{"nbformat_minor": 0, "worksheets": [{"cells": [{"source": ["Active Contours using Parameteric Curves\n", "=========================================\n", "\n*Important:* Please read the [installation page](http://gpeyre.github.io/numerical-tours/installation_matlab/) for details about how to install the toolboxes.\n", "$\\newcommand{\\dotp}[2]{\\langle #1, #2 \\rangle}$\n", "$\\newcommand{\\enscond}[2]{\\lbrace #1, #2 \\rbrace}$\n", "$\\newcommand{\\pd}[2]{ \\frac{ \\partial #1}{\\partial #2} }$\n", "$\\newcommand{\\umin}[1]{\\underset{#1}{\\min}\\;}$\n", "$\\newcommand{\\umax}[1]{\\underset{#1}{\\max}\\;}$\n", "$\\newcommand{\\umin}[1]{\\underset{#1}{\\min}\\;}$\n", "$\\newcommand{\\uargmin}[1]{\\underset{#1}{argmin}\\;}$\n", "$\\newcommand{\\norm}[1]{\\|#1\\|}$\n", "$\\newcommand{\\abs}[1]{\\left|#1\\right|}$\n", "$\\newcommand{\\choice}[1]{ \\left\\{ \\begin{array}{l} #1 \\end{array} \\right. }$\n", "$\\newcommand{\\pa}[1]{\\left(#1\\right)}$\n", "$\\newcommand{\\diag}[1]{{diag}\\left( #1 \\right)}$\n", "$\\newcommand{\\qandq}{\\quad\\text{and}\\quad}$\n", "$\\newcommand{\\qwhereq}{\\quad\\text{where}\\quad}$\n", "$\\newcommand{\\qifq}{ \\quad \\text{if} \\quad }$\n", "$\\newcommand{\\qarrq}{ \\quad \\Longrightarrow \\quad }$\n", "$\\newcommand{\\ZZ}{\\mathbb{Z}}$\n", "$\\newcommand{\\CC}{\\mathbb{C}}$\n", "$\\newcommand{\\RR}{\\mathbb{R}}$\n", "$\\newcommand{\\EE}{\\mathbb{E}}$\n", "$\\newcommand{\\Zz}{\\mathcal{Z}}$\n", "$\\newcommand{\\Ww}{\\mathcal{W}}$\n", "$\\newcommand{\\Vv}{\\mathcal{V}}$\n", "$\\newcommand{\\Nn}{\\mathcal{N}}$\n", "$\\newcommand{\\NN}{\\mathcal{N}}$\n", "$\\newcommand{\\Hh}{\\mathcal{H}}$\n", "$\\newcommand{\\Bb}{\\mathcal{B}}$\n", "$\\newcommand{\\Ee}{\\mathcal{E}}$\n", "$\\newcommand{\\Cc}{\\mathcal{C}}$\n", "$\\newcommand{\\Gg}{\\mathcal{G}}$\n", "$\\newcommand{\\Ss}{\\mathcal{S}}$\n", "$\\newcommand{\\Pp}{\\mathcal{P}}$\n", "$\\newcommand{\\Ff}{\\mathcal{F}}$\n", "$\\newcommand{\\Xx}{\\mathcal{X}}$\n", "$\\newcommand{\\Mm}{\\mathcal{M}}$\n", "$\\newcommand{\\Ii}{\\mathcal{I}}$\n", "$\\newcommand{\\Dd}{\\mathcal{D}}$\n", "$\\newcommand{\\Ll}{\\mathcal{L}}$\n", "$\\newcommand{\\Tt}{\\mathcal{T}}$\n", "$\\newcommand{\\si}{\\sigma}$\n", "$\\newcommand{\\al}{\\alpha}$\n", "$\\newcommand{\\la}{\\lambda}$\n", "$\\newcommand{\\ga}{\\gamma}$\n", "$\\newcommand{\\Ga}{\\Gamma}$\n", "$\\newcommand{\\La}{\\Lambda}$\n", "$\\newcommand{\\si}{\\sigma}$\n", "$\\newcommand{\\Si}{\\Sigma}$\n", "$\\newcommand{\\be}{\\beta}$\n", "$\\newcommand{\\de}{\\delta}$\n", "$\\newcommand{\\De}{\\Delta}$\n", "$\\newcommand{\\phi}{\\varphi}$\n", "$\\newcommand{\\th}{\\theta}$\n", "$\\newcommand{\\om}{\\omega}$\n", "$\\newcommand{\\Om}{\\Omega}$\n"], "metadata": {}, "cell_type": "markdown"}, {"source": ["This tour explores image segmentation using parametric active contours."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 2, "cell_type": "code", "language": "python", "metadata": {}, "input": ["addpath('toolbox_signal')\n", "addpath('toolbox_general')\n", "addpath('toolbox_graph')\n", "addpath('solutions/segmentation_2_snakes_param')"]}, {"source": ["Parameteric Curves\n", "------------------\n", "In this tours, the active contours are represented using parametric\n", "curve $ \\ga : [0,1] \\rightarrow \\RR^2 $.\n", "\n", "\n", "This curve is discretized using a piewise linear curve with\n", "$p$ segments, and is stored as a complex vector of points in the plane\n", "$\\ga \\in \\CC^p$."], "metadata": {}, "cell_type": "markdown"}, {"source": ["Initial polygon."