{"nbformat_minor": 0, "worksheets": [{"cells": [{"source": ["Geodesic Bending Invariants for Shapes\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 the computation of bending invariants of shapes."], "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_1_bendinginv_2d')"]}, {"source": ["Bending Invariants\n", "------------------\n", "Bending invariants replace the position of the vertices in a shape $\\Ss$ (2-D or 3-D)\n", "by new positions that are insensitive to isometric deformation of the shape.\n", "This defines a bending invariant signature that can be used for surface\n", "matching.\n", "\n", "\n", "Bending invariant were introduced in [EladKim03](#biblio).\n", "A related method was developped for brain flattening in [SchwShWolf89](#biblio).\n", "This method is related to the Isomap algorithm for manifold learning\n", "[TenSolvLang03](#biblio).\n", "\n", "\n", "We assume that $Ss$ has some Riemannian metric, for instance coming\n", "from the embedding of a surface in 3-D Euclidian space, or by restriction of\n", "the Euclian 2-D space to a 2-D sub-domain (planar shape). One thus can\n", "compute the geodesic distance $d(x,x')$ between points $x,x' \\in\n", "\\Ss$.\n", "\n", "\n", "The bending invariant $\\tilde \\Ss$ of $\\Ss$ is defined as the set of\n", "points $Y = (y_i)_j \\subset \\RR^d$ that are optimized so that the Euclidean\n", "distance between points in $Y$ matches as closely the geodesic distance\n", "between points in $X$, i.e.\n", "$$ \\forall i, j, \\quad \\norm{y_i-y_j} \\approx d(x_i,x_j) $$\n", "\n", "\n", "Multi-dimensional scaling (MDS) is a class of method that aims at\n", "computing such a set of points $Y \\in \\RR^{d \\times N}$ in $\\RR^d$\n", "such that\n", "$$ \\forall i, j, \\quad \\norm{y_i-y_j} \\approx \\de_{i,j} $$\n", "where $\\de \\in \\RR^{N \\times N}$ is a input data matrix.\n", "For a detailed overview of MDS, we refer to the book [BorgGroe97](#biblio)\n", "\n", "\n", "In this tour, we apply two specific MDS algorithms (strain and stress\n", "minimization) with input $\\de_{i,j} = d(x_i,x_j)$.\n", "\n", "2-D Shapes\n", "----------\n", "We consider here the case where $\\Ss$ is a sub-domain of $\\RR^2$.\n", "\n", "\n", "A binary shape $\\Ss$ is represented as a binary image $S \\in \\RR^Q$\n", "of $Q=q \\times q$ pixels."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 3, "cell_type": "code", "language": "python", "metadata": {}, "input": ["clear options;\n", "q = 400;\n", "name = 'centaur1';\n", "S = load_image(name,q);\n", "S = perform_blurring(S,5);\n", "S = double( rescale( S )>.5 );\n", "if S(1)==1 \n", " S = 1-S;\n", "end"]}, {"source": ["Compute its boundary $b = (b_i)_{i=1}^L \\in \\RR^{2 \\times L}$."