{ "cells": [ { "cell_type": "markdown", "id": "5e45e422", "metadata": {}, "source": [ "Title: Binary Morphology\n", "Author: Thomas M. Breuel\n", "Institution: UniKL" ] }, { "cell_type": "code", "execution_count": 14, "id": "50fa3b3d", "metadata": { "collapsed": true }, "outputs": [], "source": [ "\n", "from scipy.ndimage import filters\n", "def imrow(*args,**kw):\n", " size = kw.get(\"s\",8)\n", " if \"s\" in kw: del kw[\"s\"]\n", " n = len(args)\n", " gray()\n", " subplots(1,n,figsize=(n*size,size))\n", " for i,im in enumerate(args):\n", " subplot(1,n,i+1); imshow(im,**kw)\n", "\n", "test = mean(imread(\"testimage.jpg\")/255.0,axis=2)" ] }, { "cell_type": "markdown", "id": "36df4c67", "metadata": {}, "source": [ "# Binary Morphology" ] }, { "cell_type": "markdown", "id": "41ab8742", "metadata": {}, "source": [ "(mathematical morphology)\n", "\n", "Another useful set of non-linear filters comes from *mathematical morphology*.\n", "These filters are easiest to describe on binary images, so that's what we are starting with.\n", "\n", "Generally, given an image containing shapes (identified by pixels with value 1), \n", "in binary mathematical morphology, we try to fit a second shape (the mask)\n", "into that shape somehow. This is illustrated by the following images denoting the four\n", "basic operations of mathematical morphology: erosion, dilation, opening, and closing.\n", "\n", "![Erosion](files/Figures/erosion.png)\n", "![Dilation](files/Figures/dilation.png)\n", "![Opening](files/Figures/opening.png)\n", "![Closing](files/Figures/closing.png)\n", "\n", "(images from Wikipedia)" ] }, { "cell_type": "code", "execution_count": 15, "id": "44311067", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "# circular structuring elements\n", "from scipy.ndimage import morphology\n", "xs,ys = meshgrid(range(20),range(20))\n", "m3 = ((xs-10)**2+(ys-10)**2)<=9\n", "m8 = ((xs-10)**2+(ys-10)**2)<=64\n", "imrow(m3,m8,interpolation='nearest',s=4)" ] }, { "cell_type": "code", "execution_count": 9, "id": "9564cf58", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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0R9zrypeW/v7778jPz0d+fj727NmDihUr+kSI5SxbtgyjR4/G3/72N4wfPz7g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\nAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# morphologial dilation\n", "imrow(test,morphology.binary_dilation(test,m8))" ] }, { "cell_type": "code", "execution_count": 10, "id": "9e0ed3e3", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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ERJWsR48eeO+998z65pXqs88+w9q1a1FXV4d777037uoUpDKugIiIapAGa77v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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "# morphological erosion\n", "imrow(test,morphology.binary_erosion(test,m3))" ] }, { "cell_type": "code", "execution_count": 11, "id": "de9a3f66", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Dhw/naDSasI1JBFLqwrKsnNh4xBFHcDgcVhFBqWtmVp/bts19+vTx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\nXdSiRYuYTKuaplEkEqFgMEi33347PfT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C4bCaF5o1CdHo0aPx0EMP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3E9/k8++QTlypVDgwYNIq8HVUyP3bN582bs3LkTK1aswBtvvIGNGzdmu7+4Hr9t2/j666/Rt29f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\nEEpEREREREQxwyCUiIiIiIiIYub/AwMScW/CQx20AAAAAElFTkSuQmCC\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# morphological