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 3, "cell_type": "code", "language": "python", "metadata": {}, "input": ["gamma0 = [0.78 0.14 0.42 0.18 0.32 0.16 0.75 0.83 0.57 0.68 0.46 0.40 0.72 0.79 0.91 0.90]' + ...\n", " 1i* [0.87 0.82 0.75 0.63 0.34 0.17 0.08 0.46 0.50 0.25 0.27 0.57 0.73 0.57 0.75 0.79]';"]}, {"source": ["Number of points of the discrete curve."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 4, "cell_type": "code", "language": "python", "metadata": {}, "input": ["p = 256;"]}, {"source": ["Shortcut to re-sample a curve according to arc length."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 5, "cell_type": "code", "language": "python", "metadata": {}, "input": ["curvabs = @(gamma)[0;cumsum( 1e-5 + abs(gamma(1:end-1)-gamma(2:end)) )];\n", "resample1 = @(gamma,d)interp1(d/d(end),gamma,(0:p-1)'/p, 'linear');\n", "resample = @(gamma)resample1( [gamma;gamma(1)], curvabs( [gamma;gamma(1)] ) );"]}, {"source": ["Initial curve $ \\ga_1(t) $."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 6, "cell_type": "code", "language": "python", "metadata": {}, "input": ["gamma1 = resample(gamma0);"]}, {"source": ["Display the initial curve."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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"output_type": "display_data"}], "prompt_number": 7, "cell_type": "code", "language": "python", "metadata": {}, "input": ["clf;\n", "h = plot(gamma1([1:end 1]), 'k');\n", "set(h, 'LineWidth', 2); axis('tight'); axis('off');"]}, {"source": ["Shortcut for forward and backward finite differences."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 8, "cell_type": "code", "language": "python", "metadata": {}, "input": ["BwdDiff = @(c)c - c([end 1:end-1]);\n", "FwdDiff = @(c)c([2:end 1]) - c;\n", "dotp = @(c1,c2)real(c1.*conj(c2));"]}, {"source": ["The tangent to the curve is computed as\n", "$$ t_\\ga(s) = \\frac{\\ga'(t)}{\\norm{\\ga'(t)}} $$\n", "and the normal is $ n_\\ga(t) = t_\\ga(t)^\\bot. $\n", "\n", "\n", "Shortcut to compute the tangent and the normal to a curve."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 9, "cell_type": "code", "language": "python", "metadata": {}, "input": ["normalize = @(v)v./max(abs(v),eps);\n", "tangent = @(gamma)normalize( FwdDiff(gamma) );\n", "normal = @(gamma)-1i*tangent(gamma);"]}, {"source": ["Move the curve in the normal direction, by computing $ \\ga_1(t) \\pm \\delta n_{\\ga_1}(t) $."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 10, "cell_type": "code", "language": "python", "metadata": {}, "input": ["delta = .03;\n", "gamma2 = gamma1 + delta * normal(gamma1);\n", "gamma3 = gamma1 - delta * normal(gamma1);"]}, {"source": ["Display the curves."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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"output_type": "display_data"}], "prompt_number": 11, "cell_type": "code", "language": "python", "metadata": {}, "input": ["clf;\n", "hold on;\n", "h = plot(gamma1([1:end 1]), 'k'); set(h, 'LineWidth', 2); \n", "h = plot(gamma2([1:end 1]), 'r--'); set(h, 'LineWidth', 2); \n", "h = plot(gamma3([1:end 1]), 'b--'); set(h, 'LineWidth', 2); \n", "axis('tight'); axis('off');"]}, {"source": ["Evolution by Mean Curvature\n", "---------------------------\n", "A curve evolution is a series of curves $ s \\mapsto \\ga_s $ indexed by\n", "an evolution parameter $s \\geq 0$. The intial curve $\\ga_0$ for\n", "$s=0$ is evolved, usually by minizing some energy $E(\\ga)$ in a gradient descent\n", "$$ \\frac{\\partial \\ga_s}{\\partial s} = \\nabla E(\\ga_s). $$\n", "\n", "\n", "Note that the gradient of an energy is defined with respect to the\n", "curve-dependent inner product\n", "$$ \\dotp{a}{b} = \\int_0^1 \\dotp{a(t)}{b(t)} \\norm{\\ga'(t)} d t. $$\n", "The set of curves can thus be thought as being a Riemannian surface.