wolffd@0: % Consider matching sources to detections
wolffd@0: 
wolffd@0: %  s1 d2  
wolffd@0: %         s2 d3
wolffd@0: %  d1
wolffd@0: 
wolffd@0: %a  = bipartiteMatchingHungarian([52;0.01])
wolffd@0: 
wolffd@0: % sources(:,i) = [x y] coords
wolffd@0: sources = [0.1 0.7; 0.6 0.4]';
wolffd@0: detections = [0.2 0.2; 0.2 0.8; 0.7 0.1]';
wolffd@0: dst = sqdist(sources, detections);
wolffd@0: 
wolffd@0: % a = [2 3] which means s1-d2, s2-d3
wolffd@0: a = bipartiteMatchingHungarian(dst);
wolffd@0: a2 = bipartiteMatchingIntProg(dst);
wolffd@0: assert(isequal(a(:),a2(:)))
wolffd@0: 
wolffd@0: 
wolffd@0: figure(1); clf
wolffd@0: bipartiteMatchingDemoPlot(sources, detections, a)
wolffd@0: 
wolffd@0: 
wolffd@0: 
wolffd@0: 
wolffd@0: %%%% Flip roles of sources and detections
wolffd@0: 
wolffd@0: %dst  = dst';
wolffd@0: dst = sqdist(detections, sources);
wolffd@0: % a = [0 1 2] which means d1-0, d2-s1, d3-s2
wolffd@0: a = bipartiteMatchingHungarian(dst);
wolffd@0: 
wolffd@0: a2 = bipartiteMatchingIntProg(dst);
wolffd@0: assert(isequal(a(:),a2(:)))
wolffd@0: 
wolffd@0: figure(2); clf
wolffd@0: bipartiteMatchingDemoPlot(detections, sources, a) % swapped args
wolffd@0: 
wolffd@0: 
wolffd@0: 
wolffd@0: 
wolffd@0: %%%%%%%%%% Move s1 nearer to d1
wolffd@0: %  d2  
wolffd@0: %         s2 d3
wolffd@0: %  s1 d1
wolffd@0: 
wolffd@0: sources = [0.1 0.3; 0.6 0.4]';
wolffd@0: detections = [0.2 0.2; 0.2 0.8; 0.7 0.1]';
wolffd@0: dst = sqdist(sources, detections);
wolffd@0: 
wolffd@0: % a = [2 3] which means s1-d2, s2-d3
wolffd@0: a = bipartiteMatchingHungarian(dst);
wolffd@0: [a2, ass] = bipartiteMatchingIntProg(dst);
wolffd@0: assert(isequal(a(:),a2(:)))
wolffd@0: 
wolffd@0: 
wolffd@0: figure(3); clf
wolffd@0: bipartiteMatchingDemoPlot(sources, detections, a)
wolffd@0: 
wolffd@0: 
wolffd@0: 
wolffd@0: %%%%%%%%%%
wolffd@0: 
wolffd@0: % Use random points
wolffd@0: 
wolffd@0: % Generate 2D data from a mixture of 2 Gaussians (from netlab demgmm1)
wolffd@0: randn('state', 0); rand('state', 0);
wolffd@0: gmix = gmm(2, 2, 'spherical');
wolffd@0: ndat1 = 10; ndat2 = 10; ndata = ndat1+ndat2;
wolffd@0: %gmix.centres =  [0.3 0.3; 0.7 0.7]; 
wolffd@0: %gmix.covars = [0.01 0.01];
wolffd@0: gmix.centres =  [0.5 0.5; 0.5 0.5];
wolffd@0: gmix.covars = [0.1 0.01];
wolffd@0: [x, label] = gmmsamp(gmix, ndata);
wolffd@0: 
wolffd@0: ndx = find(label==1);
wolffd@0: sources = x(ndx,:)';
wolffd@0: ndx = find(label==2);
wolffd@0: detections = x(ndx,:)';
wolffd@0: dst = sqdist(sources, detections);
wolffd@0: 
wolffd@0: [a, ass] = bipartiteMatchingIntProg(dst);
wolffd@0: [a2] = bipartiteMatchingHungarian(dst);
wolffd@0: assert(isequal(a(:), a2(:)))
wolffd@0: 
wolffd@0: figure(4); clf
wolffd@0: bipartiteMatchingDemoPlot(sources, detections, a)
wolffd@0: 
wolffd@0: % only match 80% of points
wolffd@0: p1 = size(sources, 2);
wolffd@0: p2 = size(detections, 2);
wolffd@0: nmatch = ceil(0.8*min(p1,p2));
wolffd@0: a2 = bipartiteMatchingIntProg(dst, nmatch);
wolffd@0: figure(5); clf
wolffd@0: bipartiteMatchingDemoPlot(sources, detections, a2)
wolffd@0: 
wolffd@0: 
wolffd@0: %%% swap roles
wolffd@0: 
wolffd@0: ndx = find(label==2);
wolffd@0: sources = x(ndx,:)';
wolffd@0: ndx = find(label==1);
wolffd@0: detections = x(ndx,:)';
wolffd@0: dst = sqdist(sources, detections);
wolffd@0: 
wolffd@0: % only match 80% of points
wolffd@0: p1 = size(sources, 2);
wolffd@0: p2 = size(detections, 2);
wolffd@0: nmatch = ceil(0.8*min(p1,p2));
wolffd@0: a2 = bipartiteMatchingIntProg(dst, nmatch);
wolffd@0: figure(6); clf
wolffd@0: bipartiteMatchingDemoPlot(sources, detections, a2)