opening\n", "imrow(test,morphology.binary_opening(test,m3))" ] }, { "cell_type": "code", "execution_count": 12, "id": "e5a60824", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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bzpCpaEOIFUWhatWq0Z49e6QBKtropptuIuCkRzQdX+4kUpxJqQDQsmXLaOnS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\nh/XHH3+ooaFBn3zyi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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "# morphological closing\n", "imrow(test,morphology.binary_closing(test,m8))" ] }, { "cell_type": "markdown", "id": "3164dd68", "metadata": {}, "source": [ "(mathematical definitions)\n", "\n", "Mathematically, these operations can be defined in terms of sets.\n", "Let the pixels of the image be given by the set $A$\n", "and those of the mask by the set $B$.\n", "\n", "Denote by $B_z$ the set of translated points $B_z = \\\\{b+z | b\\in B\\\\}$.\n", "\n", "- Erosion: $A \\ominus B = \\\\{z \\in E | B_z \\subseteq A \\\\}$\n", "- Dilation: $A \\oplus B = \\\\{z \\in E | B_z \\cap A \\neq \\oslash \\\\}$\n", "- Opening: $A \\circ B = (A \\ominus B) \\oplus B$\n", "- Closing: $A \\bullet B = (A \\oplus B) \\ominus B$\n", "\n", "The set operations are as usual. \n", "We also need reflection of a set of points through the origin,\n", "$\\hat{B} = \\\\{-x | x\\in B\\\\}$" ] }, { "cell_type": "markdown", "id": "90d2493b", "metadata": {}, "source": [ "(Python equivalents of other oprations)\n", "\n", "\n", "Incidentally, remember how we can implement these binary operations on images:\n", "\n", "- $I^c$ = `1-image`\n", "- $\\hat{I}$ = `I[::-1,::-1]`\n", "- $B_z$ = `roll(roll(B,z[0],0),z[1],1)`\n", "- $A\\cap B$ = `minimum(A,B)`\n", "- $A\\cup B$ = `maximum(A,B)`" ] }, { "cell_type": "markdown", "id": "468cf1f8", "metadata": {}, "source": [ "(minimum / maximum filter equivalents)\n", "\n", "Erosion and dilation can also be thought of as _local minima_ and _local maxima_ filters over binary images, defined over a region determined by the mask $B$.\n", "\n", "The minimum and maximum filters from the library effectively compute morphological operations over rectangles." ] }, { "cell_type": "markdown", "id": "16da7d97", "metadata": {}, "source": [ "(mathematical properties)\n", "\n", "There are also some mathematical properties these operations satisfy,\n", "somewhat similar to what we found for linear filters (not exhaustive):\n", "\n", "_translation invariance_ or _shift invariance_\n", "\n", "duality:\n", "\n", "$$A \\oplus B = (A^c \\ominus \\hat{B})^c$$\n", "$$A \\bullet B = (A^c \\circ \\hat{B})^c$$" ] }, { "cell_type": "markdown", "id": "06999270", "metadata": {}, "source": [ "(properties of dilation)\n", "\n", "commutativity: \n", "\n", "$$A \\oplus B = B \\oplus A$$\n", "\n", "associativity: \n", "\n", "$$(A\\oplus B)\\oplus C = A\\oplus (B\\oplus C)$$\n", "\n", "distributivity over set union: \n", "\n", "$$A\\oplus (B\\cup C) = A\\oplus B \\cup A \\oplus C$$" ] }, { "cell_type": "markdown", "id": "c7c6946a", "metadata": {}, "source": [ "(properties of erosion)\n", "\n", "NB: these