\n", "\n", "\n", "The simplest evolution is the mean curvature evolution.\n", "It corresponds to minimization of the curve length\n", "$$ E(\\ga) = \\int_0^1 \\norm{\\ga'(t)} d t $$\n", "\n", "\n", "The gradient of the length is\n", "$$ \\nabla E(\\ga)(t) = -\\kappa_\\ga(t) n_\\ga(t) $$\n", "where $ \\kappa_\\ga $ is the curvature, defined as\n", "$$ \\kappa_\\ga(t) = \\frac{1}{\\norm{\\ga'(t)}} \\dotp{ t_\\ga'(t) }{ n_\\ga(t) } . $$\n", "\n", "\n", "\n", "Shortcut for normal times curvature $ \\kappa_\\ga(t) n_\\ga(t) $."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 12, "cell_type": "code", "language": "python", "metadata": {}, "input": ["normalC = @(gamma)BwdDiff(tangent(gamma)) ./ abs( FwdDiff(gamma) );"]}, {"source": ["Time step for the evolution.\n", "It should be very small because we use an explicit time stepping and the\n", "curve has strong curvature."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 13, "cell_type": "code", "language": "python", "metadata": {}, "input": ["dt = 0.001 / 100;"]}, {"source": ["Number of iterations."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 14, "cell_type": "code", "language": "python", "metadata": {}, "input": ["Tmax = 3 / 100;\n", "niter = round(Tmax/dt);"]}, {"source": ["Initialize the curve for $s=0$."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 15, "cell_type": "code", "language": "python", "metadata": {}, "input": ["gamma = gamma1;"]}, {"source": ["Evolution of the curve."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 16, "cell_type": "code", "language": "python", "metadata": {}, "input": ["gamma = gamma + dt * normalC(gamma);"]}, {"source": ["To stabilize the evolution, it is important to re-sample the curve so\n", "that it is unit-speed parametrized. You do not need to do it every time\n", "step though (to speed up)."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 17, "cell_type": "code", "language": "python", "metadata": {}, "input": ["gamma = resample(gamma);"]}, {"source": ["__Exercise 1__\n", "\n", "Perform the curve evolution.\n", "You need to resample it a few times."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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SRJqfFu3KERNxzZjf7ffDHrcpb5Dq06zQi1sS/CdhzMm/gMBsUJwqlO+xqtq+vBn2ckjB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\nlr01mzN9BI3vmEVwt6iAVZl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"output_type": "display_data"}], "prompt_number": 18, "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo1()"]}, {"collapsed": false, "outputs": [], "prompt_number": 19, "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}, {"source": ["Geodesic Active Contours\n", "------------------------\n", "Geodesic active contours minimize a weighted length\n", "$$ E(\\ga) = \\int_0^1 W(\\ga(t)) \\norm{\\ga'(t)} d t, $$\n", "where $W(x)>0$ is the geodesic metric, that should be small in areas\n", "where the image should be segmented.\n", "\n", "\n", "Create a synthetic weight $W(x)$."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 20, "cell_type": "code", "language": "python", "metadata": {}, "input": ["n = 200;\n", "nbumps = 40;\n", "theta = rand(nbumps,1)*2*pi;\n", "r = .6*n/2; a = [.62*n .6*n];\n", "x = round( a(1) + r*cos(theta) );\n", "y = round( a(2) + r*sin(theta) );\n", "W = zeros(n); W( x + (y-1)*n ) = 1;\n", "W = perform_blurring(W,10);\n", "W = rescale( -min(W,.05), .3,1);"]}, {"source": ["Display the metric."