return M\n", | |
| "M = m_array(2,2) # Should output same array than in the paper.\n", | |
| "M" | |
| ], | |
| "language": "python", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "metadata": {}, | |
| "output_type": "pyout", | |
| "prompt_number": 5, | |
| "text": [ | |
| "array([[ 0., 0., 1., 0., 1., 0.],\n", | |
| " [ 0., 1., 0., 1., 1., 0.],\n", | |
| " [ 1., 1., 0., 0., 1., 1.],\n", | |
| " [ 0., 0., 1., 0., 1., 0.]])" | |
| ] | |
| } | |
| ], | |
| "prompt_number": 5 | |
| }, | |
| { | |
| "cell_type": "code", | |
| "collapsed": false, | |
| "input": [ | |
| "from matplotlib.pyplot import imshow\n", | |
| "plt.imshow(M, cmap='Greys', interpolation='nearest')\n", | |
| "plt.savefig('M_array_small.png')" | |
| ], | |
| "language": "python", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "metadata": {}, | |
| "output_type": "display_data", | |
| "png": 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| |
| "text": [ | |
| "<matplotlib.figure.Figure at 0x11268af98>" | |
| ] | |
| } | |
| ], | |
| "prompt_number": 6 | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Matrix of required size\n", | |
| "\n", | |
| "We are going to generate a matrix of size $519\\times 514$ ($k_1 = 9$, $k_2=2$), truncate it down to $320\\times 240$, stitch four of thos together with a cross in the middle so that the whole thing is $\\pi$-rotation invariant." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "collapsed": false, | |
| "input": [ | |
| "def cross_stitch(r, v, full_matrix):\n", | |
| " m = full_matrix[:r,:v]\n", | |
| " answer = zeros((2*r+1,2*v+1))\n", | |
| " answer[:r,:v] = m\n", | |
| " answer[:r,v+1:] = m[:,::-1]\n", | |
| " answer[r+1:,:v] = m[::-1]\n", | |
| " answer[r+1:,v+1:] = m[::-1,::-1]\n", | |
| " return answer\n", | |
| "plt.imshow(cross_stitch(4, 6, m_array(2,2)), cmap='Greys', interpolation='nearest') # Image should be \\pi-rotation invariant" | |
| ], | |
| "language": "python", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "metadata": {}, | |
| "output_type": "pyout", | |
| "prompt_number": 7, | |
| "text": [ | |
| "<matplotlib.image.AxesImage at 0x11287c7b8>" | |
| ] | |
| }, | |
| { | |
| "metadata": {}, | |
| "output_type": "display_data", | |
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| "text": [ | |
| "<matplotlib.figure.Figure at 0x1127a45f8>" | |
| ] | |
| } | |
| ], | |
| "prompt_number": 7 | |
| }, | |
| { | |
| "cell_type": "code", | |
| "collapsed": false, | |
| "input": [ | |
| "M = m_array(k1,k2) # May take some time (around 5 mins on my machine)" | |
| ], | |
| "language": "python", | |
| "metadata": {}, | |
| "outputs": [], | |
| "prompt_number": 8 | |
| }, | |
| { | |
| "cell_type": "code", | |
| "collapsed": false, | |
| "input": [ | |
| "final_matrix = cross_stitch(320, 240, M)\n", | |
| "plt.imshow(final_matrix, cmap='Greys', interpolation='nearest')\n", | |
| "#To save, we use PIL to avoid unwanted interpolation\n", | |
| "from PIL import Image\n", | |
| "im = Image.fromarray(final_matrix*255)\n", | |
| "im = im.convert('RGB')\n", | |
| "im.save('M_641x481_2.bmp')" | |
| ], | |
| "language": "python", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "metadata": {}, | |
| "output_type": "display_data", | |
| "png": 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9k88O1yUO5wwOr+KtWmAWfE5Htr7Cm/e5c8Hzw+BDfVgAMH/Jc8wPkcoP+HPO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\n7ZPao2SzCs/wqXNTfNg6de3OVZHrVpz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| |
