{"metadata": {"signature": "sha256:b57ba0cce2f85978e6bb816bb1af3e0d3fbe6c24ff7a499b9579d2ea77e0e90e", "name": ""}, "worksheets": [{"metadata": {}, "cells": [{"level": 1, "metadata": {}, "cell_type": "heading", "source": ["Active Contours using Parameteric Curves"]}, {"metadata": {}, "cell_type": "markdown", "source": ["This tour explores image segmentation using parametric active contours.\n", "$\\newcommand{\\dotp}[2]{\\langle #1, #2 \\rangle}$\n", "$\\newcommand{\\qandq}{\\quad\\text{and}\\quad}$\n", "$\\newcommand{\\qwhereq}{\\quad\\text{where}\\quad}$\n", "$\\newcommand{\\qifq}{ \\quad \\text{if} \\quad }$\n", "$\\newcommand{\\ZZ}{\\mathbb{Z}}$\n", "$\\newcommand{\\RR}{\\mathbb{R}}$\n", "$\\newcommand{\\CC}{\\mathbb{C}}$\n", "$\\newcommand{\\pa}[1]{\\left(#1\\right)}$\n", "$\\newcommand{\\si}{\\sigma}$\n", "$\\newcommand{\\Nn}{\\mathcal{N}}$\n", "$\\newcommand{\\Bb}{\\mathcal{B}}$\n", "$\\newcommand{\\EE}{\\mathbb{E}}$\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", "$\\newcommand{\\al}{\\alpha}$\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": ["*Important:* Please read the [installation page](http://gpeyre.github.io/numerical-tours/installation_python/) for details about how to install the toolboxes."]}, {"prompt_number": 1, "metadata": {}, "cell_type": "code", "outputs": [{"output_type": "stream", "stream": "stdout", "text": ["Populating the interactive namespace from numpy and matplotlib\n"]}, {"output_type": "stream", "stream": "stderr", "text": ["WARNING: pylab import has clobbered these variables: ['pylab']\n", "`%matplotlib` prevents importing * from pylab and numpy\n"]}], "input": ["from __future__ import division\n", "from nt_toolbox.general import *\n", "from nt_toolbox.signal import *\n", "%pylab inline\n", "%matplotlib inline\n", "%load_ext autoreload\n", "%autoreload 2"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Parameteric Curves\n", "-------------------\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", "$\\ga \\in \\CC^p$.\n", "\n", "Initial polygon."]}, {"prompt_number": 2, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["gamma0 = array([.78, .14, .42, .18, .32, .16, .75, .83, .57, .68, .46, .40, .72, .79, .91, .90]) + 1j*array([.87, .82, .75, .63, .34, .17, .08, .46, .50, .25, .27, .57, .73, .57, .75, .79])"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Display the initial curve."]}, {"prompt_number": 3, "metadata": {}, "cell_type": "code", "outputs": [{"metadata": {}, "output_type": "display_data", "png": 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"text": [""]}], "input": ["periodize = lambda gamma: concatenate((gamma, [gamma[0]]))\n", "def cplot(gamma,s='b',lw=1): \n", " plot(real(periodize(gamma)), imag(periodize(gamma)), s, linewidth=lw)\n", " axis('equal')\n", " axis('off')\n", "cplot(gamma0,'b.-');"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Number of points of the discrete curve."]}, {"prompt_number": 4, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["p = 256"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Shortcut to re-sample a curve according to arc length."]}, {"prompt_number": 5, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["interpc = lambda x,xf,yf: interp(x,xf,real(yf)) + 1j * interp(x,xf,imag(yf))\n", "curvabs = lambda gamma: concatenate( ([0], cumsum( 1e-5 + abs(gamma[:-1:]-gamma[1::]) ) ) )\n", "resample1 = lambda gamma,d: interpc(arange(0,p)/float(p), d/d[-1],gamma)\n", "resample = lambda gamma: resample1( periodize(gamma), curvabs(periodize(gamma)) )"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Initial curve $ \\ga_1(t)$."]}, {"prompt_number": 6, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["gamma1 = resample(gamma0)"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Display the initial curve."]}, {"prompt_number": 7, "metadata": {}, "cell_type": "code", "outputs": [{"metadata": {}, "output_type": "display_data", "png": 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"text": [""]}], "input": ["cplot(gamma1, 'k')"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Shortcut for forward and backward finite differences."]}, {"prompt_number": 8, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["shiftR = lambda c: concatenate( ([c[-1]],c[:-1:]) )\n", "shiftL = lambda c: concatenate( (c[1::],[c[0]]) )\n", "BwdDiff = lambda c: c - shiftR(c)\n", "FwdDiff = lambda c: shiftL(c) - c"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "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", "Shortcut to compute the tangent and the normal to a curve."]