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test_dense_search.m
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test_dense_search.m
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% Main script
% Example to solve different multi-modal registration problems
% with the method proposed in [1], and the previous approaches in [2,3]
%
% Related work:
% [1] Briales, J., & Gonzalez-Jimenez, J. "Convex Global 3D Registration with Lagrangian Duality." In CVPR 2017
% [2] Olsson, C., & Eriksson, A. "Solving quadratically constrained geometrical problems using lagrangian duality." In ICPR 2008.
% [3] Olsson, C., Kahl, F., & Oskarsson, M. "Branch-and-Bound Methods for Euclidean Registration Problems." In TPAMI 2009.
clear all clc;
% choose the problem to solve
problemType = 'random';
% problemType = 'SpaceStation';
% problemType = 'RubikCube';
% Problem generation
% -------------------------------------------------------------------------
switch problemType
case 'random'
problem.sim = 1;
% create random problem
% number of correspondences: [nr points, nr lines, nr planes]
problem.m = [0 0 10]; % [0 0 7]; [2 4 7]
% noise in the correspondences
problem.noise = 0;
% size of the random scene
scene_radius = 10;
[correspondences, gt_T, corrupt_cost] = ...
rand_registration( problem.m, problem.noise, scene_radius, ...
problem.sim );
case 'SpaceStation'
% registration data from Space Station [2,3]
[c_p,c_l,c_pl] = correspondences_SpaceStation( );
correspondences = [c_p,c_l,c_pl];
case 'RubikCube'
% registration data from Rubik cube [2,3]
[c_p,c_l,c_pl] = correspondences_RubikCube( );
correspondences = [c_p,c_l,c_pl];
otherwise
error('Unknown problem type')
end
% Model the problem as a compressed quadratic form in R only
% -------------------------------------------------------------------------
% Compute equivalent compressed quadratic form
% q = compress_quadData( correspondences );
% sv = svd(q.Q_);
% Sanity check: Sum of costs and compressed quad form must be equivalent
% abs( q.eval(vec(gt_T)) - sum(cost(correspondences,gt_T)) )
% Marginalize the quadratic function wrt translation using Schur complement
% t_idxs = 10:12;
% [q_margin, A] = marginalize(q,t_idxs);
% Solve the problem with our method
% ------------------------------------------------------------------------
% scale_list = [gt_T.s];
opts.solver = 2; % 1 bisection, 2 dense-search
if problem.sim
if opts.solver == 1
bisection_t = struct('s', [], 'sim', [], 'H', [], 'dstar', [], ...
'f', [], 'sum_cost', [], 'costs', [], 'centroid_t', []);
bisection_t(1).s = 0.01;
bisection_t(2).s = 5;
opts.max_iter = 30;
opts.cost_threshold = 1e-4;
opts.quite = 1;
opts.show_statistic = 1;
opts.draw_results = 0;
disp("Computing...")
fprintf("Ground truth scaling is %d\n", gt_T.s)
[out_t, bisection_t] = solveByBisection(...
opts, correspondences, bisection_t);
elseif opts.solver == 2
dense_search_t.s_min = 0.1;
dense_search_t.s_interval = 0.05;
dense_search_t.s_max = 5;
opts.max_iter = 200;
opts.cost_threshold = 1e-3;
opts.quite = 1;
opts.show_statistic = 1; % 0: no outputs, 1: rough outputs 2: detailed
opts.draw_results = 0;
[res_t, dense_search_t] = solveByDenseSearch(...
opts, correspondences, dense_search_t);
[~, k] = min([res_t(:).f]);
out_t = res_t(k);
end
else
% Compute equivalent compressed quadratic form
q = compress_quadData( correspondences );
[out_t.R, out_t.t, out_t.dstar, times] = method_RCQP(...
correspondences, 'header_all');
H = SimPose(out_t.t, out_t.R, 1);
f = q.eval(vec(H));
gap = (f - out_t.dstar) / out_t.dstar;
disp("========================================")
fprintf('Optimality gap is f^star-d^star=%E\n',gap);
disp("========================================")
end
% scale_list = 1:100;
% bisection_a = 0;
% bisection_b = 10;
%
% cost_pre = norm(correspondences.cost(SimPose()));
% pick_color = getColors(length(scale_list));
% [axes_h, fig_h] = createFigHandleWithNumber(1,10,"Debug",1,1);
% for k = 1:length(scale_list)
% for i = 1:size(correspondences,2)
% plot3(axes_h(1), ...
% correspondences(i).model.x(1), ...
% correspondences(i).model.x(2), ...
% correspondences(i).model.x(3), ...