are not the same as dilation\n", "\n", "alternative to associativity:\n", "\n", "$(A\\ominus B)\\ominus C = A\\ominus (B\\oplus C)$\n", "\n", "distributivity:\n", "\n", "$$A \\ominus (B \\cup C) = A\\ominus B \\cup A \\ominus C$$" ] }, { "cell_type": "markdown", "id": "9df5fcff", "metadata": {}, "source": [ "(idempotency and monotonicity)\n", "\n", "\n", "opening and closing are _idempotent_: \n", "\n", "$$(A \\bullet B) \\bullet B = A \\bullet B$$\n", "\n", "monotonicity properties:\n", "\n", "$$(A \\ominus B) \\subseteq (A \\circ B) \\subseteq A \\subseteq (A \\bullet B) \\subseteq (A \\oplus B)$$\n", "\n", "if origin is in $B$ and $B \\subseteq C$ :\n", "\n", "$$A \\oplus B\\subseteq A\\oplus C$$ " ] }, { "cell_type": "code", "execution_count": 13, "id": "99bb2dde", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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AAAAAUJCAFQAAAACgIAErAAAAAEBBAlYAAAAAgIIErAAAAAAABQlYAQAAAAAK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\nOxaHDx+Oe+65J9I0LXPoAFB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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "d = zeros((12,12))\n", "for i in range(12): d[i,i] = 1\n", "imrow(d,morphology.binary_erosion(test,d),morphology.binary_opening(test,d),interpolation='none')" ] }, { "cell_type": "markdown", "id": "3de93d84", "metadata": {}, "source": [ "As you can see, this kind of \"detects patterns\" in the image." ] }, { "cell_type": "markdown", "id": "86ea4ad4", "metadata": {}, "source": [ "Hit or Miss Transform\n", "=====================\n", "\n", "There is a useful combination of these operations called the *hit or miss transform*.\n", "\n", "$A \\odot (B,C) = (A \\ominus B) \\cap (A^c \\ominus C)$" ] }, { "cell_type": "code", "execution_count": 14, "id": "fd717dc8", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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8+umnJiMjw3z77bemtrbWDB061HR2dv7oZ0kihBBCwi6edHtE/EOXX2ZeunSp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\nVCTw9wAAAABJRU5ErkJggg==\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "b = zeros((12,12))\n", "for i in range(12): b[i,i] = 1 \n", "c = zeros((12,12))\n", "c[11,0] = 1\n", "c[0,11] = 1\n", "import numpy\n", "imrow(bitwise_and(morphology.binary_erosion(test,b),morphology.binary_erosion(1-test,c)))" ] }, { "cell_type": "markdown", "id": "38f442fa", "metadata": {}, "source": [ "# Hit-or-Miss Example" ] }, { "cell_type": "markdown", "id": "36187a1e", "metadata": {}, "source": [ "Let's say we want to find the letter \"I\" in this image.\n", "\n" ] }, { "cell_type": "code", "execution_count": 44, "id": "1c6006c4", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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niHfhwgUml8vNHoVO39S2bVumVCoFMe/evcu8vb0ljTV16lSTz8fY2FhB+cTE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\nrf8DBkBzNTOY00UAAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "caps0 = 1*(mean(imread(\"caps.png\"),2)<0.5)\n", "gray(); figsize(12,6); imshow(caps0)" ] }, { "cell_type": "markdown", "id": "99feb155", "metadata": {}, "source": [ "Usually, images are noisy and degraded. We can simulate that with this simple document image degradation model. Noise means that we can't do pixel accurate matching.