{ "cells": [ { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\n", "\n", "<< back to chapter content

Last updated: 12/09/2016

\n", " show/hide source code\n", " " ], "text/plain": [ "" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%matplotlib inline\n", "import sys\n", "sys.path.insert(0,'..')\n", "from IPython.display import HTML,Image,SVG,YouTubeVideo\n", "from helpers import header\n", "\n", "HTML(header())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Contour features\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## chain code algorithm\n", "Chain code algorithm is a method that describes the contour of a connected set as an ordered set of pixels (see below)." ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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cervRfQHTYzBa8NQ3YLEiP/+O602mL+bY/SW6L+LiKfxlDL/1Gjy3NUOnZ9F9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"text/plain": [ "" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Image('http://homepages.ulb.ac.be/~odebeir/data/chain.png')" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "The algorithm starts from an arbitrary pixel of the contour, e.g. found by rasterazing the image, the first object point detected being used.\n", "\n", "at each iteration on try to find the next border pixel, the order of test is givenby the arrows in the upper right corner, starting from the direction just after the direction of arrival, i.e. the first direction(3) correspond to the first detected object pixel starting from (1) because (1) is the first direction after (0) which is the direction of 'arrival' of the raster. The new search position is given by :\n", "\n", "$$mod_7 (n+5)$$\n", "\n", "so here the next search direction is\n", "\n", "$$mod_7 (3+5) = 1$$\n", "\n", "for the second step, the found direction is (2), the next search direction is \n", "\n", "$$mod_7 (2+5) = 0$$\n", "\n", "the process is iterated until the first pixel is reached again.\n", "\n", "Polygon area and centroid can be computed from the chain code, if $(x_i,y_i)$ if the sequence of object contour,\n", "\n", "for a chain of $n$ pixels, the area is \n", "\n", "$$Area = \\frac{\\sum_{i=0}^{n-1}(x_i+x_{mod_n(i+1)})(y_1-y_{mod_n(i-1)})}{2} $$\n", "\n", "and centroïd is\n", "\n", "$$g_x = \\frac{\\sum_{i=0}^{n-1}(x_i+x_{mod_n(i+1)})^2(y_1-y_{mod_n(i-1)})^2}{Area} $$\n", "\n", "$$g_y = \\frac{\\sum_{i=0}^{n-1}(y_i+y_{mod_n(i+1)})^2(x_1-x_{mod_n(i-1)})^2}{Area} $$\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ ">see also:\n", "* Chain coding [DIP](../00-Preface/06-References.ipynb#[DIP]) p484\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## polygonal approximation\n", "\n", "tbd..." ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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wIiIidu7c+eTJEwBQVVV1c3MbN25cV34GveMqy97+7jAZAADEDD22BM8f2uO/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"text/plain": [ "" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Image('http://homepages.ulb.ac.be/~odebeir/data/polygon.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2D shape descriptors (contours)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Form factor\n", "\n", "$$Formfactor = \\frac {4 \\pi Area}{Perimeter} $$\n", "\n", "### Convexity\n", "\n", "$$Convexity = \\frac {Convex Perimeter}{Perimeter} $$\n", "\n", "$$Solidity = \\frac {Area}{Convex Area} $$\n", "\n", "### Moments\n", "One define moments such as ($f$ is considered here as a constant e.g. $1$)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$ m_{pq} = \\sum_{p= -\\infty}^{+\\infty}\\sum_{q=-\\infty}^{+\\infty} x^p \\; y^q \\; f(x,y) $$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "moments are centralized with respect to the object centroïd" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$ \\mu_{pq} = \\sum_{p= -\\infty}^{+\\infty}\\sum_{q=-\\infty}^{+\\infty} (x-\\bar x)^p \\; (y-\\bar y)^q \\; f(x,y) $$ \n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "principal direction is given by\n", "\n", "$$\\theta = \\tan^{-1} \\big(\\frac{2\\;\\mu_{11}}{\\mu_{20}-\\mu_{02}}\\big)$$\n", "\n", "\n", "\n", "$$\n", "M = \n", "\\begin{bmatrix}\n", " \\mu_{20} & \\mu_{11} \\\\\n", " \\mu_{11} & \\mu_{02} \\\\\n", "\\end{bmatrix}\n", "$$\n", "\n", "eigen values of $M$ are\n", "\n", "$$\n", "\\lambda_i = \\frac{\\mu_{20} + \\mu_{02}}{2} \\pm \\frac{\\sqrt{4{\\mu}_{11}^2 + ({\\mu}_{20}-{\\mu}_{02})^2 }}{2}\n", "$$\n", "\n", "**Eccentricity** is given by\n", "\n", "$$\\sqrt{1 - \\frac{\\lambda_2}{\\lambda_1}}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Aspect ratio\n", "\n", "The aspect ratio is given by the ratio between major and minor axes. The major axis is length of the major axis of the ellipse that has the same normalized second central moments as the shape, similarily, the minor axis is the length of the ellipse mino axis.