61 lines
2.3 KiB
Mathematica
61 lines
2.3 KiB
Mathematica
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% Shark 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 shark sequence
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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 algorithms "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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% loads the matrix P3_gt containing the ground thruth data: P3_gt([t t+T t+2*T],:) contains the 3D coordinates of the J points at time t
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% (T is the number of frames, J is the number of points)
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load('jaws.mat');
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[T, J] = size(P3_gt); T = T/3;
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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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% runs the non-rigid structure from motion algorithm
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use_lds = 1;
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max_em_iter = 60;
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tol = 0.0001;
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K = 2; % number of deformation shapes
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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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MD = zeros(T,J);
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[P3, S_hat, V, RO, Tr, Z] = em_sfm(p2_obs, MD, K, 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 unresolvable ambiguities:
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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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if Zerror2 < Zerror1,
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avg_zerror = 100*Zerror2;
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P3(2*T+1:3*T,:) = -(P3(2*T+1:3*T,:) - mean(P3(2*T+1:3*T,:),2)*ones(1,J));
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else
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avg_zerror = 100*Zerror1;
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P3(2*T+1:3*T,:) = P3(2*T+1:3*T,:) - mean(P3(2*T+1:3*T,:),2)*ones(1,J);
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end
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fprintf('Average reconstruction error in Z: %f%%\n', avg_zerror);
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vis_reconstruction(P3_gt, P3);
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