\n", "\n" ] }, { "cell_type": "code", "execution_count": 47, "id": "a5818466", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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wlkpTz4empEvPrrZUlz27wNOeOU3k9uza2dlxvYFSLViwQFadYu+tMXt2NV2b\nuujbt6/senXt2RU7H1evXq2TzwxjjOXl5RnkPKszZM+uqakpO3TokKTjqqqqYg0bNjRI/epP1VMn\ndpfAUOdRRdP3m7W1tWj+n3/+WfadFwBszpw5ondS1fPV9vQ3XY+v1mgMKkzt14Dc8GPqM/20zdgt\nLy/H/fv3eYPdAQh+CRhDZWUlRo8eLTvmYnV1NUJCQrB7927Bc7DF8u7evRvW1tay6tLVtWvXADzt\nhdW3B7muPIv99Pf3l/zLccOGDbzeEyLN1atXtb5eXV2N+/fvC+I72tjYYPDgwYKnMRqDIcaxPgvF\nxcVITU3lljWNKS0uLoaZmZlB687Pz8fNmzfh5eWlc+/ehQsXsGnTpjp5Tw1BdW3u3r0bu3fv1jnO\n7k8//WTQJyJqi5O8atUq3vKSJUsEk+t0sXv3buTl5emcPyQkxOCT4oyhsrISJ06c0ClcXmlpKXbv\n3g0TExOdJiPqQls5Cxcu1OtOtrqZM2eKrhd7ahnwNFpJfHy8YP2bb76p15NtLS0teeOjVSMH1OXn\n5+PChQu8dbm5uYJxvrXS+nPi/3l4eDBfX1/WuXNnrifHxsaGe/3Jkye8ZU2t7xUrVkhqoauStbU1\nO3r0KLeN1OcwS+3Z/eqrr/T6xa2eWrRowQIDA7nyr1y5ws6dO8cYY2z9+vWsrKxMdtm19ezeuHGD\nnTx5kt27d4+5u7uzgQMHGuSYBgwYoNNTr1TOnTvH7OzsJNej3rOr6clmxkiBgYHs9OnTLCQkRHA8\nx44dY7du3WKBgYEsMDBQdh1OTk68Z5Dr0rMbGBjIduzYwW0jp2e3Xbt2vONp27at5DLc3NwE4wHl\n9uwC//sqGj16NOvQoYNoHoVCwZ1zdVLr++6773S+fuXUod6zO3nyZEnbW1lZ8cbL1TZWTVNycXFh\nGRkZXDlHjx7VmLdBgwaCY/7zzz8NMp7Z2tqae+8CAwPZkydPuDpOnTrFrX/ttdf0ruu9997jyo6K\niuLGXtZF6tu3L1u1alWt15K+4x3d3d1ZXl4eY4yx2bNna31iWWBgIEtKSuLVP3/+fFn1du3alYWG\nhmo8rprvsdyni4mlmmJjY5mVlZXB3ztLS0sWGBjI3nnnHdFjW7JkCevdu7fB623evLngqbGMMVZQ\nUMA8PDwMWteMGTNEj03bNj4+Pry8w4cP16tnvUGDBrzxw6Ghoaxr164a848bN45X/927d1nz5s1r\nvU54x6fAjYS9AAAIaUlEQVTxlRqys7MZY0+HD3Ts2JGdPHlS0Lht0qSJpJNHiRKlFzuJTT5asWLF\nM98vSpSet3Tnzh326NEj3mflxx9/fOb7RYnSy5Y00WkYgyrWrIODA4YNG4aEhIRnFn6MEPJseXp6\nYtmyZYiNjRW8tmDBgmewR4Q831q0aCF4aminTp30ug1MCNGd4v97YDUqLS1FdXU1GjVqhJKSEgwc\nOBCffvop4uPjYWdnh/DwcERGRuLBgweIjIzkF/6CjAslhOiuqKhI9Ck7LVq04I0NJYTwqf+7ffTo\nkdHnahDyKtHUpK21sZuamorg4GAolUqUlZXB2toa+/fvh729Pbp164aioiI0atQIiYmJaN68Ob9w\nauwS8tJR/8qoqqrCuHHjsGvXrme0R4S8GBo0aIAff/yRty4pKUkQCpMQIo/sxi7wdEalv78/Jk+e\njKqqKpSUlGDp0qWwt7fHggULsHz5chQWFlLPLiGvgLCwMKxYsQIZGRmYNGkSqqurtc4EJ4QQQuqC\n7Mbuw4cP4efnJwjo7uXlhRMnTnBjd/v06SN4iAI1dgkhhBBCSF3Q1KStdYJaamoqHBwcMGnSJHTq\n1AnTpk1DSUkJcnNz4eTkBABwcnKqk6eIEEIIIYQQIkWtjd2qqiokJiZi1qxZSExMRMOGDUWHK1Av\nLiGEEEIIed7U2th1dXWFq6sr99zykSNHIjExEc7OzhR6jBBCCCGEPNdqbew6OzujWbNmuH37NgAg\nPj4ebdu2RVBQEKKjowEA0dHRGDp0qHH3lBBCCCGEEIlqnaD2119/YciQIcjIyABjDFVVVfjiiy8w\ncuRICj1GCCGEEEKeC3qFHlN58uQJXFxckJCQgPXr11PoMUIIIYQQ8lyQHY2hpvj4eLRq1QrNmjVD\nTEwMQkJCADyNw7t3717995IQQgghhBADktTY3b59O8aOHQsAFHqMEEIIIYQ893QexlBRUQEXFxck\nJSXBwcEBTZo0QWFhIfe6ra0tCgoK+IXTMAZCCCGEEFIH9B7GcOjQIXTu3BkODg4AwD05DaDQY4QQ\nQggh5Pmkc2N327Zt3BAGAAgODqbQY4QQQggh5Lmm0zCGkpISNG/eHKmpqWjUqBEAoKCgAKNGjUJG\nRgbc3d2xc+dO2NjY8AunYQyEEEIIIaQOGCT0mFTU2CWEEEIIIXXBIKHHCCGEEEIIeZFQY5cQQggh\nhLy0TIxZuBFHSBBCCCGEEFIr6tklhBBCCCEvLWrsEkIIIYSQl5bRGruxsbHw8vKCp6cnli9fbqxq\nyAtAqVQiICAAbdu2Rbt27bBu3ToAT8PXDRgwAK1bt8bAgQPx4MEDbptly5bB09MTXl5eiIuLe1a7\nTp6B6upq+Pn5ISgoCABdJ0TcgwcPMHLkSHh7e8PHxwfnz5+na4UILFu2DG3btkX79u0xbtw4lJeX\n03XyKmJGUFVVxVq2bMlSU1NZRUUF69ixI0tKSjJGVeQFkJOTwy5fvswYY6yoqIi1bt2aJSUlsbCw\nMLZ8+XLGGGORkZEsPDycMcbYjRs3WMeOHVlFRQVLTU1lLVu2ZNXV1c9s/0nd+uqrr9i4ceNYUFAQ\nY4zRdUJETZw4kW3atIkxxlhlZSV78OABXSuEJzU1lXl4eLDHjx8zxhgbNWoU27JlC10nryCj9Owm\nJCSgVatWcHd3h6mpKcaMGYN9+/YZoyryAnB2doavry8AwMrKCt7e3sjKykJMTAxCQkIAACEhIdi7\ndy