% 'color', pick_color{k}, 'Marker', 'o');
% end
% scaling = (bisection_a + bisection_b)/ 2;
% scaling = gt_T.s;
% corrected_points = [correspondences.point];
% transform([correspondences.point], ...
% SimPose(zeros(3,1), eye(3), scaling));
%
%
% q = compress_quadData( correspondences );
% [R,t,dstar,times] = method_RCQP( correspondences, 'header_all' );
% H = SimPose(t,R, 1);
% f = q.eval(vec(Pose(t,R)));
% gap = (f-dstar)/dstar;
% disp("========================================")
% fprintf('Optimality gap is f^star-d^star=%E\n',gap);
% disp("========================================")
% if dstar < cost_pre
% disp("---------------------------")
% corrected_points = [correspondences.point];
% % corrected_points(i).x
% % correspondences(i).point.x
% transform([correspondences.point], ...
% SimPose(zeros(3,1), eye(3), 1/scaling));
% % corrected_points(i).x
% % correspondences(i).point.x
% % corrected_points = transform([correspondences.point], H);
%
% % update a and b
% % bisection_a =
% % bisection_b =
% cost_pre = dstar;
% end
% for i = 1:size(correspondences,2)
% plot3(axes_h(1), ...
% correspondences(i).point.x(1), ...
% correspondences(i).point.x(2), ...
% correspondences(i).point.x(3), ...
% 'color', pick_color{k}, 'Marker', '*');
% end
% end
%%
% H = SimPose(t,R, gt_T.s);
[axes_h, fig_h] = createFigHandleWithNumber(2,1,"simRCQP",1,1);
if problem.sim && opts.solver == 1
% initial status
cur_axes = 1;
cur_fig =1;
opts.plotting.model = 0;
opts.plotting.corrected_source = 0;
opts.plotting.corrected2target = 0;
opts.plotting.source2target = 1;
opts.plotting.source_points = 1;
title_txt = "Optimization cost and scaling is " ...
+ "(" + num2str(abs(out_t.f)) ...
+ ", " + num2str(out_t.s) + ")";
plotCorrespondences(opts, axes_h, cur_axes, ...
out_t.centroid_t.point, ...
correspondences, out_t.sim, out_t.s, title_txt)
% results
cur_axes = 2;
cur_fig = 2;
opts.plotting.model = 0;
opts.plotting.corrected_source = 1;
opts.plotting.corrected2target = 1;
opts.plotting.source2target = 0;
opts.plotting.source_points = 0;
title_txt = "Optimization cost and scaling is " ...
+ "(" + num2str(abs(out_t.f)) ...
+ ", " + num2str(out_t.s) + ")";
plotCorrespondences(opts, axes_h, cur_axes, ...
out_t.centroid_t.point, ...
correspondences, out_t.sim, out_t.s, title_txt)
gt_T.sim
out_t.sim.sim
fprintf("Noise level: %.2f\n", problem.noise)
fprintf("Geodestic: %.3f\n", norm(gt_T.sim \ out_t.sim.sim))
elseif problem.sim && opts.solver == 2
cur_axes = 1;
cur_fig =1;
opts.plotting.model = 0;
opts.plotting.corrected_source = 0;
opts.plotting.corrected2target = 0;
opts.plotting.source2target = 1;
opts.plotting.source_points = 1;
title_txt = "Optimization cost and scaling is " ...
+ "(" + num2str(abs(out_t.f)) ...
+ ", " + num2str(out_t.s) + ")";
plotCorrespondences(opts, axes_h, cur_axes, ...
[], ...
correspondences, out_t.sim, out_t.s, title_txt)
cur_axes = 2;
cur_fig = 2;
s_v = [res_t(:).s];
d_star_v = [res_t(:).dstar];
f_v = [res_t(:).f];
scatter(axes_h(cur_axes), s_v, d_star_v, 'bo')
scatter(axes_h(cur_axes), s_v, f_v, 'g*')
scatter(axes_h(cur_axes), gt_T.s, 0, 100,'r^', 'fill')
viewCurrentPlot(axes_h(cur_axes), [], [], 0)
else
plotCorrespondences(opts, axes_h, cur_axes, ...
[], ...
correspondences, H, [], "test")
gt_T.T
H.sim
fprintf("Noise level: %.2f\n", problem.noise)
fprintf("Geodestic: %.3f\n", norm(gt_T.T \ H.sim))
end
% plotCorrespondences(axes_h, cur_axes, ...
% out_t.centroid_t.point, ...
% correspondences, out_t.sim, out_t.s, title_txt)