WebSVN – seema-scanner – Diff – /matlab/alignSubScansMarkers.m


function MSE = alignSubScansMarkers(calibrationFileName, alnFileName)
%ALIGNSUBSCANSMARKERS Determines an exact alignment of sub scans (scans
% from e.g. one revolution of the rotation stage). 
% The method searches for circular white markers of a specific diameter.
% White frames corresponding to each sub scan must be available.
% A coarse alignment in the form of an aln-file must be provided. 
%
% 2017 Jakob Wilm, DTU
 
initialAlign = readMeshLabALN(alnFileName);
 
calibration = readOpenCVXML(calibrationFileName);
 
% correct for Matlab 1-indexing in principle point coordinates
calibration.K0(1:2, 3) = calibration.K0(1:2, 3)+1;
calibration.K1(1:2, 3) = calibration.K1(1:2, 3)+1;
 
% full projection matrices in Matlab convention
P0 = transpose(calibration.K0*[eye(3) zeros(3,1)]);
P1 = transpose(calibration.K1*[calibration.R1 calibration.T1']);
 
% matlab cam params for undistortion
camParams0 = cameraParameters('IntrinsicMatrix', calibration.K0', 'RadialDistortion', calibration.k0([1 2 5]), 'TangentialDistortion', calibration.k0([3 4]));
camParams1 = cameraParameters('IntrinsicMatrix', calibration.K1', 'RadialDistortion', calibration.k1([1 2 5]), 'TangentialDistortion', calibration.k1([3 4]));
 
% matlab struct for triangulation
camStereoParams = stereoParameters(camParams0, camParams1, calibration.R1', calibration.T1');
 
nSubScans = length(initialAlign);
 
% 3D coordinates of markers in local camera frame
E = cell(nSubScans, 1);
 
% 3D coordinates of markers in global initial alignment
Eg = cell(size(E));
 
% find 3D markers coordinates 
for i=1:nSubScans
 
    % load point cloud
    pc = pcread(initialAlign(i).FileName);
    Q = pc.Location;
    idString = strsplit(initialAlign(i).FileName, {'.ply', '_'});
    idString = idString{end-1};
    
    % load white frames
    scanDir = strsplit(initialAlign(i).FileName, '/');
    scanDir = fullfile(scanDir{1:end-1});
    frame0 = imread(fullfile(scanDir, ['sequence_' idString], 'frames0_0.png'));
    frame1 = imread(fullfile(scanDir, ['sequence_' idString], 'frames1_0.png'));
 
    e0Coords = autoDetectMarkers(frame0, P0, Q);
    e1Coords = autoDetectMarkers(frame1, P1, Q);
    
    %e0Coords = manuallyDetectMarkers(frame0, P0, Q);
    %e1Coords = manuallyDetectMarkers(frame1, P1, Q);
    
    %e0Coords = undistortPoints(e0Coords, camParams0);
    %e1Coords = undistortPoints(e1Coords, camParams1);
 
    % match ellipse candidates between cameras based on projection
    E0 = projectOntoPointCloud(e0Coords, P0, Q);
    E1 = projectOntoPointCloud(e1Coords, P1, Q);
 
    matchedPairs = nan(size(E0, 1), 2);
    nMatchedPairs = 0;
    for j=1:size(E0, 1)
        
        % should use pdist2 instead..
        sqDists = sum((E1 - repmat(E0(j,:), size(E1, 1), 1)).^2, 2);
        
        [minSqDist, minSqDistIdx] = min(sqDists);
 
        if(minSqDist < 1^2)
            nMatchedPairs = nMatchedPairs + 1;
            matchedPairs(nMatchedPairs, :) = [j, minSqDistIdx];
        end
    end
    matchedPairs = matchedPairs(1:nMatchedPairs, :);
    
    % triangulate marker centers (lens correction has been performed)
    [E{i}, e] = triangulate(e0Coords(matchedPairs(:, 1),:), e1Coords(matchedPairs(:, 2),:), camStereoParams);
    E{i} = E{i}(e<3.0, :);
    display(e);
    
    % write point cloud with marker (debugging)
    pcDebug = pointCloud([pc.Location; E{i}], 'Color', [pc.Color; repmat([255, 0, 0], size(E{i}, 1), 1)]);
    pcwrite(pcDebug, 'pcDebug.ply');
    
    % bring markers into initial alignment
    [U,~,V] = svd(initialAlign(i).Rotation);
    Ri = U*V';
    Ti = initialAlign(i).Translation;
    
    Eg{i} = E{i}*Ri' + repmat(Ti', size(E{i}, 1), 1);
end
 
% show found markers in initial alignment
figure;
hold('on');
for i=1:nSubScans
    % fix Ri to be orthogonal
    [U,~,V] = svd(initialAlign(i).Rotation);
    Ri = U*V';
    