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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/ld9sTCde6p+gXq+P71kmft0m/NcCAITEGhjwP+fOPteqTO6seoWzXOPAF198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\nKGAAgJD+H7JfGDy94GvXAAAAAElFTkSuQmCC\n", "output_type": "display_data"}], "prompt_number": 21, "cell_type": "code", "language": "python", "metadata": {}, "input": ["clf;\n", "imageplot(W);"]}, {"source": ["Pre-compute the gradient $\\nabla W(x)$ of the metric."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 22, "cell_type": "code", "language": "python", "metadata": {}, "input": ["options.order = 2;\n", "G = grad(W, options);\n", "G = G(:,:,1) + 1i*G(:,:,2);"]}, {"source": ["Shortcut to evaluate the gradient and the potential along a curve."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 23, "cell_type": "code", "language": "python", "metadata": {}, "input": ["EvalG = @(gamma)interp2(1:n,1:n, G, imag(gamma), real(gamma));\n", "EvalW = @(gamma)interp2(1:n,1:n, W, imag(gamma), real(gamma));"]}, {"source": ["Create a circular curve $\\ga_0$."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 24, "cell_type": "code", "language": "python", "metadata": {}, "input": ["r = .98*n/2;\n", "p = 128; % number of points on the curve\n", "theta = linspace(0,2*pi,p+1)'; theta(end) = [];\n", "gamma0 = n/2*(1+1i) + r*(cos(theta) + 1i*sin(theta));"]}, {"source": ["Initialize the curve at time $t=0$ with a circle."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 25, "cell_type": "code", "language": "python", "metadata": {}, "input": ["gamma = gamma0;"]}, {"source": ["For this experiment, the time step should be larger, because the\n", "curve is in $[1,n] \\times [1,n]$."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 26, "cell_type": "code", "language": "python", "metadata": {}, "input": ["dt = 1;"]}, {"source": ["Number of iterations."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 27, "cell_type": "code", "language": "python", "metadata": {}, "input": ["Tmax = 5000;\n", "niter = round(Tmax/dt);"]}, {"source": ["Display the curve on the back ground;"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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s+vpaF+DhVXOz2Qx3cNbPLiwspNoFGWVmkQszMOXcFxcXZnZ8fPzu3TtLci/N\nhJ2fn+vlVpqujQtWV1f1aWr7gvSBkaN3Vj6QgeURp2NgTEo+yEz0yh4ysBzJe0Wib9OcWt1sZtfX\n15r2UNMgTXI0m01dleuntMTHOwaFudfc3BxJWKS63W44+6UMTAfA0dGR5sB0q+XM7XZbR0K4887m\n5mbvQvi5uTmiV8YRwPIl1wOJdntrytQOhDpzKYyp1cLh4aGGEMOtwqyn24JRyhEnHzkMW87rCkbd\nDk9OTtT/UCOKinP1el1r3hW6Hj16ZGabm5uKahpCTHVyQWbxvs0v3n7ACOZ8B9QcXQvmDBlY7uR6\nILG35kKX4dfX17oM1wW4tw7Sp2HpR6PRSLULMhokxiZcaNxut/vmXmZ2enqqFFwvrjeLUu7lg4dm\ntrq6Gm5uMDc3V/a1FkSvDCMDyyOWNgMjKFe4so8Dr1NO5XQyLJTKxnQ9Hs7kN5tNTX6IpsdardZ9\n7YKQbancy8xarVa43ZemP1W1cXJyouRMM1sq09jc3NQ+BsrAVNSzuLgYzn6Ff29q/xoegAysAMjD\ngIExeBgRMrD8CifD8pWHhbmXVySqnlBzWrqa1qyGf+Drl8NSRqa+ItLtdlO5l5ldXl6qPl651+7u\nrt8eHByEZagqPnz8+LEqDzc2NixZXFGv15V7Eb3iQgDLtfwWdNjtCFSpVBS0lpaWLJmZL5VKGjYM\ny+iXlpZ6S6UJY1Hodru9FfOnp6eq2QlbziuAnZ6e6mIlXAK4ubmpI0Ejirq4qVQqc3Nz/ys7RCQY\nQsw7CjqAAdyKXqRfkSADK4BcF3R4N3FdSnujDTNrNBq6VFdttJKztbU1v+g2ljBHwvfuCnMvVW0c\nHh6q4aFuNZCoQcWrqyu96HrFlXKtrq6GXwzXs/8qd++RHOPdWzDkYUAPpr4iRQZWDHks6Eht2ayJ\nLlF2tby8rCkT307Mgm70YQbGHFhmhXXzNzc3vtGXJbXyu7u7qWbzfv96va7ZL7WcVwa2tLSUyr0q\nyc7d+XhfFAoZWGGEb07O14CZmf0veiFCZGBFkseiRM/Dwv299PHNzY2uxL1SUbfkXhFJ7bYcZmAq\nNfzll180+6V5L61kV9eopaWlra0tS9Ysq4y+0Wh4Gep8rRb+pan+YxgHAljB5LSgw/dD8Y1XzGx+\nfj4MYB7qCF1Z5r1RwsHDVABTrPLqeX2g0BUu+dra2grbHnoA0/UN0SsHGEIsHgrrUXgLi4v+cbfT\nmeEjwSjIwIotR3lY7yZhqT6HnnKRe2WKv