流形学习（LLE）源代码（matlab编写）

% Course n?1 for "A Matlab Tour of Fast Marching Methods" % first set up path path(path, 'toolbox_fast_marching/'); path(path, 'toolbox_fast_marching/data/'); path(path, 'toolbox_fast_marching/toolbox/'); rep = 'images/raw/'; if ~exist(rep) mkdir(rep); end test_2d = 0; test_3d = 0; test_sampling = 0; test_heuristic = 0; test_voronoi = 0; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 2D shortest paths if test_2d n = 200; name = 'road2'; name = 'mountain'; name = 'cavern'; W = imread([name '.png']); W = rescale( double(W) ); W = W + 0.01; [start_points,end_points] = pick_start_end_point(W); % options.nb_iter_max = Inf; % options.Tmax = sum(size(W)); options.end_points = end_points; disp('Performing front propagation.'); [D,S] = perform_fast_marching_2d(W, start_points, options); disp('Extracting path.'); p = extract_path_2d(D,end_points, options); clf; D1 = D; I = find(isinf(D)); J = find(~isinf(D)); D1(I) = max(D(J)); imagesc(D1'); axis image; axis off; axis xy; colormap jet(256); saveas(gcf, [rep name '-dist-function.jpg'], 'jpg'); clf; plot_fast_marching_2d(W,S,p,start_points,end_points); colormap jet(256); saveas(gcf, [rep name '-shortest-path-2d.jpg'], 'jpg'); clf; contour(D1',50); axis image; axis off; axis xy; colormap jet(256); saveas(gcf, [rep name '-dist-function-contour.jpg'], 'jpg'); % essayer avec d'autres images : 'road2.png' 'moutain.png' % essayer avec d'autres type d'?nergies (gradient filtr?s). end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Voronoi cels if test_voronoi n = 300; name = 'constant'; name = 'mountain'; [M,W] = load_potential_map(name, n); if strcmp(name, 'mountain') W = rescale(W,0.05,1); end m = 50; % number of center points if ~exist('start_points') || size(start_points,2)~=m start_points = floor( rand(2,m)*(n-1) ) +1; start_points = unique(start_points', 'rows')'; end disp('Performing front propagation.'); [D,Z,Q] = perform_fast_marching_2d(W, start_points); clf; hold on; imagesc(D'); axis image; axis off; plot(start_points(1,:), start_points(2,:), '.'); hold off; axis xy; colormap gray(256); saveas(gcf, [rep name '-voronoi-dist.jpg'], 'jpg'); faces = compute_voronoi_triangulation(Q); hold on; sel = randperm(max(Q(:))); imagesc(sel(Q)'); axis image; axis off; plot(start_points(1,:), start_points(2,:), 'b.', 'MarkerSize', 20); plot_edges(compute_edges(faces), start_points, 'k'); hold off; axis tight; axis image; axis off; colormap jet(256); saveas(gcf, [rep name '-voronoi-triangulation.jpg'], 'jpg'); end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 3D shortest paths if test_3d n = 60; % gaussian weight (path will avoid center of the cube) x = -1:2/(n-1):1; [X,Y,Z] = meshgrid(x,x,x); sigma = 0.3; W = 1./(1 + exp( -(X.^2+Y.^2+Z.^2)/sigma^2 ) ); k = 18; start_points = [n-k;k;k]; end_points = [k;n-k;n-k]; options.nb_iter_max = Inf; options.end_points = end_points; [D,S] = perform_fast_marching_3d(W, start_points, options); p = extract_path_3d(D,end_points); % draw the path plot_fast_marching_3d(D,S,p,start_points,end_points); saveas(gcf, [rep 'shortest-path-3d.jpg'], 'jpg'); end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % farthest point sampling if test_sampling % test for farthest point sampling n = 300; name = 'bump'; name = 'gaussian'; name = 'road2'; name = 'mountain'; [M,W] = load_potential_map(name, n); % plot sampling location i = 0; for nbr_landmarks = 50:50:300 i = i+1; disp('Perform farthest point sampling'); landmark = farthest_point_sampling( W, [], nbr_landmarks ); clf; hold on; imagesc(M'); plot(landmark(1,:), landmark(2,:), 'b.', 'MarkerSize', 20); hold off; axis tight; axis image; axis off; colormap gray(256); saveas(gcf, [rep 'farthest-sampling-' num2str(nbr_landmarks) '.jpg'], 'jpg'); [D,Z,Q] = perform_fast_marching_2d(W, landmark); faces = compute_voronoi_triangulation(Q); hold on; imagesc(M'); axis image; axis off; plot(landmark(1,:), landmark(2,:), 'b.', 'MarkerSize', 20); plot_edges(compute_edges(faces), landmark, 'k'); hold off; axis tight; axis image; axis off; colormap gray(256); saveas(gcf, [rep name '-sampling-triangulation-' num2str(nbr_landmarks) '.jpg'], 'jpg'); end end %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % heuristic computation if test_heuristic n = 200; name = 'cavern'; name = 'mountain'; name = 'road2'; weight = 0.9; W = imread([name '.png']); W = rescale( double(W) ); W = W + 0.01; % [start_points,end_points] = pick_start_end_point(W); % compute heuristic [H,S] = perform_fast_marching_2d(W, end_points); % options.nb_iter_max = Inf; options.end_points = end_points; disp('Performing front propagation.'); [D,S] = perform_fast_marching_2d(W, start_points, options, H*weight); disp('Extracting path.'); p = extract_path_2d(D,end_points, options); clf; plot_fast_marching_2d(W,S,p,start_points,end_points); colormap jet(256); saveas(gcf, [rep name '-heuristic' num2str(weight) '.jpg'], 'jpg'); end