}, {"prompt_number": 9, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["normalize = lambda v: v/maximum(abs(v),1e-10)\n", "tangent = lambda gamma: normalize( FwdDiff(gamma) )\n", "normal = lambda gamma: -1j*tangent(gamma)"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Move the curve in the normal direction, by computing $ \\ga_1(t) \\pm \\delta n_{\\ga_1}(t) $."]}, {"prompt_number": 10, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["delta = .03\n", "gamma2 = gamma1 + delta * normal(gamma1)\n", "gamma3 = gamma1 - delta * normal(gamma1)"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Display the curves."]}, {"prompt_number": 11, "metadata": {}, "cell_type": "code", "outputs": [{"metadata": {}, "output_type": "pyout", "text": ["(0.13822079913787064,\n", " 0.93899831377290144,\n", " 0.053329237592183561,\n", " 0.89990886424047734)"], "prompt_number": 11}, {"metadata": {}, "output_type": "display_data", "png": 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6mOFeLsO1kfYQ7C14uAO/31jgeywDIGWGgZqypY9pK9BqZTQ0dYgcaAzTtFkm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\nSvCYdYgc0BXczykvmAnz+X6BFe585r8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"text": [""]}], "input": ["cplot(gamma1, 'k')\n", "cplot(gamma2, 'r--')\n", "cplot(gamma3, 'b--')\n", "axis('tight') \n", "axis('off')"], "collapsed": false, "language": "python"}, {"level": 2, "metadata": {}, "cell_type": "heading", "source": ["Evolution by Mean Curvature"]}, {"metadata": {}, "cell_type": "markdown", "source": ["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", "$$ \\kappa_\\ga(t) = \\frac{1}{\\norm{\\ga'(t)}} \\dotp{ t_\\ga'(t) }{ n_\\ga(t) }\u00a0. $$\n", "\n", "\n", "\n", "Shortcut for normal times curvature $ \\kappa_\\ga(t) n_\\ga(t) $."]}, {"prompt_number": 12, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["normalC = lambda gamma: BwdDiff(tangent(gamma)) / abs( FwdDiff(gamma) )"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "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."]}, {"prompt_number": 13, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["dt = 0.001 / 100"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Number of iterations."]}, {"prompt_number": 14, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["Tmax = 3.0 / 100\n", "niter = round(Tmax/dt)"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Initialize the curve for $s=0$."]}, {"prompt_number": 15, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["gamma = gamma1"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Evolution of the curve."]}, {"prompt_number": 16, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["gamma = gamma + dt * normalC(gamma)"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "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)."]}, {"prompt_number": 17, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["gamma = resample(gamma)"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["**Exercise 1:** Perform the curve evolution.\n", "You need to resample it a few times."]}, {"prompt_number": 18, "metadata": {}, "cell_type": "code", "outputs": [{"metadata": {}, "output_type": "display_data", "png": 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yPz5ggn9H1oDqobTSqymD8n5V9rU3RaGVTbeYcP2limN/QmDPEm2WpeiIl1me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"text": [""]}], "input": ["run -i nt_solutions/segmentation_2_snakes_param/exo1"], "collapsed": false, "language": "python"}, {"level": 2, "metadata": {}, "cell_type": "heading", "source": ["Geodesic Active Contours"]}, {"metadata": {}, "cell_type": "markdown", "source": ["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."]}, {"metadata": {}, "cell_type": "markdown", "source": ["Size of the image $n$."]}, {"prompt_number": 19, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["n = 200"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Create a synthetic weight $W(x)$."]}, {"prompt_number": 20, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["nbumps = 40\n", "theta = random.rand(nbumps,1)*2*pi\n", "r = .6*n/2\n", "a = array([.62*n,.6*n])\n", "x = around( a[0] + r*cos(theta) )\n", "y = around( a[1] + r*sin(theta) )\n", "W = zeros([n,n])\n", "for i in arange(0,nbumps):\n", " W[int(x[i]),int(y[i])] = 1\n", "W = gaussian_blur(W,6.0)\n", "W = rescale( -minimum(W,.05), .3,1)"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Display the metric $W$."]