0xKs1I9KsPWG461uDcAAAzkSURBVO12Wx+EHS99IwKv\n3DEzjRw+efIkzL1STTf8z3M0xIsMrJAo6ECBVefn9UGn3Z7tI8GIyMCKKo+F9XY7uxpXptXbt94/\nTv05cruh+BPrCZbfdjqd3ie80+mE9Tia7tKqZEvaYCr3UrfD7e3tsOGhqucXG41ff2enw6sVOzKw\nAiMPQ8F49CL3ygcysGLLaR42Ft77PCyEC/cSs56Jt7C+kWzsHqnaQs1mqcJQ/eNbrZbu44sfzKxU\nKqm+tNFoWNKd2X9QGZimu3zq657cixcoBwhghUcMu4MPbalkQF34dKptt9s6vSpiqSy7Wq2GjfXC\nchKkhKUZV1dXKos/OjryW9+JVLFHcWhpaUnPrYYNFYH6drxU042VlRVvuuHzXkboyhHeXWAsETkX\nRi+K5vOkxJbq+FUYuop9VPhoofIt9T5Xk72zszN9RffR0Jb6PjQaDQ1t+c6ZZlYul0nCQqncy8xO\nTk7UzPD169d+q6bylgwJPn361MyePHmiogyNFupX+WBj2PFSL0G9Xk/lXt2kDAT5wFsLCfIw5A65\nV74xB4ZA4efD+vY+16xMaq96JWepwoEPPvjAkj3JlI3NJydQKjskzMD0HJ6enr59+9bMXr58aWbf\nfvutmf3888+6/4cffmhJ+lupVJTsamZLyZY/pb4vgd/WFxb+93fJvfKIDAy3kYchF1LRa4aPBJND\nBoYehc/DNL/VarV04a+Npn744Qcz++6778zsxx9/VEN0JVhPnjwxs88///yzzz4zs+fPn1uQGeg+\nqQr7wmYDYY6r6sHz83M9w69evTKzr7/+2sy+//573V+NepV4PX78WCuUxYs/w8UMv25H4COH6uY8\nlX8N00cAQz9FjWGp9Ukq31BBgU6v//znP83sq6++evPmjSVDVR9//LGZ7e3t6YysagJfuhSuZ/IK\n+74jisWJaqnnWdUcKpDxHvO6p4Zn9a3Ly0uNPYZ7DlQqlTB0zZXL4Z+Z3r+EWWAIEXdgLBGxCaMX\nw4ZFQAaGu6XyMCvKJa3nB8qotKhWG9grD/MBLvnXv/5lZjc3N1pFqw3sNepVKpXCag4f9VL2EOZh\nfZvlZ6GDfqoxfF/DtqAMB/0qlYrKMfTs+VZeumeqkbyewHCR+P8aoITLFegxXwxkYLhXt0sqhuxL\nRa/ZPRBMFRkYBlCwKTFPicIrfX2xfXcT2FevXmkR7osXLywpprdkHbQvrbUgk0jlYamdo8Pbvrna\nhKSaQPptJxiUu6sbZPho+wr/BT0JjUZD+ZaeN+W7/uxpCbO+tbW1Faaz/roQvQqLAIbBFCyGIQq1\nev3W5xyWBUMAw8AKE8N80ynNzWgCRouUlRB89913yqtCc3Nz3hvJzN69e2dmNzc3v7ZCX1y0ZJpn\naWlJvznMwMK/67fKUSqVSljE6EnP2FMx3xM57GKc2g05TMu8PXzq0d7TyDgsIFQitby8/PjxY/9z\nyrE+/fRT3V+9o549e2Zmjx8/1muhHyR6gTkwDCM1H8aUGGakkexjadYzU4vCIAPDkHSmyGkqFs7o\nVKvVcN8pTcN8+eWXZtZsNv/9739bslxJ2dXHH3+smRvlMb4tiPIS5WEqUFxZWakH2YMnOvq7Si/0\nO/1W91felkp0xjIxFu521mq1lEoqy/RtuvQ4w5mwSqXS+2hrtZq+eM9at3AbmkajoexWn6rs0LdT\n0e/UE7u2tqZXJB29UFQEMDxITocTU+XdijoKYFqtrNP34uLiRx99ZEltve6/sbGhPhE65yoGnJ6e\n6kcUgbQg9/j4WD+iCKHdsFI7YOmUrT+9ubmp07rin07iCwsLHslSj38ovc0Jz87OFH3132ll8dnZ\nmRYVhOuyFxYWtPOWHp6G+1ZWVm6tLA4+Tj1O7x+vTxX29D/qb1kS1bzH/PLKyq0H3+kwCFBkDCHi\noSivx3T1Rq9ZPRJkBBkYRpDTlc6eHyhtUk4gSgjW1taUkCl5UvriOzLrU8+rNATnWznrW8q31IX9\np59+MrOdnR0lbUrglMwpz3vx4oU+UAmJvrW+vq5ULMxmhsrAwn5OyniUIO7u7obrtX/88Ucz29/f\n132UJ6kaZXNzU/UXKrLw4vjenan7PsM+kBiOKOrf94FKfatcLvc25y1O5y3chQCG0eR6SgxZcGvG\ny6zTbhO4IAQwjEO+UjHPD3ymx5JUQPnHysqKOtBrEsurG/SBci/9bKfTCVMQJRYnJye//PKLJZ3X\n//GPf9gdS6SV/H355Ze//e1vzeyLL76wZHat2+16duIPr9vtDp6X9G6OfHx8bGY//vjj3//+dzP7\n61//amZfffWVmb19+1b310SXcsFPPvlEz4AXxOvJURYV7pvc91H5F/VchRt6uUq1eusxdzolci8k\nCGAYkzCGGakYRpUKXe2bm76jkSgyAhjGp3c40SJOxbyVlG+MYkH1nXIjpVx+q+mucKuwer2uTcV0\nH82E7e/v64vad/ie9lRKif785z+rXl95klKuhYWFcGPiMIkZUG8GpoLDV69e/e1vfzOzP/3pT70P\nT3tSq0CxXC4rIdO/4/N84WLn9/J0Sv/Xrxlb6h/pdss9PwgQwDBuOUrFegvBvfGE6jvC5VO+r5Ui\ninfx0CCbvqUTvSWl8Knhsnu8fPnSkh7tH374oW61fCpcnjX4EKJHl75FHP/3f/9n90ZW/5fDThze\nLmSUpWm9oesBvwQFQUqOCejtYc+kBQaROk6IXrgXGRgmJi+pWJhPKHGZm5sLR8mUxHQ6Hd/uy5KV\nyysrK8q9wk2H5+bmNFj32WefmZl62A9CP66U7vr6urc1xgOk/gULOnHcQ6OXT548URm9FlyriKNW\nq/XudvZ+hC4MjwwMk0QqhkEQvfAgZGCYvN5UzGI9SaU6x3tCZkHFvKaCvEmg8iRNMmn9b6VS0aee\nS5nZX/7yl3v+rn6b5sD0S2q12gMKN3qFj1nzdqurq5pm00xYX3/4wx/M7IsvvlDbeC0qUPsr73E1\n0AMjdGEEZGCYit5+4aRiBdebjhO9MCQyMExRvurs7fYEj2/QFa4v7nQ6mlhSHuYl72Heo6mj58+f\n/+c//7Gktl61+Polm5ubn3/+uZn95je/0T3NbH19XRNRYR42eOGfbwAdLtDW2oDnz5//7ne/s6Rm\n8ptvvjGzZrO5vb1tZlpS/cc//tHMvvzyy08++cSS7lZq7Fuv198zB9b7lZiPAcwQAQxTl7swJh4S\nwnHFbrcbtm/3QnN9oEIPLaV68eLF73//e0u2aFG9hje/V8W8Wg6qL+LW1pYaXgwxXtfzgC2JkXok\nair/4sULjXAqnimYXV9f+3ct2XDy2bNnemCKwQqo1Wr1ni6IZF0YIwIYZiRHE2MYCKEL41YacLU8\nMCl5H1AKC+51e3Nzo8INFXFopO7k5ETDhsq91NRD64UrlYoWPisl8r3BfANJu7f1+/3ChczqkX98\nfKwsULd6VJ1ORwmW8kXVzfsOk6luIOnBw7y/xJgVMjDMWmpE0cjGcoTQhUkiA0OW5P1853mYUivd\nKvu5vr7W8mElZ/qi0iPvi6+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"output_type": "display_data"}], "prompt_number": 