8AYN++fRg7dixMTU3h7u6OVq1aISEh4ZntP6k7mZmZOHjwIKZOncpNcKXrhKh7+PAhTp06hcmT\nJwMATExMYG1tTdcK4WncuDFMTU1RWlqKqqoqlJaWomnTpnSdvIKM0tjNyspCs2bNuGVXV1dkZWUZ\noyrygklLS8Ply5fRvXt35ObmwsnJCQDg5OSE3NxcAEB2djZcXV25bej6eXXMmzcPK1euRL16//tq\nouuEqEtNTYWDgwMmTZqETp06Ydq0aSgpKaFrhfDY2tpi/vz5cHNzQ9OmTWFjY4MBAwbQdfIKMkpj\nl56cRsQUFxdjxIgRWLt2LffYaRWFQqH1uqFr6uV34MABODo6ws/PT/MjH+k6IQCqqqqQmJiIWbNm\nITExEQ0bNkRkZCQvD10rJCUlBWvWrEFaWhqys7NRXFyMrVu38vLQdfJqMEpj18XFBUqlkltWKpW8\nX0vk1VNZWYkRI0ZgwoQJGDp0KICnv6jv3r0LAMjJyYGjoyMA4fWTmZkJFxeXut9pUqfOnDmDmJgY\neHh4YOzYsTh69CgmTJhA1wkRcHV1haurK7p27QoAGDlyJBITE+Hs7EzXCuFcvHgRPXr0gJ2dHUxM\nTDB8+HCcPXuWrpNXkFEau126dMHff/+NtLQ0VFRUYMeOHQgODjZGVeQFwBjDlClT4OPjg7lz53Lr\ng4ODER0dDQCIjo7mGsHBwcHYvn07KioqkJqair///hvdunV7JvtO6s6XX34JpVKJ1NRUbN++HX37\n9sVPP/1E1wkRcHZ2RrNmzXD79m0AQHx8PNq2bYugoCC6VgjHy8sL586dQ1lZGRhjiI+Ph4+PD10n\nryCjPEHNxMQE33zzDQIDA1FdXY0pU6bA29vbGFWRF8Dp06exdetWdOjQAX5+fgCehndZuHAhRo0a\nhU2bNsHd3R07d+4EAPj4+GDUqFHw8fGBiYkJvv32W7qV9ApSved0nRAx69evx/jx41FRUYGWLVsi\nKioK1dXVdK0QTseOHTFx4kR06dIF9erVQ6dOnTB9+nQUFRXRdfKKUTBNg+MIIYQQQgh5wdET1Agh\nhBBCyEuLGruEEEIIIeSlRY1dQgghhBDy0qLGLiGEEEIIeWlRY5cQQgghhLy0qLFLCCGEEEJeWv8H\nPBe6LtzAeJQAAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "caps = 1-mean(imread(\"caps.png\"),2)\n", "caps -= amin(caps); caps /= amax(caps)\n", "caps = filters.gaussian_filter(caps+0.0,1.0)\n", "caps += 0.4*(rand(*caps.shape)-0.5)\n", "caps = 1*(caps>0.5)\n", "imshow(caps)" ] }, { "cell_type": "code", "execution_count": 48, "id": "db3411e2", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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LFy7g0qVLAICXXnoJJ0+ejMvQBD4PzpKSEhw/fhzHjx+PWjvE1X5qa2uRkpICl8vFOzgP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\nEREREcnW/wcEzYcYHpfIHAAAAABJRU5ErkJggg==\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "subplot(121); imshow(caps0[:,:100])\n", "subplot(122); imshow(caps[:,:100])" ] }, { "cell_type": "markdown", "id": "8d702dbb", "metadata": {}, "source": [ "Here is the template for the letter.\n" ] }, { "cell_type": "code", "execution_count": 49, "id": "077628cc", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "template = 1*(mean(imread(\"I.png\"),2)<0.5)\n", "gray(); imshow(template)" ] }, { "cell_type": "markdown", "id": "19e456ab", "metadata": {}, "source": [ "We require most of the pixels to be present. Since the edge of the character may be degraded, we are using a slightly smaller template to match the inside pixels. We obtain that template using mathematical morphology.\n", "\n" ] }, { "cell_type": "code", "execution_count": 50, "id": "11747c50", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "inner = morphology.binary_erosion(template,iterations=1)\n", "imshow(inner)" ] }, { "cell_type": "markdown", "id": "dba336ae", "metadata": {}, "source": [ "When we match with this template, we get a large number of false matches and one true match.