}, {"prompt_number": 21, "metadata": {}, "cell_type": "code", "outputs": [{"metadata": {}, "output_type": "display_data", "png": 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jBX6NSARaVajjgFaBqg9VUORE8FJrAAgR7A2t4MxQalEnME1/Ne1Vj6DbYT8+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\nlXLwWMggRPAB4dbBEBn46uO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"text": [""]}], "input": ["imageplot(W)"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Pre-compute the gradient $\\nabla W(x)$ of the metric."]}, {"prompt_number": 22, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["G = grad(W)\n", "G = G[:,:,0] + 1j*G[:,:,1]"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Display the image of the magnitude $\\norm{\\nabla W(x)}$ of the gradient."]}, {"prompt_number": 23, "metadata": {}, "cell_type": "code", "outputs": [{"metadata": {}, "output_type": "display_data", "png": 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UtkBhRT4M7NhVcVV8omsSAJsSYwqPtKcAlyGzqcOs7IBbAreHPWdZVoE2grG+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\nAGwySiR+O+EAm0niriQAOBH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"text": [""]}], "input": ["imageplot(abs(G))"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Shortcut to evaluate the gradient and the potential along a curve."]}, {"prompt_number": 24, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["EvalG = lambda gamma: bilinear_interpolate(G, imag(gamma), real(gamma))\n", "EvalW = lambda gamma: bilinear_interpolate(W, imag(gamma), real(gamma))"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Create a circular curve $\\ga_0$."]}, {"prompt_number": 25, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["r = .98*n/2 # radius\n", "p = 128 # number of points on the curve\n", "theta = transpose( linspace(0, 2*pi, p + 1) )\n", "theta = theta[0:-1]\n", "gamma0 = n/2 * (1 + 1j) + r*(cos(theta) + 1j*sin(theta))"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Initialize the curve at time $t=0$ with a circle."]}, {"prompt_number": 26, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["gamma = gamma0"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["For this experiment, the time step should be larger, because the\n", "curve is in $[0,n-1] \\times [0,n-1]$."]}, {"prompt_number": 27, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["dt = 1"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Number of iterations."]}, {"prompt_number": 28, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["Tmax = 5000\n", "niter = round(Tmax/ dt)"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Display the curve on the background."]}, {"prompt_number": 29, "metadata": {}, "cell_type": "code", "outputs": [{"metadata": {}, "output_type": "display_data", "png": 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rBPRaAb1/TCQSgdvWpgbQ0VHXmbGZEEEXeulpD4seH3msovu6lP7mOA5isZg3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\n++ecg2g2iwRLbdSXj+PLyOnHLwwtIuj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"text": [""]}], "input": ["lw = 2\n", "clf\n", "imageplot(transpose(W))\n", "cplot(gamma, 'r', lw)"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["The gradient of the energy is\n", "$$ \\nabla E(\\ga) = -W(\\ga(t)) \\kappa_\\ga(t) n_\\ga(t) + \\dotp{\\nabla W(\\ga(t))}{ n_\\ga(t) } n_\\ga(t). $$"]}, {"metadata": {}, "cell_type": "markdown", "source": ["Pointwise innerproduct on the curve."]}, {"prompt_number": 30, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["dotp = lambda c1,c2: real(c1)*real(c2) + imag(c1)*imag(c2)"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Evolution of the curve according to this gradient."]}, {"prompt_number": 31, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["N = normal(gamma)\n", "g = - EvalW(gamma) * normalC(gamma) + dotp(EvalG(gamma), N) * N\n", "gamma = gamma - dt*g"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["To avoid the curve from being poorly sampled, it is important to\n", "re-sample it evenly."]}, {"prompt_number": 32, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["gamma = resample(gamma)"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["**Exercise 2:** Perform the curve evolution."]