28, "cell_type": "code", "language": "python", "metadata": {}, "input": ["lw = 2;\n", "clf; hold on;\n", "imageplot(W);\n", "h = plot(imag(gamma([1:end 1])),real(gamma([1:end 1])), 'r');\n", "set(h, 'LineWidth', lw);\n", "axis('ij');"]}, {"source": ["The gradient of the energy is\n", "$$ \\nabla E(\\ga) = -W(\\ga(t)) \\kappa_\\ga(t) n_\\ga(t) + \\dotp{\\nabla W(\\ga(t))}{ n_\\ga(t) } n_\\ga(t). $$\n", "\n", "\n", "Evolution of the curve according to this gradient."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 29, "cell_type": "code", "language": "python", "metadata": {}, "input": ["N = normal(gamma);\n", "g = - EvalW(gamma).*normalC(gamma) + dotp(EvalG(gamma), N) .* N;\n", "gamma = gamma - dt*g;"]}, {"source": ["To avoid the curve from being poorly sampled, it is important to\n", "re-sample it evenly."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 30, "cell_type": "code", "language": "python", "metadata": {}, "input": ["gamma = resample( gamma );"]}, {"source": ["__Exercise 2__\n", "\n", "Perform the curve evolution."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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+/zOfAbC0tHTnXXfJJ9/Yv9/TFru6rTfq9VQ63XGyiS0mjAQJBYxYkjofWoYkAjG+ugMr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\nHHAxW+qQqnkJ1KuaMYfeK67QgZHVhO/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ZcwAAAABJRU5ErkJggg==\n", "output_type": "display_data"}], "prompt_number": 31, "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo2()"]}, {"collapsed": false, "outputs": [], "prompt_number": 32, "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}, {"source": ["Medical Image Segmentation\n", "--------------------------\n", "One can use a gradient-based metric to perform edge detection in medical\n", "images.\n", "\n", "\n", "Load an image $f$."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 33, "cell_type": "code", "language": "python", "metadata": {}, "input": ["n = 256;\n", "f = rescale( sum(load_image('cortex', n), 3 ) );"]}, {"source": ["Display."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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MJjkG0Eywyg8GA7OICiczmQzYK7ig1WrhthIvi2hVTL0lXIl/emexGjuHzWaz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sEuhgUHFuwLY23q9XpRFEn1hy+Hw6EyM2ATWBr29/f/9m//1szq9fof/MEffOUrXzGz1dXVe/fu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\ntRaLxfr9PhZcrVZpepnB4oWIV9AhXgMv3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"output_type": "display_data"}], "prompt_number": 34, "cell_type": "code", "language": "python", "metadata": {}, "input": ["clf;\n", "imageplot(f);"]}, {"source": ["An edge detector metric can be defined as a decreasing function of the\n", "gradient magnitude.\n", "$$ W(x) = \\psi( d \\star h_a(x) )\n", " \\qwhereq d(x) = \\norm{\\nabla f(x)}. $$\n", "where $h_a$ is a blurring kernel of width $a>0$.\n", "\n", "\n", "Compute the magnitude of the gradient."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 35, "cell_type": "code", "language": "python", "metadata": {}, "input": ["options.order = 2;\n", "G = grad(f,options);\n", "d = sqrt(sum(G.^2,3));"]}, {"source": ["Blur it by $h_a$."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 36, "cell_type": "code", "language": "python", "metadata": {}, "input": ["a = 3;\n", "d = perform_blurring(d,a);"]}, {"source": ["Compute a decreasing function of the gradient to define $W$."