| "text": [ | |
| "<matplotlib.figure.Figure at 0x112881400>" | |
| ] | |
| } | |
| ], | |
| "prompt_number": 35 | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## 3x3 pixels\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "collapsed": false, | |
| "input": [ | |
| "def three_by_three(image):\n", | |
| " answer = zeros(array(image.shape)*3)\n", | |
| " for i in range(0, image.shape[0]):\n", | |
| " for j in range(0, image.shape[1]):\n", | |
| " if image[i,j] > 0:\n", | |
| " answer[i*3+1, j*3+1] = 1\n", | |
| " return answer\n", | |
| "M_test = m_array(2,2)\n", | |
| "plt.imshow(three_by_three(M_test), cmap='Greys', interpolation='nearest') \n", | |
| "figure()\n", | |
| "plt.imshow(three_by_three(cross_stitch(4, 6, m_array(2,2))), cmap='Greys', interpolation='nearest') " | |
| ], | |
| "language": "python", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "metadata": {}, | |
| "output_type": "pyout", | |
| "prompt_number": 57, | |
| "text": [ | |
| "<matplotlib.image.AxesImage at 0x113a1f978>" | |
| ] | |
| }, | |
| { | |
| "metadata": {}, | |
| "output_type": "display_data", | |
| "png": "iVBORw0KGgoAAAANSUhEUgAAAWwAAAD7CAYAAABOi672AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nTRhsSWri/wFQQg3Uo/7ZyQAAAABJRU5ErkJggg==\n", | |
| "text": [ | |
| "<matplotlib.figure.Figure at 0x114ed8cc0>" | |
| ] | |
| }, | |
| { | |
| "metadata": {}, | |
| "output_type": "display_data", | |
| "png": "iVBORw0KGgoAAAANSUhEUgAAAWAAAAD8CAYAAABJsn7AAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nwACQhAAGgCQEMAAkIYABIAkBDABJ/gcHu+BcykZ5lQAAAABJRU5ErkJggg==\n", | |
| "text": [ | |
| "<matplotlib.figure.Figure at 0x111dde978>" | |
| ] | |
| } | |
| ], | |
| "prompt_number": 57 | |
| }, | |
| { | |
| "cell_type": "code", | |
| "collapsed": false, | |
| "input": [ | |
| "figure()\n", | |
| "final_matrix_3x3 = three_by_three(final_matrix)\n", | |
| "plt.imshow(final_matrix_3x3, cmap='Greys', interpolation='nearest') # B&W inverted when using imshow.\n", | |
| "im = Image.fromarray(final_matrix_3x3*255)\n", | |
| "im = im.convert('RGB')\n", | |
| "im.save('M_641x481_2_3x3.bmp')" | |
| ], | |
| "language": "python", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "metadata": {}, | |
| "output_type": "display_data", | |
| "png": 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| |
| "text": [ | |
| "<matplotlib.figure.Figure at 0x11518ccc0>" | |
| ] | |
| } | |
| ], | |
| "prompt_number": 48 | |
| }, | |
| { | |
| "cell_type": "code", | |
| "collapsed": false, | |
| "input": [ | |
| "im = Image.open(\"M_641x481.bmp\")\n", | |
| "im = Image.fromarray(three_by_three(array(im)[:,:,0])*255)\n", | |
| "plt.imshow(im, cmap='Greys', interpolation='nearest') # B&W inverted when using imshow.\n", | |
| "im = im.convert('RGB')\n", | |
| "im.save('M_641x481_3x3.bmp')\n" | |
| ], | |
| "language": "python", | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "metadata": {}, | |
| "output_type": "display_data", | |
| "png": 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| |
| "text": [ | |
| "<matplotlib.figure.Figure at 0x114799518>" | |
| ] | |
| } | |
| ], | |
| "prompt_number": 58 | |
| } | |
| ], | |
| "metadata": {} | |
| } | |
| ] | |
| } |
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