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 4, "cell_type": "code", "language": "python", "metadata": {}, "input": ["b = compute_shape_boundary(S);\n", "L = size(b,2);"]}, {"source": ["Display the shape."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": 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"output_type": "display_data"}], "prompt_number": 5, "cell_type": "code", "language": "python", "metadata": {}, "input": ["lw = 2;\n", "clf; hold on;\n", "imageplot(-S);\n", "plot(b(2,:), b(1,:), 'r', 'LineWidth', lw); axis ij;"]}, {"source": ["Geodesic Distance\n", "-----------------\n", "We consider the geodesic distance obtained by contraining the shortest\n", "curve to be inside $\\Ss$\n", "$$ d(x,x') = \\umin{ \\ga } \\int_0^1 \\abs{\\ga'(t)} d t, $$\n", "where $\\ga$ should satisfy\n", "$$ \\ga(0)=x, \\quad \\ga(1)=x' \\qandq \\forall t \\in [0,1], \\: \\ga(t) \\in \\Ss. $$\n", "\n", "\n", "The geodesic distance map $U(x) = d(x,x_0)$ to a starting point $x_0$\n", "can be computed in $O(q^2 \\log(q))$ operations on a grid of $q \\times\n", "q$ points using the Fast Marching algorithm.\n", "\n", "\n", "\n", "Design a constraint map for the Fast-Marching, to enforce the propagation\n", "inside the shape."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 6, "cell_type": "code", "language": "python", "metadata": {}, "input": ["S1 = perform_convolution(S, ones(3)/9)<.01; S1=double(S1==0);\n", "C = zeros(q)-Inf; C(S1==1) = +Inf;\n", "options.constraint_map = C;"]}, {"source": ["Shortcut to compute the geodesic distance to some point $x$."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 7, "cell_type": "code", "language": "python", "metadata": {}, "input": ["geod = @(x)perform_fast_marching(ones(q), x, options);"]}, {"source": ["Compute the geodesic distance to a point $x$"], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 8, "cell_type": "code", "language": "python", "metadata": {}, "input": ["x = [263; 55];\n", "options.nb_iter_max = Inf;\n", "U = geod(x);"]}, {"source": ["Display the distance and geodesic curves."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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iecrJLkTVc+i9rbhvcHe63D5U9pJnmrc2Ar7JRjstmRnsQiSTxW6q8pm49z69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\nCKmS/w+MYT4SLxWu5QAAAABJRU5ErkJggg==\n", "output_type": "display_data"}], "prompt_number": 9, "cell_type": "code", "language": "python", "metadata": {}, "input": ["clf;\n", "options.display_levelsets = 1;\n", "options.pstart = x;\n", "options.nbr_levelsets = 60;\n", "U(S==0) = Inf;\n", "display_shape_function(U, options);"]}, {"source": ["__Exercise 1__\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": 10, "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo1()"]}, {"collapsed": false, "outputs": [], "prompt_number": 11, "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}, {"source": ["Geodesic Distance Matrix\n", "------------------------\n", "We define a set $X = (x_i)_{i=1}^n \\in \\RR^{2 \\times N} \\subset \\Ss$\n", "of sampling points.\n", "\n", "\n", "Total number $N$ of sampling points."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 12, "cell_type": "code", "language": "python", "metadata": {}, "input": ["N = 1000;"]}, {"source": ["The sampling is made of $N_0$ points on the boundary $b$,\n", "and $N-N_0$ points inside the shape $\\Ss$.\n", "\n", "\n", "Number of points on the boundary."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 13, "cell_type": "code", "language": "python", "metadata": {}, "input": ["N0 = round(.4*N);"]}, {"source": ["Sampling on the boundary."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 14, "cell_type": "code", "language": "python", "metadata": {}, "input": ["I = round(linspace(1,L+1,N0+1));\n", "X = round(b(:,I(1:end-1)));"]}, {"source": ["Add $N-N_0$ points inside the shape."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 15, "cell_type": "code", "language": "python", "metadata": {}, "input": ["[y,x] = meshgrid(1:q,1:q);\n", "I = find(S==1);\n", "I = I(randperm(length(I))); I = I(1:N-N0);\n", "X(:,end+1:N) = [x(I),y(I)]';"]}, {"source": ["Display the sampling points."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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Fy/+qJGvdbnd4btjiL4r1mZvU3/SH26wgQBbifm76s2+crS4dJCQvfC7/3aB+\nYxa0hvPPx54oxFU7NjjJi+JAiFeIUAPDLaKZhKrjqA51i1lnQV9Ysys8vU+6//76VpRWntmlZ2oe\nwVa8ZnjfI3V3IEQf2NYyuYjd10PLkFjlaN+RQcEy4SCFVBEhD7B1zO9QW+jDf7PXHtPvXkSLzdsr\nF2wxPPn3bRFG0YS4Mefi2oCFEkE5pYWycTL72XSL0fDkdLRyU0Q8kmpWbZ98/vEDCrcXyOzEvDue\nZFuMiV5I0YS4q2DWjDmJiPp+eDElvbof8ys05VXNIhyapnH1OOyU1+P5kMr5XP4Ws3JacA9qYFuq\n3bWrc60tpb87jsP778DqsU2XagY/L978UawOdtcRH3WNEC55MFlrHY47hO2NAIbjOD7tP2PFgZAH\nEQaYb4H+t0Xv+/qWstoi6LV5sCkAa7abJtBnOthK01j8vR7E+J+57kDaIwj8CkkcuyrFqr7rIRn0\n2rqWUgxrWpVylLG8gD5Tv2lDn5dyDa3Ri+/8kyxPs5I/zEkbCscL+uz18M7ThUcQwLY2LQsxN2tD\nXwzTR5fSGmTVYcX6ccetqyqsxcIfYNPkUv+ezOkJS7c1cyswjiQO3KKjXPGKRjwh92/i4LDqAspt\nddRE7YqP9LYJ4y9nlVSOvRHAduXckbbJbFwQaI48GnE8sLF9zzMwEUkcW4pahP4yBUZK1UI//3eD\n2Y8UMtwOcSBX+JYL/im53GPNiOk0vzG7qmiZRSTXRnq88StPBmlyEXdFH9h+5qZvfNcq3WAsnbHp\ne+El0xQJfUv6Dqqq7qHH+q1Pzm74Of389LMOszCF1WonFr0IYFvKxrBHJpE6cp3w7joniBAqRgJY\n1GHWGsDSNVSXSVfrD8tFreJeOf9emXuMwdRSxfXaPasYQB8YblQPMM6dpV0pP+KO5qGmHq9zH1x5\nJxs2elt2wxt8j/Hf8zm5iJW1rHs+IaMPbEvB2OH7qOeVKg4wmqhawkXdaUKvWNPu5bvoVumz+W3c\n+J7YVc4nWhHA9vOZcePWP/rBlXdkZ5RoZmzq6c3aUEdF5+bQEufTYzMEsM0EbTLf/vZ5KYiaqHN5\nt3G7E0spOUY68elRzpOspibalvu+pMO8s3EvM/IMmyGJYzNz0ze+a20oOzLDzu5sRcweW9OcHSOz\ndeQ/Zf2P7vN9VdI1pxxmU1iyfmLRiAC2mdty6JVLSjNXKbK0O7dyNaVZUrPO29PzfkL3Nc0MY8qr\na4Fzi0Y0IWKYc8K4403scuy6WHIdoH5jy9531USvLRHANnBhTSAAAAwBSURBVJPNP5w3d/jTH8+5\nu/qllM7c8TfkzXZXTXKpPPHbpXB9nmMbmm6mipUwDmwzQe/Fm5uzXDJXk2YQcfjZkpGBXNEOpCFq\nfM1QurZjuu//L76qMR01sG18fvt/Rw3/4kdrJWPt8+/cyXCM83fB3IvRu7Jo/RrKqoaQ+rEI77Op\nm/pfGH0bLUUm4tXOqIFhzB2tN4oVlibvaApI4QMhCyOq0nVMSbVIIds0Z9gdNaHPxbbsjwM0ogaG\nYZ+f5MpipXUc2K9Kf588yC6THTEWVddGhr69RRC90pAf/Ya4q36vnFkK26AGhjHBfcUayIW4WKuT\nKz2zNG0imiOxVF2zGrrKKiPk5s76eL0kzkvucj0sd4YhYxzYZmbNshqt7e+Z4hPSODBx5eFWsuOI\nK8dTHjQdruS7uLy27g/a/XNrHf71fWnSIYs70HBdYSHUwDZj6A+7XA87I1ZPK1WyWk0Xmr7a90wF\n8VEjjYETrzdy5ZGgDwyWPD/ToAuaqrLv7kbu7Lz3hPzdPW7L044sAhgGPFufu7XYyqbIVwecNb1u\nUnulx52Di6fvSWHKstWqvFCjCRFjvG+ayfcx+qa8pu6unrLSULNt6tpw1zBt8dzBxUH+4RuvNvwI\nAQyPapvT9q/JSBcgM5ncpa3oelOyfWM9pefSt2B+QiH/sIizvQ2aEDHAuXMm31v54J9m4X+EKKW4\nBVp2HFjTZBxfr6ykajWO8/s96xNOQo0Ahsmagk3FJ0A2bT1eww34hR+Z+aVn1n4dXZa8X8hVJYat\njwCGXknDjsZ3mobqz+TCu/KGZo6nnlgc223Uaq9k+yh1c8qxf1ayReIM1OgDwxylCdp/XLJUS8+z\nP+xvybGf7YXpZs1Gr6vWb9NFc0r1nQdFCskZMhc50VCjBoZeivLojuilWuffvulTRcQltW1Wwp4Y\nVQ7nPUc13KaX3aj//M9kHBsigGFA0r0/M2IlPR/nr+xSyfR9a17/R3ZzDUWj6Z6YXOeTD2JG1nnA\nczpBRemkYt+r0fSZhw4BDJO5qBxJ3v2SfyN/bpzhcmVi2lY55/f2eU+y6oJTNmdcFMmy39TYBtpW\nE0dWYtjqCGAY0Jgi+I8mSORunCFUvCbTFXxhNPVv6PC7Q/BNCS14wgKXVfXtwEe1LTfTDUYMWxoB\nDL26bs70TUFUrLlj/c/LtmIFb7989xWSO4H16D4PyaUS5evf0nwNIwhg6NKbQ19ag7Sp5IFiS6pm\nQOnj4p58Fyw9VTdFLummw/ZihS9fCd71K9gEAQx38dd/LZ8sLh4Gs/Q3ePXjI4Q56S8bV9YyzZKP\navKpV5zDdItBhZE7sCyOAIYutckRpqw/mwkSDji7cfaHdI8e2cobXb/r6jyWM09U72+Rf1fOOaEw\nYWxRDGRGr5aZdv9oh5p+8g9/Sf3jPTvn72rCQJKclszXelPVp2W1y34XCBDA8ChX/QlfvnGG/6zh\nIYXicvcZH5LT4rMnalZDbjl2no26W38de6MJEQM+s+Rl2/Fc4bG8wvBZtsde3tAznfalsW6r5R+W\nhIeWTnry4IH74GfN/FFoeD2nvTMTECnUTv4UMyzkGliueerQl0d3XMyFXarsyPcRf1/zlNsPKw25\nfAuLIoChS6Eoycab/O/i0oWXm7xVqHWp1jku13hVkukQwizyPd6yC3D+10UTIp7QkCuYu3FGqaXu\nhdMuUFje6xxgR1gCAQydbi4+hEmDpBj1bKGW7f/Ltav+Pqyu7/zqo2uAOLc0mhAxpJRGX7+qshee\n4uZP0lYeaUIspb3VMwj4WwOmIo0evcSKRTYDvok8N+5DXV+5TXjxwIlRwGNoQkQXcSbfSo9XqQOj\nFhjKE0w92EZX25YY1WlLBGYigKGdOJOvMGCrojw9Vf86n6Ia9PY34JeZjYBJCGCYKRvMGnIFcymI\n2UnHf2Zgdr7LgRPDgGEEMLRrmcm3ox4mTW+R3ZmHkyNymysNfTufvrbuCNhFAEOXXFWp9bPF96/p\n6aWlnWJVd1FEzSjvn/R6YDqyENHLeyd2hkULa1ermew8XPhNuele2Rn2XcIdB+n1QCdqYJhDznof\nWW2pdP/UAd9Rj/kMqBR2+B07CqyDGhh6Oeev1aMJ9Yi+yXx/VQ8T75KVWfzGXQF2RABDF3Ec2Fdr\nXNn2HvDnUdOcCKjRhIh2+hjTEY2iG9gHN3z6rrV5pU8r3SMtRXo90I0AhnZNtYThGPbvtXN9wf/H\nb3MRQ4W8RKE/zJFeD4whgGHYWXZnC/HZ0SWMZP8CwHumtxAPVjWh/kElDNAigKFLGLTOV6IHD+zF\nY1vSq1UfVWkvL4nHwLtxOxW8leL+8blY8YLrOdzzclpKPcHyDccCvBgBDK93DQDSjVpeeDHXbjpD\nAAO6kUaPhRic2EKYtvg4TB4R8Bj6wGBPmKTu0pwII71H8l5e0uuNHBHwMAIYLIna3AxUTNSVp9Jt\n1f4hhgEJAhheL4gBaTT48e3BNLpu+EK8AqoIYLBggU6gBQ4BeBkCGJbyb2KO1ze4pfmH6R7H3XsM\nDgOuSKOHHUHxnR0KFkeFN1/buWNJvXSgG/AO1MCwDjOJD8mNQLM9eUQqQEYAgx3eH96fE1gU0+jN\nCiMZ0QuoIoDBGGNp9F1WPS5gLgIYlvbOxIeuxPp/3nlEwC8QwIAfGUnHIIYBBDBYF/WE5bvEXlvc\n62LYSv18wERM5gtrzkL/E5Z8cpvm4kfeTTM4DMCJGhhWYLjc/+sP8/5oHZL52mol8BQGMsOmpPiu\n3JfkeH09TDyikJnB2sDNqIHBpmvBXY9eh7EqSzjcLRzmbGawNnA/AhjM+sSwqKy3iroU0IgmRJjn\nnFPfdOv1V3trjer9RwTchixEmJcW4Wk6nxnlqfTPiub11WBhghk2QwCDZeX6SvSGt3CPFQBN6APD\n+vzxCXVmY5gLHkjHwERT2AkBDGaJTW2tn3qRkWkSowfA0ghgMCvJpF9nyqXyIAEtYhg2QACDZddM\n+n246+PdDh/4QwCDcZ9bXAq+C4zcx+R3sntcqXEaPEygFVmIMC4YBJYtzf2noLc05HG8AZD0emyA\nAAbLagW9D/7/N97ZRGkuJv2nMxdbOCRgPpoQsQ6veWowu0Ge6ZHohW0RwGBZX7aeiRh23maFEAUU\n0IQIvFjupp2lnI7QdxkTTaZAFybzxQpcIZXD5I3BTuU7hNWnf7RyjMAAmhCxAl947NJ0c7Mlezr2\ny+Xe+rxkoZkUGEMAwy7cYS16JXubrXiV3iKGYXkEMGzBagriXwwLUjmiuzOH4wTynwXWRQDD4uJS\n3mgMA5AgCxHraEijNx4V/uVeRcHY+EEBraiBwb4g1xzAPghgMO5aC1HFMIs1lXCfz8fZF4FtMA4M\nxl0DWGk+3+AJFzywCGpgME4RkL6jpohewEKogWEJTpVcSFUMWAk1MKygOXoBsI8ABvuCiRCbPjV9\nRwA8iQAG49Q59HG8ogkRMI4ABsuSHPqGoOQclTDANAIYViPEMJfWw4hhgFkEMFjW3gxIuyGwDAIY\njKMrC9gVAQz2EcOALRHAYF/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"output_type": "display_data"}], "prompt_number": 16, "cell_type": "code", "language": "python", "metadata": {}, "input": ["clf; hold on;\n", "imageplot(1-S);\n", "plot(X(2,:), X(1,:), 'r.', 'MarkerSize', 15);\n", "axis('ij');"]}, {"source": ["The geodesic distance matrix $\\de \\in \\RR^{N \\times N}$ is defined as\n", "$$ \\forall i,j=1,\\ldots,N, \\quad\n", " \\de_{i,j} = d(x_i,x_j). $$"], "metadata": {}, "cell_type": "markdown"}, {"source": ["__Exercise 2__\n", "\n", "Compute the geodesic distance matrix $\\de$."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [], "prompt_number": 17, "cell_type": "code", "language": "python", "metadata": {}, "input": ["exo2()"]}, {"collapsed": false, "outputs": [], "prompt_number": 18, "cell_type": "code", "language": "python", "metadata": {}, "input": ["%% Insert your code here."]