\n", "\n", "$$Aspect Ratio = \\frac {Max\\: diameter}{Min\\: diameter} $$\n", "\n", "The equivallent diameter is the diameter of the disk having the same area.\n", "\n", "$$Eq.dia. = \\sqrt { \\frac 4 \\pi Area} $$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ">see also:\n", "* 2D shape descriptors (contours) [DIP](../00-Preface/06-References.ipynb#[DIP]) p.499 , [IPH](../00-Preface/06-References.ipynb#[IPH]) p.490\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fourier contour description\n", "\n", "Contour can be seen as a 1D periodic function, e.g. by taking the distance to the centroïd as a function of an angle (see below).\n", "The circle has obviously a constant radius whereas the square presents a variable distance..." ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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dXl7RbFR48WF33/LyC5/8/Fdqrlz85QvPlJVV7N17c2FhscPhnMpY1QT89m99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\nIxPTXUqdQzBvrUThYCxKhKDsQSYqBopUzQBiMrUYLcwKElZYRMSJX+1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"text/plain": [ "" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Image('http://homepages.ulb.ac.be/~odebeir/data/unwrapped.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Still, there is a problem when $r(\\theta)$ is not a function, as illustrated below, for a same $\\theta$, there is two different $r(\\theta)$." ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Image('http://homepages.ulb.ac.be/~odebeir/data/unwrap2.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One solution, is to use the curvilinear coordinate along the contour and to express the radius with respect to that coordinate.\n", "\n", "In the example below, one use the distance to the centroid of each contour pixel (chain) as a 1D contour description." ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from skimage.morphology import disk, square\n", "import matplotlib.pyplot as plt\n", "from skimage.measure import label, regionprops, find_contours\n", "\n", "im = np.zeros((40,80))\n", "im[10:10+21,10:10+21] = disk(10)\n", "im[10:10+21,50:50+21] = square(21)\n", "\n", "lab = label(im)\n", "props = regionprops(lab)\n", "\n", "plt.figure(figsize=[10,5])\n", "plt.imshow(lab,interpolation='nearest')\n", "\n", "for obj in props:\n", " perim = find_contours(lab,obj.label-1)[0]\n", " plt.plot(obj.centroid[1],obj.centroid[0],'o')\n", " plt.plot(perim[:,1],perim[:,0])" ] }, { "cell_type": "code", "execution_count": 27, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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P1WddsCB9Wh9+qOJr2JD5kQ1N7KtXM7dtqw6yhQvbdrA9flx995Urq9rNiVsn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\nAlIYCCGEgBQGQgghAPwfLr/S58m3PIYAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "labels = ['disk','square']\n", "for i,obj in enumerate(props):\n", " perim = find_contours(lab,obj.label-1)[0]\n", " xy = perim - obj.centroid\n", " r = np.sqrt(xy[:,0]**2+xy[:,1]**2) \n", " plt.plot(r,label=labels[i])\n", "plt.gca().set_ylim([0,15])\n", "plt.xlabel('position on the contour') \n", "plt.ylabel('distance to centroid') \n", "plt.legend(loc=0);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the example above, the disk exhibits an irregular profile due to its discrete representation.\n", "\n", "The 1D signalm obtained are periodic by definition. Let's compute a Fourier transform on them." ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from numpy.fft import fft, fftshift\n", "plt.figure(figsize=[20,3])\n", "for i,obj in enumerate(props):\n", " perim = find_contours(lab,obj.label-1)[0]\n", " xy = perim - obj.centroid\n", " r = np.sqrt(xy[:,0]**2+xy[:,1]**2) \n", " R = fft(r)\n", " plt.subplot(2,1,i+1)\n", " plt.plot(np.power(fftshift(R),2),label=labels[i])\n", " \n", " plt.legend(loc=0);\n", " plt.gca().set_ylim([0,1000])\n", " plt.gca().set_xlim([0,r.shape[0]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that the Fourier power spectrum of the circle is almost in the continuous part (zero frequency is centered). On the contrary, the square exhibits an important contribution at a frequency corresponding to the oscillations." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fractal analysis\n", "\n", "The measure of a length is related to the scale used. If the scale is small, the details measured are more numerous and the overall length is higher. In many situations the dependency between scale $\\lambda_i$ and total length $L_2$ the following equation is verified (with a constant $f$) :\n", "\n", "$$ \\log L_2(X,\\lambda_i) = f \\; \\log \\lambda_i $$\n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ ">see also:\n", "* Minkowski fractal dimension [IPH](../00-Preface/06-References.ipynb#[IPH]) p442\n" ] }, { "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": "2.7.11" } }, "nbformat": 4, "nbformat_minor": 0 }