matlab/shapes_6_medialaxis.ipynb

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"$\\newcommand{\\qandq}{\\quad\\text{and}\\quad}$\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 studies the computation of the medial axis using the Fast\n", "Marching."], "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/shapes_6_medialaxis')"]}, {"source": ["Voronoi Diagram\n", "---------------\n", "The Voronoi diagram is the segmentation of the image given by the region\n", "of influence of the set of starting points.\n", "\n", "\n", "Load a distance map."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 3, "cell_type": "code", "language": "python", "metadata": {}, "input": ["n = 200;\n", "W = load_image('mountain', n);\n", "W = rescale(W,.25,1);"]}, {"source": ["Select seed points."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 4, "cell_type": "code", "language": "python", "metadata": {}, "input": ["pstart = [[20;20] [120;100] [180;30] [60;160]];\n", "nbound = size(pstart,2);"]}, {"source": ["Display the map and the points."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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1QoMrnVaJLMSlooJl0elB6iYgxjBHtmhhP99SoAM8e4ULbKK75zuH9rEjtkTh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\nzT/RY44AAAAASUVORK5CYII=\n", "output_type": "display_data"}], "prompt_number": 5, "cell_type": "code", "language": "python", "metadata": {}, "input": ["ms = 20;\n", "clf; hold on;\n", "imageplot(W);\n", "h = plot(pstart(2,:), pstart(1,:), '.r'); set(h, 'MarkerSize', ms);"]}, {"source": ["Compute the geodesic distant to the whole set of points."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 6, "cell_type": "code", "language": "python", "metadata": {}, "input": ["[D,S,Q] = perform_fast_marching(W, pstart);"]}, {"source": ["Display the geodesic distance."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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Xt4iBXPkqvIZJHPi55uBGDcKEsJ8npJPyMbAgvLpLgUl/068bYFWQvsEf4/1Q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\n", "output_type": "display_data"}], "prompt_number": 7, "cell_type": "code", "language": "python", "metadata": {}, "input": ["clf; hold on;\n", "imageplot(convert_distance_color(D, W));\n", "h = plot(pstart(2,:), pstart(1,:), '.r'); set(h, 'MarkerSize', ms);"]}, {"source": ["Display the Voronoi Segmentation."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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"output_type": "display_data"}], "prompt_number": 8, "cell_type": "code", "language": "python", "metadata": {}, "input": ["clf; hold on;\n", "imageplot(Q);\n", "h = plot(pstart(2,:), pstart(1,:), '.r'); set(h, 'MarkerSize', ms);\n", "colormap jet(256);"]}, {"source": ["Medial Axis from the Voronoi Map\n", "--------------------------------\n", "The medial axis is difficult to extract from the singularity of the\n", "distance map. It is much more robust to extract it from the\n", "discontinuities in the Voronoi index map |Q|.\n", "\n", "\n", "Compute the derivative, the gradient."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 9, "cell_type": "code", "language": "python", "metadata": {}, "input": ["G = grad(Q);"]}, {"source": ["Take it modulo |nbound|."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 10, "cell_type": "code", "language": "python", "metadata": {}, "input": ["G(G<-nbound/2) = G(G<-nbound/2) + nbound;\n", "G(G>nbound/2) = G(G>nbound/2) - nbound;"]}, {"source": ["Compute the norm of the gadient."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 11, "cell_type": "code", "language": "python", "metadata": {}, "input": ["G = sqrt(sum(G.^2,3));"]}, {"source": ["Compute the medial axis by thresholding the gradient magnitude."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 12, "cell_type": "code", "language": "python", "metadata": {}, "input": ["B = 1 - (G>.1);"]}, {"source": ["Display."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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"output_type": "display_data"}], "prompt_number": 13, "cell_type": "code", "language": "python", "metadata": {}, "input": ["clf; hold on;\n", "imageplot(B);\n", "h = plot(pstart(2,:), pstart(1,:), '.r'); set(h, 'MarkerSize', ms);"]}, {"source": ["Skeleton of a Shape \n", "--------------------\n", "The sekeleton, also called Medial Axis, is the set of points where the\n", "geodesic distance is singular.\n", "\n", "\n", "A binary shape is represented as a binary image."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 14, "cell_type": "code", "language": "python", "metadata": {}, "input": ["n = 200;\n", "name = 'chicken';\n", "M = load_image(name,n);\n", "M = perform_blurring(M,5);\n", "M = double( rescale( M )>.5 );\n", "if M(1)==1 \n", "    M = 1-M;\n", "end"]}, {"source": ["Compute its boundary, that is going to be the set of starting points."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 15, "cell_type": "code", "language": "python", "metadata": {}, "input": ["pstart = compute_shape_boundary(M);\n", "nbound = size(pstart,2);"]}, {"source": ["Display the metric."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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"output_type": "display_data"}], "prompt_number": 16, "cell_type": "code", "language": "python", "metadata": {}, "input": ["lw = 2;\n", "clf; hold on;\n", "imageplot(-M);\n", "h = plot(pstart(2,:), pstart(1,:), 'r'); set(h, 'LineWidth', lw); axis ij;"]}, {"source": ["Parameters for the Fast Marching: constant speed |W|, but retricted using |L| to the\n", "inside of the shape."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 17, "cell_type": "code", "language": "python", "metadata": {}, "input": ["W = ones(n);\n", "L = zeros(n)-Inf; L(M==1) = +Inf;"]}, {"source": ["Compute the fast marching, from the boundary points."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 18, "cell_type": "code", "language": "python", "metadata": {}, "input": ["options.constraint_map = L;\n", "[D,S,Q] = perform_fast_marching(W, pstart, options);\n", "D(M==0) = Inf;"]}, {"source": ["Display the distance function to the boundary."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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"output_type": "display_data"}], "prompt_number": 19, "cell_type": "code", "language": "python", "metadata": {}, "input": ["clf;\n", "hold on;\n", "display_shape_function(D);\n", "h = plot(pstart(2,:), pstart(1,:), 'r'); set(h, 'LineWidth', lw); axis ij;"]}, {"source": ["Display the index of the closest boundary point."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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"output_type": "display_data"}], "prompt_number": 20, "cell_type": "code", "language": "python", "metadata": {}, "input": ["clf;\n", "hold on;\n", "display_shape_function(Q);\n", "h = plot(pstart(2,:), pstart(1,:), 'r'); set(h, 'LineWidth', lw); axis ij;"]}, {"source": ["__Exercise 1__\n", "\n", "Compute the norm of the gradient |G| modulo |nbound|. Be careful to remove the boundary\n", "of the shape from this indicator. Display the thresholded gradient map.\n", "radient\n", "ompute the norm of the gadient.\n", "emove the boundary to the skeletton."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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"output_type": "display_data"}], "prompt_number": 21, "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo1()"]}, {"collapsed": false, "outputs": [], "prompt_number": 22, "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}, {"source": ["__Exercise 2__\n", "\n", "Display the Skeleton obtained for different threshold values."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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"output_type": "display_data"}], "prompt_number": 23, "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo2()"]}, {"collapsed": false, "outputs": [], "prompt_number": 24, "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}, {"source": ["Skeletton\n", "---------"], "metadata": {}, "cell_type": "markdown"}], "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"}]}}}