https://github.com/ruqihuang/AdjointFmaps
Revision 702a3902f859cde5970deb97200347502ecb181a authored by ruqihuang on 24 July 2017, 21:09:41 UTC, committed by ruqihuang on 24 July 2017, 21:09:41 UTC
1 parent 6812206
Tip revision: 702a3902f859cde5970deb97200347502ecb181a authored by ruqihuang on 24 July 2017, 21:09:41 UTC
modify Change_of_basis_F9.m
modify Change_of_basis_F9.m
Tip revision: 702a390
Change_of_basis_F8.m
% Readme: we first select randomly 25 pairs of deformed spheres, and then
% recover the p2p maps from the ground-truth functional maps. A fixed set
% of random pairs and pre-computed result from the paper [RMC15] are loaded
% in line 19~20. (Unfortunately we lost the random pairs
% used in producing the result in the paper)
clear; close all; clc;
addpath(genpath('data'));
addpath(genpath('external'));
addpath(genpath('utils'));
% %% generate random pairs of deformed spheres.
% ra = randi(64, 50, 2);
% ra = unique(ra, 'rows');
% idx = find(ra(:, 1) - ra(:, 2) ~= 0);
% ra = ra(idx, :);
% t = randperm(33);
% ra = ra(t(1:25), :);
%% Pre-load random pairs and results from [RMC15]
load rand_sph.mat;
load cpd_results.mat;
%% Recovery
E1 = zeros(1922, 25);
E2 = E1;
E3 = E1;
for i = 1:25
test_shape1 = sprintf('deform_sph_%d.off', ra(i, 1));
test_shape2 = sprintf('deform_sph_%d.off', ra(i, 2));
S1 = read_off_shape(test_shape1);
S2 = read_off_shape(test_shape2);
% Number of basis functions
nk = 60;
% dimensionality of the functional map (nk x nk2)
nk2 = 20;
% Compute the LB eigenbasis
S1 = compute_laplacian_basis(S1, nk);
S2 = compute_laplacian_basis(S2, nk);
% Compute initial (slightly perturbed identity) map
P2 = 1:length(S1.evecs);
P1 = 1:length(S2.evecs);
C = S2.evecs'*S2.A*S1.evecs(P1, :);
C12 = C;
e = ones(length(S2.evecs), 1); e = S2.evecs'*S2.A*e;
k1_const = S1.evecs*C12'*e;
K = S1.evecs'*S1.A*diag(k1_const)*S1.evecs;
X12 = C12/K;
cvx_begin quiet
variable H(nk, nk) semidefinite
minimize( norm(X12 - H*C12, 'fro'))
cvx_end
[e,v] = eig(diag(S2.evals),H);
e = e*diag(1./sqrt(diag(e'*H*e)));
[v, order] = sort(diag(v));
e = e(:,order);
% Compute the functional map with respect to this new basis.
C2 = (S2.evecs*e)\S1.evecs(P1, 1:nk);
C2r = C2(1:nk,1:nk2);
% Covert to p2p map
[~, matches1] = icp_refine(S1.evecs, S2.evecs, C, 0);
[~, matches2] = icp_refine(S1.evecs,(S2.evecs*e),C2r,0);
error1 = eval_geodesic_error(S1, matches1, P1)/sqrt(6);
error2 = eval_geodesic_error(S1, M(:, i), P1)/sqrt(6);
error3 = eval_geodesic_error(S1, matches2, P1)/sqrt(6);
E1(:, i) = error1;
E2(:, i) = error2;
E3(:, i) = error3;
fprintf(sprintf('the %d-th pair done.\n', i));
end
%% Plot the results.
nr = length(reshape(E1, [], 1));
figure; plot(sort(reshape(E1, [], 1))*100, linspace(0, 1, nr)*100, 'k', 'LineWidth', 3);
hold on; plot(sort(reshape(E2, [], 1))*100, linspace(0, 1, nr)*100, 'b', 'LineWidth', 3);
hold on; plot(sort(reshape(E3, [], 1))*100, linspace(0, 1, nr)*100, 'r', 'LineWidth', 3);
ylabel('% of Correspondences', 'FontSize',25);
xlabel('% of Geodesic Error', 'FontSize',25);
ylim([80, 100]);
xlim([0, 8]);
leg = legend('NN-search', '[RMC15]', 'Our scheme' ,'Location', 'southeast');
set(leg, 'FontSize', 25);
% print('sphere_collection', '-r400', '-dpng');
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