}, {"source": ["Display the geodesic matrix for $1 \\leq i,j \\leq N_0$\n", "(points along the boundary $b$)."], "metadata": {}, "cell_type": "markdown"}, {"collapsed": false, "outputs": [{"metadata": {}, "png": 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coOtC9W4fhRG7yK+KL41kK1JF2oC9hzWfCW1HzNYQLy8zUvZGrecATFVVPfowl16FTGVU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\nuMX/NrWu6JVQuitHCSk7pNRKKVcjs9v/kMlLUW/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2XPKQLAB7rrAJUQFMRe1Ozhcguidk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\nsJ6gbiIMN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GEXyozFW3tGSRzpaYA0HQK7PaW0ynnoj8722sA/j8ZnDqrAZmGb0YvVpeO+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"output_type": "display_data"}], "prompt_number": 19, "cell_type": "code", "language": "python", "metadata": {}, "input": ["clf;\n", "imageplot(delta(1:N0,1:N0));\n", "colormap(jet(256));"]}, {"source": ["Bending Invariant with Strain Minimization\n", "------------------------------------------\n", "The goal is to compute a set of points $Y = (y_i)_{i=1}^N$ in\n", "$\\RR^d$, (here we use $d=2$) stored in a matrix $Y \\in \\RR^{d \\times N}$\n", "such that\n", "$$ \\forall i, j, \\quad D^2(Y)_{i,j} \\approx \\de_{i,j}^2\n", " \\qwhereq D^2(Y)_{i,j} = \\norm{y_i-y_j}^2. $$\n", "\n", "\n", "This can be achieved by minimzing a $L^2$ loss\n", "$$ \\umin{Y} \\norm{ D^2(Y)-\\de^2 }^2 =\n", " \\sum_{i\n", "\n", "\n", "* [EladKim03] A. Elad and R. Kimmel, [On bending invariant signatures for surfaces][1], IEEE Transactions onPattern Analysis and Machine Intelligence, Vol. 25(10), p. 1285-1295, 2003.\n", "* [SchwShWolf89] E.L. Schwartz and A. Shaw and E. Wolfson, [A Numerical Solution to the Generalized Mapmaker's Problem: Flattening Nonconvex Polyhedral Surfaces][2], IEEE Transactions on Pattern Analysis and Machine Intelligence, 11(9), p. 1005-1008, 1989.\n", "* [TenSolvLang03] J. B. Tenenbaum, V. de Silva and J. C. Langford, [A Global Geometric Framework for Nonlinear Dimensionality Reduction][3], Science 290 (5500): 2319-2323, 22 December 2000\n", "* [Kruskal64] J. B. Kruskal, [Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis][4], Psychometrika 29 (1): 1?27, 1964.\n", "* [Leeuw77] J. de Leeuw, [Applications of convex analysis to multidimensional scaling][5], in Recent developments in statistics, pp. 133?145, 1977\n", "* [BorgGroe97] I. Borg and P. Groenen, [Modern Multidimensional Scaling: theory and applications][6], New York: Springer-Verlag, 1997.\n", "\n", "[1]:http://dx.doi.org/10.1109/TPAMI.2003.1233902\n", "[2]:http://dx.doi.org/10.1109/34.35506\n", "[3]:http://dx.doi.org/10.1126/science.290.5500.2319\n", "[4]:http://dx.doi.org/10.1007/BF02289565\n", "[5]:http://statistics.ucla.edu/preprints/uclastat-preprint-2005:35\n", "[6]:http://www.springeronline.com/0-387-25150-2"], "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"}]}}}