{"nbformat_minor": 0, "worksheets": [{"cells": [{"source": ["Shape Retrieval with Geodesic Descriptors\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 numerical tour explores the use of geodesic distances within shapes\n", "to perform shape retrieval.\n", "\n", "\n", "This tour is mostly inspired from the following work:\n", "\n", "\n", "_Matching 2D and 3D Articulated Shapes using Eccentricity_,\n", "A. Ion, N. M. Artner, G. Peyre, W. G. Kropatsch and L. Cohen,\n", "Preprint Hal-00365019, January 2009."], "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_5_geodesic_descriptors')"]}, {"source": ["Geodesic Distances Within a Binary Shape\n", "----------------------------------------\n", "By restricting shortest path to lie within a shape, one create a geodesic\n", "metric that is different from the Euclidean one if the shape is not\n", "convex.\n", "\n", "\n", "A binary shape is represented as a binary image."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 3, "cell_type": "code", "language": "python", "metadata": {}, "input": ["n = 200;\n", "name = 'centaur1';\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": ["Display the shape."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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"output_type": "display_data"}], "prompt_number": 4, "cell_type": "code", "language": "python", "metadata": {}, "input": ["clf;\n", "imageplot(-M);"]}, {"source": ["Compute its boundary"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 5, "cell_type": "code", "language": "python", "metadata": {}, "input": ["bound = compute_shape_boundary(M);\n", "nbound = size(bound,2);"]}, {"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": 6, "cell_type": "code", "language": "python", "metadata": {}, "input": ["W = ones(n);\n", "L = zeros(n)-Inf; L(M==1) = +Inf;"]}, {"source": ["Initial point for the geodesic computation."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 7, "cell_type": "code", "language": "python", "metadata": {}, "input": ["start_points = [95; 20];"]}, {"source": ["Compute the geodesic distance without constraint using Fast Marching.\n", "It is simply the Euclidean distance."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 8, "cell_type": "code", "language": "python", "metadata": {}, "input": ["options.constraint_map = [];\n", "D0 = perform_fast_marching(W, start_points, options);\n", "D0(M==0) = Inf;"]}, {"source": ["Display Euclidean distance."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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d2RNVkjUSjwKAHGhpIXneh6gR/uLQnKpzzy3Ercf155VYvi58ytq4cIEPGgq7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\n", "output_type": "display_data"}], "prompt_number": 9, "cell_type": "code", "language": "python", "metadata": {}, "input": ["clf;\n", "options.display_levelsets = 1;\n", "options.pstart = start_points;\n", "options.nbr_levelsets = 30;\n", "display_shape_function(D0, options);"]}, {"source": ["Compute the geodesic distance with constraints using Fast Marching."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 10, "cell_type": "code", "language": "python", "metadata": {}, "input": ["options.constraint_map = L;\n", "D = perform_fast_marching(W, start_points, options);"]}, {"source": ["Display geodesic distance."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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SY36/+DpVL8omZb9M8HBDblcLvcxyoNRLXpz+SGTVoQMbJOpB9whWtXdBvWsh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\nAAAASUVORK5CYII=\n", "output_type": "display_data"}], "prompt_number": 11, "cell_type": "code", "language": "python", "metadata": {}, "input": ["clf;\n", "options.nbr_levelsets = 60;\n", "display_shape_function(D, options);"]}, {"source": ["__Exercise 1__\n", "\n", "Using |options.nb_iter_max| display the progression of the Fast\n", "Marching."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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fMssk3qRn7gq+vpvLAViRV+TzEvnMsX93w25HxS3IDdYRzEYmPZsr1tEki5Vc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\nAABJRU5ErkJggg==\n", "output_type": "display_data"}], "prompt_number": 12, "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo1()"]}, {"collapsed": false, "outputs": [], "prompt_number": 13, "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}, {"source": ["Compute a geodesic curve."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 14, "cell_type": "code", "language": "python", "metadata": {}, "input": ["end_points = [27;112];\n", "p = compute_geodesic(D,end_points);"]}, {"source": ["Display the path."