https://github.com/ruqihuang/AdjointFmaps
Tip revision: d41efaa1636fb8cc0da8f09d89f4a1cae0172320 authored by ruqihuang on 24 August 2017, 07:39:27 UTC
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Tip revision: d41efaa
Adjoint_regularization_F10.m
% This code implements a basic version of the algorithm described in:
%
% Informative Descriptor Preservation via Commutativity for Shape Matching,
% Dorian Nogneng and Maks Ovsjanikov, Proc. Eurographics 2017
%
% To try it, simply run this file in MATLAB. This should produce
% a map (correspondence) between a pair of meshes from the FAUST dataset,
% and create an image that visualizes this correspondence.
%
% This code was written by Etienne Corman and modified by Maks Ovsjanikov.
%clear all; close all;
clear; close all;
addpath(genpath('data'));
addpath(genpath('external'));
addpath(genpath('utils'));
load Faust_without_forcing_diagnoality_ERGB.mat;
%% Load meshes and compute Laplacian eigendecomposition
% Number of basis vectors for computing the functional map.
% Larger is usually better (more accurate results) but somewhat slower.
numEigsSrc = 60;
numEigsTar = 60;
meshes = dir('data/FAUST/*.off');
rng('default');
rng(2);
tars = randperm(100);
epss1 = 500;
epss = 0.000000453999298;
allerrsA = [];
allerrsICPA = [];
allerrsNA = [];
allerrsICPNA = [];
meanerrs = [];
for k=1:1:length(meshes)
srcmesh = meshes(k).name;
tarmesh = meshes(tars(k)).name;
% [X, T] = readOff(['./Mesh/' srcmesh]);
Src = read_off_shape(['data/FAUST/' srcmesh]);
fprintf('%s vs %s\n',srcmesh,tarmesh);
%fprintf('reading the source shape...');tic;
Src = compute_laplacian_basis(Src, 200);
%fprintf('done (found %d vertices)\n',Src.nv);toc;
%fprintf('reading the target shape...');tic;
Tar = read_off_shape(['data/FAUST/' tarmesh]);
Tar = compute_laplacian_basis(Tar, 200);
%fprintf('done (found %d vertices)\n',Tar.nv);toc;
% a few landmark correspondences (to avoid symmetry flipping).
landmarks1 = (500:1000:3000)';
%landmarks1 = dijkstra_fps(Src,20);
landmarks2 = landmarks1;
landmarks = [landmarks1 landmarks2(:,1)];
SrcLaplaceBasis = Src.evecs; SrcEigenvalues = Src.evals;
TarLaplaceBasis = Tar.evecs; TarEigenvalues = Tar.evals;
Src.evecs = SrcLaplaceBasis(:,1:numEigsSrc); Src.evals = SrcEigenvalues(1:numEigsSrc);
Tar.evecs = TarLaplaceBasis(:,1:numEigsTar); Tar.evals = TarEigenvalues(1:numEigsTar);
%% Descriptors
fct_src = [];
% fprintf('Computing the descriptors...\n');tic;
fct_src = [fct_src, waveKernelSignature(SrcLaplaceBasis, SrcEigenvalues, Src.A, 200)];
fct_src = [fct_src, waveKernelMap(SrcLaplaceBasis, SrcEigenvalues, Src.A, 200, landmarks(:,1))];
fct_tar = [];
fct_tar = [fct_tar, waveKernelSignature(TarLaplaceBasis, TarEigenvalues, Tar.A, 200)];
fct_tar = [fct_tar, waveKernelMap(TarLaplaceBasis, TarEigenvalues, Tar.A, 200, landmarks(:,2))];
% Subsample descriptors (for faster computation). More descriptors is
% usually better, but can be slower.