}, {"prompt_number": 33, "metadata": {}, "cell_type": "code", "outputs": [{"metadata": {}, "output_type": "display_data", "png": 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2unqYORPIzo75dkzx+UjEX3gBSEmhE9SoUUBODrcbpv7VWyR8hM3bJfp19HaL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\nnuqrr6K98UZKM4yx4cWcgsmUW/820ZWDYiKRSMmdGyPzlpY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44YXieSgkFlO3\nbBGNRrLhKJPtwBFGdziEWA8fLrYRI4RFQWkp0BGVHeSO4hhr/FF8Tah/VQUAuq7PB0Z90+dx3JBI\nwLZtXj79NJdt2/Koqcll794cmps9BAIeWlrctLR4iEYdxOM2YjE7sZgDXQe7PY7DEcfhSOBwxPD5\n2snODpGbGyYvL0RJSStlZS0MHuxn6NAAI0e24POlFdR3p9FH0sMEvErTtC7ahhUKhUKhUCgUCoVC\noVAoFAqFQqFQKBQKhUKhUCgUCoVCoVAoFAqFQqFQKBQKhUKhUCgUCoVCoVAoFAqFQqFQKBQKhUKh\nUCgUCoVCoVAoFAqFQqFQKBQKhUKhUCgUCoVCoVAoFAqFQqFQKBQKA/8fhHefZZS+LAoAAAAASUVO\nRK5CYII=\n", "text": [""]}], "input": ["run -i nt_solutions/segmentation_2_snakes_param/exo2"], "collapsed": false, "language": "python"}, {"level": 1, "metadata": {}, "cell_type": "heading", "source": ["Medical Image Segmentation"]}, {"metadata": {}, "cell_type": "markdown", "source": ["One can use a gradient-based metric to perform edge detection in medical\n", "images.\n", "\n", "Load an image $f$."]}, {"prompt_number": 34, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["n = 256\n", "name = 'nt_toolbox/data/cortex.bmp'\n", "f = load_image(name, n)"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Display."]}, {"prompt_number": 35, "metadata": {}, "cell_type": "code", "outputs": [{"metadata": {}, "output_type": "display_data", "png": 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sUl7k4ib4yXvQarWQzWZhs9lw8uRJXL16FU6nEz/+8Y+lRZylTFYo+H2q0Ql/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"text": [""]}], "input": ["imageplot(f)"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "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", "Compute the magnitude of the gradient."]}, {"prompt_number": 36, "metadata": {}, "cell_type": "code", "outputs": [{"metadata": {}, "output_type": "display_data", "png": 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ZjsFgEIlxMpmUYFUul/HAAw/gwoULmJiYwM7ODo4ePYrDhw/jpZdekhqepQMP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\njI+PY2ZmR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4CIBKudnR3ZFgEQxenRo0dRWVmJy5cvIxAIiAN4Op3G+Pg4AMjQNpfLIZPJ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\nKCgoKCgoKCgoKCgoKCgoKCgoKCjcT/g/oefE/O95424AAAAASUVORK5CYII=\n", "text": [""]}], "input": ["G = grad(f)\n", "d0 = sqrt(sum(G**2, 2))\n", "imageplot(d0)"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Blur it by $h_a$."]}, {"prompt_number": 37, "metadata": {}, "cell_type": "code", "outputs": [{"metadata": {}, "output_type": "display_data", "png": 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jH7/4u7/GzyVv0mIseAcuCHJX3tvaE1JR2Ug60HeSilyJ/83vK9f3XBjhf/Pr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\nBAKBQCAQCAQCgUAgMEv4DyIOFIteAmICAAAAAElFTkSuQmCC\n", "text": [""]}], "input": ["a = 2\n", "d = gaussian_blur(d0, a)\n", "imageplot(d)"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Compute a decreasing function of the gradient to define $W$."]}, {"prompt_number": 38, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["d = minimum(d, .4)\n", "W = rescale(-d, .8, 1)"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Display it."]}, {"prompt_number": 39, "metadata": {}, "cell_type": "code", "outputs": [{"metadata": {}, "output_type": "display_data", "png": 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ly8tLDYfDNFaiCjE1+ubmRp8+fZKklNtAx6rVaiVJyRxfLpfpXthHg9qPRqORkpPI03AA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\nq06no8FgoLu7O02n0wQqrESscF7DUC6XM9mZKA3xeCoLSTvGHaHuw4H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"text": [""]}], "input": ["imageplot(W)"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Number of points."]}, {"prompt_number": 40, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["p = 128"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["**Exercise 3:** Create an initial circle $\\gamma_0$ of $p$ points. When plotting the image, you need to transpose it to have axis coherent with the cplot."]}, {"prompt_number": 41, "metadata": {}, "cell_type": "code", "outputs": [{"metadata": {}, "output_type": "display_data", "png": 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F0ikadHGYlJ1Bs9lkbGyMVqvFzMwM6XRaaRGPx0MoFNLdkexO/vRP/5S/+Iu/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\nR9Zramr0Vj8ejzM8PEw+n9fGaVVVlcoaZcHD3r17GRoawrIs5ufn9S5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"text": [""]}], "input": ["run -i nt_solutions/segmentation_2_snakes_param/exo3"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Step size."]}, {"prompt_number": 42, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["dt = 2"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Number of iterations."]