84 lines
3 KiB
Mathematica
84 lines
3 KiB
Mathematica
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% Random Shapes Demo
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%
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% Copyright (c) by Lorenzo Torresani, Stanford University
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%
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% A demo of Non-Rigid Structure From Motion on artificial random
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% shapes.
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%
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%
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% The 3D reconstruction technique is based on the following paper:
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%
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% Lorenzo Torresani, Aaron Hertzmann and Christoph Bregler,
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% Learning Non-Rigid 3D Shape from 2D Motion, NIPS 16, 2003
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% http://cs.stanford.edu/~ltorresa/projects/learning-nr-shape/
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%
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%
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% Function em_sfm implements the algorithm "EM-Gaussian" and "EM-LDS" described
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% in the paper
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%
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% I recommend that you try to compile the CMEX code for the function computeH:
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% type 'mex computeH.c' in the Matlab Command Window ('mex computeH.c -l matlb' under Unix)
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%
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T = 100; % number of frames
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J = 60; % number of points
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K = 5; % number of deformation shapes
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state = 1000; % random generator state
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% generates a random sequence of non-rigid 3D motion according to
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% the deformation model described by Eq (2) and (3)
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[P3_gt, S_bar_gt, V_gt, Z_gt, RO_gt, Tr_gt] = random_nr_motion(T, J, K, state);
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% 2D motion resulting from orthographic projection (Eq (1))
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p2_obs = P3_gt(1:2*T, :);
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% removes 40% of the data
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missingdata_rate = 0.4;
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if missingdata_rate>0,
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rp = randperm(T*J);
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ind_md = rp(1:round(T*J*missingdata_rate));
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MD = zeros(T, J);
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MD(ind_md) = 1;
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[i_md, j_md] = ind2sub([T J], ind_md);
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p2_obs(sub2ind([2*T J], [i_md i_md+T], [j_md j_md])) = 0; % set to 0 the values corresponding to missing data
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else
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MD = zeros(T, J);
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end
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% runs the non-rigid structure from motion algorithm with different number of deformation shapes
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max_em_iter = 50;
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use_lds = 0; % doesn't use LDS since the data was generated at random, w/o temporal smoothness
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tol = 0.001;
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k_values = [K-1:K+1];
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Zcoords_gt = P3_gt(2*T+1:3*T,:) - mean(P3_gt(2*T+1:3*T,:),2)*ones(1,J);
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Zdist = max(Zcoords_gt,[],2) - min(Zcoords_gt,[],2); % size of the 3D shape along the Z axis for each time frame
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ze = [];
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fprintf('3D reconstruction with %f missing data...\n', missingdata_rate*100);
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for kk=k_values,
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[P3, S_hat, V, RO, Tr, Z] = em_sfm(p2_obs, MD, kk, use_lds, tol, max_em_iter);
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% Compares it with ground truth.
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% Note that there are still 2 ambiguities that cannot be resolved:
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% 1. depth direction (i.e. the shape could be "flipped" along the Z axis) -> we test both possibilities
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% 2. Z translation -> we subtract the mean of the Z coords to evaluate reconstruction results
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Zcoords_em = P3(2*T+1:3*T,:) - mean(P3(2*T+1:3*T,:),2)*ones(1,J);
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Zerror1 = mean( mean(abs(Zcoords_em - Zcoords_gt), 2)./Zdist );
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Zerror2 = mean( mean(abs(-Zcoords_em - Zcoords_gt), 2)./Zdist );
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avg_zerror = 100*min(Zerror1, Zerror2);
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ze = [ze avg_zerror];
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hold off;
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plot(k_values(1:length(ze)), ze, '-o');
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title(['3D reconstruction with ' num2str(missingdata_rate*100) '% missing data'], 'fontweight', 'bold');
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xlabel('K (number of deformation shapes)');
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ylabel('% Z error');
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grid on;
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drawnow;
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end
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