\n", "\n" ] }, { "cell_type": "code", "execution_count": 57, "id": "e0eb8356", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 57, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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NGzaQnZ1Nbm6uhB4TQgghhBC1WswBan//+9+58cYb2bVrF0opysvLeeihhxg7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\nQghRZ0llVwghhBBC1Fn/H9e1mNmAecXcAAAAAElFTkSuQmCC\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "imatch = morphology.binary_erosion(caps,structure=inner)\n", "imshow(transpose(array([imatch,imatch,caps]),[1,2,0]))" ] }, { "cell_type": "markdown", "id": "2c1f26df", "metadata": {}, "source": [ "We need a second template that asserts that the outside of the character should not contain pixels. We also construct this using mathematical morphology.\n", "\n" ] }, { "cell_type": "code", "execution_count": 52, "id": "a8f3d78e", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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uu+/Gp59+il27duEPf/gDzpw5g7fffhtTU1O4dOkSzpw5sxV9XQObEH0wchy7zol//vOf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\nRK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "outer = maximum(0,morphology.binary_dilation(template,iterations=4)-morphology.binary_dilation(template,iterations=2))\n", "imshow(outer)" ] }, { "cell_type": "markdown", "id": "df5074ad", "metadata": {}, "source": [ "We can visualize the relationship between the outer and the inner templates by combining them numerically.\n", "\n" ] }, { "cell_type": "code", "execution_count": 53, "id": "21c8a202", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 53, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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EAps2bcLo6CguXryIvr4+AEBfXx/Onz9f35IKTUmwll8eHh7GzZs3sXPnToyPjyOZTAIA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\nCkYRAQWjiICCUURAwSgioGCU/wPSwK6BWPD0rwAAAABJRU5ErkJggg==\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "imshow(inner-outer)" ] }, { "cell_type": "markdown", "id": "cdd1062f", "metadata": {}, "source": [ "We can now visualize the combination of the `imatch` and `omatch` locations.\n", "\n" ] }, { "cell_type": "code", "execution_count": 59, "id": "1f3b6c96", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 59, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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1BF9QyzDifNu2d9FLeKAdix6uzWf09p4mm9BLAf9EG2ecRzKhKS9CL/uHZR31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\nAAAAAElFTkSuQmCC\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "omatch = morphology.binary_erosion(1-caps,structure=outer)\n", "imshow(transpose(array([omatch,imatch,caps]),[1,2,0]))" ] }, { "cell_type": "markdown", "id": "ac3bd2aa", "metadata": {}, "source": [ "The actual match location is where both the inside and the outside match. This is the hit-or-miss transform.\n", "\n" ] }, { "cell_type": "code", "execution_count": 62, "id": "4bb208bc", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 62, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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HQJ/Wx2kfMF+/zsN6/tzI64+21x63PT+v6bmLbc99bFt2joJ622uxhBwLl34aYpsoBa8o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\n77n33nsZNmwYOTk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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "imshow(transpose(array([imatch*omatch,zeros(omatch.shape),caps]),[1,2,0]))" ] }, { "cell_type": "code", "execution_count": null, "id": "b58d6935", "metadata": { "collapsed": false }, "outputs": [], "source": [] } ], "metadata": {}, "nbformat": 4, "nbformat_minor": 5 }