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 37, "cell_type": "code", "language": "python", "metadata": {}, "input": ["d = min(d,.4);\n", "W = rescale(-d,.8,1);"]}, {"source": ["Display it."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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hBuwxApPn8qT882BxUr/fn06ncJuCIBgOh0jSsB1UOp3O5/P0PMIwRJXVnTt3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\nXa/XgGs///nPf/WrX4nI48eP/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/PJJ59gD7CHL5fLs9kMWVGv16PbyGQyQXX0k08+GY1G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\nPmazmZsmunVI7s0tDC55dth55ypadbjJGTO8L3Li/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"output_type": "display_data"}], "prompt_number": 38, "cell_type": "code", "language": "python", "metadata": {}, "input": ["clf;\n", "imageplot(W);"]}, {"source": ["Number of points."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 39, "cell_type": "code", "language": "python", "metadata": {}, "input": ["p = 128;"]}, {"source": ["__Exercise 3__\n", "\n", "Create an initial circle $\\gamma_0$ of $p$ points."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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tdpuCtiTBk/yNdBolcfEptHyEY1EsFv/f//t/v/qrvyoiR44cgTQGloj0cbUt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\nHkr9pwAAAABJRU5ErkJggg==\n", "output_type": "display_data"}], "prompt_number": 40, "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo3()"]}, {"collapsed": false, "outputs": [], "prompt_number": 41, "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}, {"source": ["Step size."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 42, "cell_type": "code", "language": "python", "metadata": {}, "input": ["dt = 2;"]}, {"source": ["Number of iterations."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 43, "cell_type": "code", "language": "python", "metadata": {}, "input": ["Tmax = 9000;\n", "niter = round(Tmax/dt);"]}, {"source": ["__Exercise 4__\n", "\n", "Perform the curve evolution."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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DBOqCiIEJLJC9Fq84T2cy73rnO+c4YHhkpK+3t621dTFXWZKpXuXAAiZTqQWc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\nTkSuQmCC\n", "output_type": "display_data"}], "prompt_number": 44, "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo4()"]}, {"collapsed": false, "outputs": [], "prompt_number": 45, "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}, {"source": ["Evolution of a Non-closed Curve\n", "-------------------------------\n", "It is possible to perform the evolution of a non-closed curve by adding\n", "boundary constraint\n", "$$ \\ga(0)=x_0 \\qandq \\ga(1)=x_1. $$\n", "\n", "\n", "In this case, the algorithm find a local minimizer of the geodesic\n", "distance between the two points.\n", "\n", "\n", "Note that a much more efficient way to solve this problem is to use the\n", "Fast Marching algorithm to find the global minimizer of the geodesic\n", "length.\n", "\n", "\n", "Load an image $f$."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 46, "cell_type": "code", "language": "python", "metadata": {}, "input": ["n = 256;\n", "f = rescale( sum(load_image('cortex', n), 3 ) );\n", "f = f(46:105,61:120);\n", "n = size(f,1);"]}, {"source": ["Display."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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"output_type": "display_data"}], "prompt_number": 47, "cell_type": "code", "language": "python", "metadata": {}, "input": ["clf;\n", "imageplot(f);"]}, {"source": ["__Exercise 5__\n", "\n", "Compute an edge attracting criterion $W(x)>0$, that is small in area of strong\n", "gradient."