fct_src = fct_src(:,1:40:end);
fct_tar = fct_tar(:,1:40:end);
% fprintf('done computing descriptors (%d on source and %d on target)\n',size(fct_src,2),size(fct_tar,2)); toc;
assert(size(fct_src,2)==size(fct_tar,2));
% Normalization
no = sqrt(diag(fct_src'*Src.A*fct_src))';
fct_src = fct_src ./ repmat(no, [Src.nv,1]);
fct_tar = fct_tar ./ repmat(no, [Tar.nv,1]);
% fprintf('Pre-computing the multiplication operators...');tic;
%% Multiplication Operators
numFct = size(fct_src,2);
OpSrc = cell(numFct,1);
OpTar = cell(numFct,1);
for i = 1:numFct
OpSrc{i} = Src.evecs'*Src.A*(repmat(fct_src(:,i), [1,numEigsSrc]).*Src.evecs);
OpTar{i} = Tar.evecs'*Tar.A*(repmat(fct_tar(:,i), [1,numEigsTar]).*Tar.evecs);
end
Fct_src = Src.evecs'*Src.A*fct_src;
Fct_tar = Tar.evecs'*Tar.A*fct_tar;
% fprintf('done\n');toc;
%% Fmap Computation
%fprintf('Optimizing the functional map...\n');tic;
Dlb = (repmat(Src.evals, [1,numEigsTar]) - repmat(Tar.evals', [numEigsSrc,1])).^2;
Dlb = Dlb/norm(Dlb, 'fro')^2;
constFct = sign(Src.evecs(1,1)*Tar.evecs(1,1))*[sqrt(sum(Tar.area)/sum(Src.area)); zeros(numEigsTar-1,1)];
Dlb2 = (repmat(Tar.evals, [1,numEigsSrc]) - repmat(Src.evals', [numEigsTar,1])).^2;
Dlb2 = Dlb2/norm(Dlb2, 'fro')^2;
constFct2 = sign(Tar.evecs(1,1)*Src.evecs(1,1))*[sqrt(sum(Src.area)/sum(Tar.area)); zeros(numEigsSrc-1,1)];
a = 1e-1; % Descriptors preservation
b = 0; % Commutativity with descriptors
c = 0; % Commutativity with Laplacian
funObj = @(F) deal( a*sum(sum((reshape(F, [numEigsTar,numEigsSrc])*Fct_src - Fct_tar).^2))/2 + b*sum(cell2mat(cellfun(@(X,Y) sum(sum((X*reshape(F, [numEigsTar,numEigsSrc]) - reshape(F, [numEigsTar,numEigsSrc])*Y).^2)), OpTar', OpSrc', 'UniformOutput', false)), 2)/2 + c*sum( (F.^2 .* Dlb(:))/2 ),...
a*vec((reshape(F, [numEigsTar,numEigsSrc])*Fct_src - Fct_tar)*Fct_src') + b*sum(cell2mat(cellfun(@(X,Y) vec(X'*(X*reshape(F, [numEigsTar,numEigsSrc]) - reshape(F, [numEigsTar,numEigsSrc])*Y) - (X*reshape(F, [numEigsTar,numEigsSrc]) - reshape(F, [numEigsTar,numEigsSrc])*Y)*Y'), OpTar', OpSrc', 'UniformOutput', false)), 2) + c*F.*Dlb(:));
funProj = @(F) [constFct; F(numEigsTar+1:end)];
funObj2 = @(F) deal( a*sum(sum((reshape(F, [numEigsTar,numEigsSrc])*Fct_tar - Fct_src).^2))/2 + b*sum(cell2mat(cellfun(@(X,Y) sum(sum((X*reshape(F, [numEigsTar,numEigsSrc]) - reshape(F, [numEigsTar,numEigsSrc])*Y).^2)), OpSrc', OpTar', 'UniformOutput', false)), 2)/2 + c*sum( (F.^2 .* Dlb2(:))/2 ),...