}, {"prompt_number": 43, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["Tmax = 9000\n", "niter = round(Tmax/ dt)"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["**Exercise 4:** Perform the curve evolution."]}, {"prompt_number": 44, "metadata": {}, "cell_type": "code", "outputs": [{"metadata": {}, "output_type": "display_data", "png": 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W45etRcayLBzH4aOVCpeybxpVAPgCXrsGxQsT5aEfnTxtD/37eK1VJZuANzPz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"text": [""]}], "input": ["run -i nt_solutions/segmentation_2_snakes_param/exo4"], "collapsed": false, "language": "python"}, {"level": 1, "metadata": {}, "cell_type": "heading", "source": ["Evolution of a Non-closed Curve"]}, {"metadata": {}, "cell_type": "markdown", "source": ["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 $f$."]}, {"prompt_number": 45, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["n = 256\n", "f = load_image(name, n)\n", "f = f[45:105, 60:120]\n", "n = f.shape[0]"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Display."]}, {"prompt_number": 46, "metadata": {}, "cell_type": "code", "outputs": [{"metadata": {}, "output_type": "display_data", "png": 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"text": [""]}], "input": ["imageplot(f)"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["**Exercise 5:** Compute an edge attracting criterion $W(x)>0$, that is small in area of strong\n", "gradient."]}, {"prompt_number": 47, "metadata": {}, "cell_type": "code", "outputs": [{"metadata": {}, "output_type": "display_data", "png": 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"text": [""]}], "input": ["run -i nt_solutions/segmentation_2_snakes_param/exo5"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Start and end points $x_0$ and $x_1$."]}, {"prompt_number": 48, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["x0 = 4 + 55j\n", "x1 = 53 + 4j"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Initial curve $\\ga_0$."]}, {"prompt_number": 49, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["p = 128\n", "t = transpose(linspace(0, 1, p))\n", "gamma0 = t*x1 + (1-t)*x0"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Initialize the evolution."]}, {"prompt_number": 50, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["gamma = gamma0"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Display."]}, {"prompt_number": 51, "metadata": {}, "cell_type": "code", "outputs": [{"metadata": {}, "output_type": "display_data", "png": 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CF5mj8uabMf6RR0K9ZcuWPPZGiGOHBnSRKSruuAMT/u3fQn23WbRaiCwjySVj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\nCCGEEEIIIYQQQgiRD/4fMaR/vF3vBWkAAAAASUVORK5CYII=\n", "text": [""]}], "input": ["clf\n", "imageplot(transpose(W))\n", "cplot(gamma,'r', 2)\n", "plot(real(gamma[0]), imag(gamma[0]), 'b.', markersize=20)\n", "plot(real(gamma[-1]), imag(gamma[-1]), 'b.', markersize=20);"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Re-sampling for non-periodic curves."]}, {"prompt_number": 52, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["curvabs = lambda gamma: concatenate( ([0], cumsum( 1e-5 + abs(gamma[:-1:]-gamma[1::]) ) ) )\n", "resample1 = lambda gamma,d: interpc(arange(0,p)/float(p-1), d/d[-1],gamma)\n", "resample = lambda gamma: resample1( gamma, curvabs(gamma) )"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Time step."]}, {"prompt_number": 53, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["dt = 1/10"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["Number of iterations."]}, {"prompt_number": 54, "metadata": {}, "cell_type": "code", "outputs": [], "input": ["Tmax = 2000*4/ 7\n", "niter = round(Tmax/ dt)"], "collapsed": false, "language": "python"}, {"metadata": {}, "cell_type": "markdown", "source": ["**Exercise 6:** Perform the curve evolution.\n", "Be careful to impose the boundary conditions at each step."]}, {"prompt_number": 55, "metadata": {}, "cell_type": "code", "outputs": [{"metadata": {}, "output_type": "display_data", "png": 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8Qpf85vG2WPi8vJxVdtKoVkRHc2rDBmrCw6+oz/lxceh1Oja38ck1oLKSuw8c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\nLN65E//KSl6bP5+C9u2hSVroVF3Ng/v2Ue/iwrP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LDIQFrrpxFy8vvPLuu4Zje2n+fJQF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\n", "text": [""]}], "input": ["run -i nt_solutions/segmentation_2_snakes_param/exo6"], "collapsed": false, "language": "python"}]}], "nbformat_minor": 0, "nbformat": 3}