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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kwKBfCy9qhjEJMAAiCTAAIgkwACIJMCowUQQDshciRSxcOx76hbc1IvymgQEQyV6IEODP\nrREVLwakgQEQSQODGGoW3NPAAIgkwACIJMCowP7rMCABBkAkAQZAJAEGQCQBxljMlkEZAgyASAKM\n4bTW9DAoQIABEEmAARBJgDEoA4mQToABEEmAARBJgAEQSYBRgRtlwYAEGACRBBgAkZqxFypZvjLe\nNx/SaWAARNLAKOtVG/Odhxo0MAAiaWAARNLAAIgkwACIJMAAiCTAAIgkwACIJMAAiCTAAIgkwACI\nJMAAiCTAAIgkwACIJMAAiCTAAIgkwACIJMAAiCTAAIgkwACIJMAAiCTAAIgkwACIJMAAiCTAAIgk\nwACIJMAAiCTAAIgkwACIJMAAiCTAAIgkwACIJMAAiCTAAIgkwACIJMAAiCTAAIgkwACIJMAAiCTA\nAIgkwACIJMAAiCTAAIgkwACIJMAAiCTAAIgkwACIJMAAiCTAAIgkwACIJMAAiCTAAIgkwACIJMAA\niCTAAIgkwACI9P9gU6YNouhfEwAAAABJRU5ErkJggg==\n", "output_type": "display_data"}], "prompt_number": 15, "cell_type": "code", "language": "python", "metadata": {}, "input": ["ms = 30; lw = 3;\n", "clf; hold on;\n", "imageplot(1-M);\n", "h = plot(end_points(2),end_points(1), '.b'); set(h, 'MarkerSize', ms);\n", "h = plot(start_points(2),start_points(1), '.r'); set(h, 'MarkerSize', ms);\n", "h = plot( p(2,:), p(1,:), 'g' ); set(h, 'LineWidth', lw);\n", "axis ij;"]}, {"source": ["__Exercise 2__\n", "\n", "Compute curves joining the start point to several points along the\n", "boundary."], "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": ["exo2()"]}, {"collapsed": false, "outputs": [], "prompt_number": 17, "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}, {"source": ["Local Geodesic Descriptors\n", "--------------------------\n", "In order to build shape signatures, we compute geodesic distance to all\n", "the points on the boundary. We then retrieve some caracteristics from\n", "these geodesic distance map.\n", "\n", "\n", "Select a uniform set of points on the boundary."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 18, "cell_type": "code", "language": "python", "metadata": {}, "input": ["nb_samples = 600;\n", "sel = round(linspace(1,nbound+1,nb_samples+1)); sel(end) = [];\n", "samples = bound(:,sel);"]}, {"source": ["__Exercise 3__\n", "\n", "Build a collection |E| of distance maps, so that |E(:,:,i)| is the\n", "geodesic distance to |samples(:,i)|."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 19, "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo3()"]}, {"collapsed": false, "outputs": [], "prompt_number": 20, "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}, {"source": ["normalize distances."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 21, "cell_type": "code", "language": "python", "metadata": {}, "input": ["E = E/mean(E(:));"]}, {"source": ["Display some locations"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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"output_type": "display_data"}], "prompt_number": 22, "cell_type": "code", "language": "python", "metadata": {}, "input": ["points = [[80;20] [95;112] [156;42]];\n", "col = {'r', 'g', 'b', 'k'};\n", "clf; hold on;\n", "imageplot(-M);\n", "for i=1:3\n", "    h = plot(points(2,i), points(1,i), [col{i} '.']);\n", "    set(h, 'MarkerSize', 40);\n", "end\n", "axis('ij');"]}, {"source": ["Display three different features at some locations."], "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": ["clf;\n", "col = {'r', 'g', 'b', 'k'};\n", "for i=1:3\n", "    subplot(3,1,i);    \n", "    d = E(points(1,i),points(2,i), :); \n", "    u = hist(d(:), 15); axis tight;\n", "    h = bar(u, col{i}); axis('tight');\n", "    set(gca, 'XTickLabel', []);\n", "end"]}, {"source": ["Global Geodesic Descriptors\n", "---------------------------\n", "One can retain a single statistic from the local descriptors, such as the\n", "min, max, mean or median values. The histogram of these values are the\n", "global descriptors.\n", "\n", "\n", "Compute several statistics."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 24, "cell_type": "code", "language": "python", "metadata": {}, "input": ["clear A;\n", "A{1} = max(E,[],3);\n", "A{2} = min(E,[],3);\n", "A{3} = mean(E,3);\n", "A{4} = median(E,3);\n", "titles = {'Max', 'Min', 'Mean', 'Median'};"]}, {"source": ["Display as images."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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pgvtNuhqHCVjdqBC8XifcYe/Wjz6ReyPimMi9AyuIL0dR8mf8Trmm2OTKwCEl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\nS2hghBBCasn/AIwsMjg2yRtMAAAAAElFTkSuQmCC\n", "output_type": "display_data"}], "prompt_number": 25, "cell_type": "code", "language": "python", "metadata": {}, "input": ["nbr = [20 5 30 30];\n", "options.pstart = [];\n", "clf;\n", "for i=1:4\n", "    subplot(2,2,i);\n", "    options.nbr_levelsets = nbr(i);\n", "    display_shape_function(A{i}, options);\n", "    title(titles{i});\n", "end\n", "colormap jet(256);"]}, {"source": ["Display histograms of the statistics."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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"output_type": "display_data"}], "prompt_number": 26, "cell_type": "code", "language": "python", "metadata": {}, "input": ["clf;\n", "for i=1:4\n", "    u = A{i}(M==1); u = u(u>0);\n", "    subplot(4,1,i);\n", "    hist(u, 40); axis('tight');\n", "    title(titles{i});\n", "end"]}, {"source": ["Shape Retrieval using Geodesic Historams.\n", "-----------------------------------------\n", "One can use the histograms of Eccentricity for shape retrieval."], "metadata": {}, "cell_type": "markdown"}, {"source": ["__Exercise 4__\n", "\n", "Load a library of shapes. Compute the different histograms for these\n", "shapes."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 27, "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo4()"]}, {"collapsed": false, "outputs": [], "prompt_number": 28, "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}, {"source": ["__Exercise 5__\n", "\n", "Perform the retrieval by comparing the histogram. Test diffetent metrics\n", "for the retrieval."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 29, "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo5()"]}, {"collapsed": false, "outputs": [], "prompt_number": 30, "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"}]}}}