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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UuvgLTJJUkg1MklSSDUySVJINTJJUkg1MklSSKcSRyqyu25yPd//+/eZuudoy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\nAAAASUVORK5CYII=\n", "output_type": "display_data"}], "prompt_number": 48, "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo5()"]}, {"collapsed": false, "outputs": [], "prompt_number": 49, "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}, {"source": ["Start and end points $x_0$ and $x_1$."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 50, "cell_type": "code", "language": "python", "metadata": {}, "input": ["x0 = 4 + 55i;\n", "x1 = 53 + 4i;"]}, {"source": ["Initial curve $\\ga_0$."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 51, "cell_type": "code", "language": "python", "metadata": {}, "input": ["p = 128;\n", "t = linspace(0,1,p)';\n", "gamma0 = t*x1 + (1-t)*x0;"]}, {"source": ["Initialize the evolution."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 52, "cell_type": "code", "language": "python", "metadata": {}, "input": ["gamma = gamma0;"]}, {"source": ["Display."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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4jrPnymjFk8acn583Fb3J9ScODeEbGCol271mpqdLPBIAq40GhuqgewEthQaG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\nrkJggg==\n", "output_type": "display_data"}], "prompt_number": 53, "cell_type": "code", "language": "python", "metadata": {}, "input": ["clf; hold on;\n", "imageplot(W);\n", "h = plot(imag(gamma([1:end])),real(gamma([1:end])), 'r'); set(h, 'LineWidth', 2);\n", "h = plot(imag(gamma([1 end])),real(gamma([1 end])), 'b.'); set(h, 'MarkerSize', 30);\n", "axis('ij');"]}, {"source": ["Re-sampling for non-periodic curves."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 54, "cell_type": "code", "language": "python", "metadata": {}, "input": ["curvabs = @(gamma)[0;cumsum( 1e-5 + abs(gamma(1:end-1)-gamma(2:end)) )];\n", "resample1 = @(gamma,d)interp1(d/d(end),gamma,(0:p-1)'/(p-1), 'linear');\n", "resample = @(gamma)resample1( gamma, curvabs(gamma) );"]}, {"source": ["Time step."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 55, "cell_type": "code", "language": "python", "metadata": {}, "input": ["dt = 1/10;"]}, {"source": ["Number of iterations."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 56, "cell_type": "code", "language": "python", "metadata": {}, "input": ["Tmax = 2000*4/7;\n", "niter = round(Tmax/dt);"]}, {"source": ["__Exercise 6__\n", "\n", "Perform the curve evolution.\n", "Be careful to impose the boundary conditions at each step."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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S0LyEnkM0QSkTF+6i0ruJl6MMvYuYmBHT9wXaw2w8h0OHDnV/LFyyxGz8adeu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\nC55RfAMO7NnmMtnU0sRDI+hvDHQh2pw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"output_type": "display_data"}], "prompt_number": 57, "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo6()"]}, {"collapsed": false, "outputs": [], "prompt_number": 58, "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}], "metadata": {}}], "nbformat": 3, "metadata": {"kernelspec": {"name": "matlab_kernel", "language": "matlab", "display_name": "Matlab"}, "language_info": {"mimetype": "text/x-matlab", "name": "matlab", "file_extension": ".m", "help_links": [{"url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md", "text": "MetaKernel Magics"}]}}}