a*vec((reshape(F, [numEigsTar,numEigsSrc])*Fct_tar - Fct_src)*Fct_tar') + b*sum(cell2mat(cellfun(@(X,Y) vec(X'*(X*reshape(F, [numEigsTar,numEigsSrc]) - reshape(F, [numEigsTar,numEigsSrc])*Y) - (X*reshape(F, [numEigsTar,numEigsSrc]) - reshape(F, [numEigsTar,numEigsSrc])*Y)*Y'), OpSrc', OpTar', 'UniformOutput', false)), 2) + c*F.*Dlb2(:));
funProj2 = @(F) [constFct2; F(numEigsTar+1:end)];
funProj3 = @(F) [funProj(F(1:end/2)); funProj2(F(end/2+1:end))];
%%
F_lb = zeros(numEigsTar*numEigsSrc, 1); F_lb(1) = constFct(1);
F_lb2 = zeros(numEigsTar*numEigsSrc, 1); F_lb2(1) = constFct2(1);
%%
% Compute the optional functional map using a quasi-Newton method.
options.verbose = 0;
Finit = [F_lb; F_lb2];
lb1 = diag(Src.evals(1:numEigsSrc));
lb2 = diag(Tar.evals(1:numEigsTar));
F = minConf_PQN(@(F) funObj4(F, epss1, epss, numEigsSrc, numEigsTar, funObj, funObj2, lb1, lb2), Finit, funProj3, options);
C1 = reshape(F(1:end/2),numEigsTar, numEigsSrc);
C2 = reshape(F(end/2+1:end),numEigsTar, numEigsSrc);
%%
F_lb = C1;
[F_lb2, ~] = icp_refine(Src.evecs, Tar.evecs, C1, 5);
%% Evaluation
% Compute the p2p map
% fmap before ICP (for comparison)
pF_lb = knnsearch((F_lb*Src.evecs')', Tar.evecs);
% fmap after ICP
pF_lb2 = knnsearch((F_lb2*Src.evecs')', Tar.evecs);
map_Ad = pF_lb;
map_AdICP = pF_lb2;
fps_src = dijkstra_fps(Tar, 300);
% compute the errors
fprintf('errors with adjoint:\n');
errsA = dijkstra_pairs(Src,[pF_lb(fps_src) fps_src])/Src.sqrt_area;
fprintf('Mean map error (without ICP): %f\n',mean(errsA));
errsICPA = dijkstra_pairs(Src, [pF_lb2(fps_src) fps_src])/Src.sqrt_area;
fprintf('Mean map error (with ICP): %f\n', mean(errsICPA));
allerrsA = [allerrsA errsA];
allerrsICPA = [allerrsICPA errsICPA];
hold off;
nr = length(reshape(allerrsA,[],1));
plot(sort(reshape(allerrsA,[],1)),linspace(0,1,nr),'-g','LineWidth',2);
hold on;
plot(sort(reshape(allerrsICPA,[],1)),linspace(0,1,nr),'--g','LineWidth',2);
axis([0 0.25 0 1]);
pause(0.01);
end
FigHandle = figure('Position', [100, 100, 800, 600]);
hold on;
set(gca,'FontSize',20);
orangec = [1 0.7 0];
nr = length(reshape(allerrsCF,[],1));
title('FAUST (100 pairs) [without forcing diagonality]','FontSize',24,'FontWeight','b');
plot(sort(reshape(allerrsICPA,[],1)),linspace(0,1,nr),'--','LineWidth',3,'Color',orangec);
plot(sort(reshape(allerrsA,[],1)),linspace(0,1,nr),'-','LineWidth',3,'Color',orangec);
plot(sort(reshape(allerrsICPCF,[],1)),linspace(0,1,nr),'--','LineWidth',3,'Color',[0 0.7 0.2]);
plot(sort(reshape(allerrsCF,[],1)),linspace(0,1,nr),'-','LineWidth',3,'Color',[0 0.7 0.2]);
axis([0 0.25 0 1]);
xlabel('Geodesic Error','FontSize',24,'FontWeight','b');
ylabel('Fraction of Correspondences','FontSize',24,'FontWeight','b');
h_legend = legend('Adjoint Regularization + ICP','Adjoint Regularization',...
'[ERGB] + ICP','[ERGB]',...
'Location','southeast');
set(h_legend,'FontSize',22);
box on;