    % bring point cloud into initial alignment
    pc = pcread(initialAlign(i).FileName);
    tform = affine3d([Ri' [0;0;0]; initialAlign(i).Translation' 1]);
    pcg = pctransform(pc, tform);
   
    pcshow(pcg);
    xlabel('x');
    ylabel('y');
    zlabel('z');
    
    plot3(Eg{i}(:,1), Eg{i}(:,2), Eg{i}(:,3), '.', 'MarkerSize', 15);
    title('Initial Alignment');
end
 
% match markers between poses using initial alignment
Pg = {};
P = {};
for i=1:nSubScans
    for j=1:size(Eg{i}, 1)
        pg = Eg{i}(j,:);
        p = E{i}(j,:);
        matched = false;
        for k=1:size(Pg, 2)
            clusterCenter = mean(cat(1, Pg{:,k}), 1);
            if(sum((pg - clusterCenter).^2) < 3^2)
                % store in global frame
                Pg{i,k} = pg;
                % store in local frame
                P{i,k} = p;
                matched = true;
                break;
            end
        end
        % create new cluster
        if(not(matched))
            Pg{i,end+1} = pg;
            P{i,end+1} = p;
        end 
    end
end
 
% run optimization
alignment = groupwiseOrthogonalProcrustes(P, initialAlign);
 
% show found markers in optimized alignment
figure;
hold('on');
for i=1:nSubScans
    % fix Ri to be orthogonal
    [U,~,V] = svd(alignment(i).Rotation);
    Ri = U*V';
    Ti = alignment(i).Translation;
    
    Ea = E{i}*Ri' + repmat(Ti', size(E{i}, 1), 1);
    
    % bring point cloud into optimized alignment
    pc = pcread(initialAlign(i).FileName);
    tform = affine3d([Ri' [0;0;0]; initialAlign(i).Translation' 1]);
    pcg = pctransform(pc, tform);
   
    pcshow(pcg);
    xlabel('x');
    ylabel('y');
    zlabel('z');
    
    plot3(Ea(:,1), Ea(:,2), Ea(:,3), '.', 'MarkerSize', 15);
    title('Optimized Alignment');
end
 
% write to ALN file
for i=1:length(alignment)
    alignment(i).FileName = initialAlign(i).FileName;
end
 
writeMeshLabALN(alignment, strrep(alnFileName, '.aln', 'Optimized.aln'));
 
end
 
function e = autoDetectMarkers(frame, P, pointCloud)
 
    % create mask based on morphology
    bw = imbinarize(rgb2gray(frame));
    cc = bwconncomp(bw);
    rp = regionprops(cc, 'Area', 'Solidity', 'Eccentricity', 'Centroid');
    idx = ([rp.Area] > 100 & [rp.Area] < 1000 & [rp.Solidity] > 0.9);
    
    initialGuesses = cat(1, rp(idx).Centroid);
 
    [e, ~] = detectMarkersSubpix(frame, initialGuesses, P, pointCloud);
 
    figure; 
    imshow(frame);
        hold('on');
    plot(e(:,1), e(:,2), 'rx', 'MarkerSize', 15);
    drawnow;
end
 
function e = manuallyDetectMarkers(frame, P, pointCloud)
    
    e = [];
	%edges = edge(rgb2gray(frame), 'Canny', [0.08 0.1], 2);
 
    figure; 
    hold('on');
    imshow(frame);
    title('Close figure to end.');
    set(gcf, 'pointer', 'crosshair'); 
    set(gcf, 'WindowButtonDownFcn', @clickCallback);
    
    uiwait;
 
    function clickCallback(caller, ~)
        
        p = get(gca, 'CurrentPoint'); 
        p = p(1, 1:2);
 
        [el, ~] = detectMarkersSubpix(frame, p, P, pointCloud);
        e = [e; el(:, 1:2)];
        
        if(not(isempty(el)))
            figure(caller);
            hold('on');
            plot(el(1), el(2), 'rx', 'MarkerSize', 15);
        end
    end
    
end
 
function [e, conf] = detectMarkersSubpix(frame, initGuesses, P, Q)
 
    % create mask based on morphology
    bw = imbinarize(rgb2gray(frame));
    cc = bwconncomp(bw);
    labels = labelmatrix(cc);
 
    % project point cloud into image
    q = [Q ones(size(Q,1),1)]*P;
    q = q./[q(:,3) q(:,3) q(:,3)];
    
    e = zeros(size(initGuesses));
    conf = zeros(size(initGuesses, 1), 1);
    
    nMarkersFound = 0;
    
    for i=1:size(initGuesses, 1)
        
        labelId = labels(round(initGuesses(i,2)), round(initGuesses(i,1)));
        labelMask = (labels == labelId);
        labelMask = imdilate(labelMask, strel('disk', 3, 0));
        
        if(sum(sum(labelMask)) < 10 || sum(sum(labelMask)) > 1000)
            continue;
        end
        
        % determine 3D points that are part of the marker
        % note: we should probably undistort labelMask
        pointMask = false(size(q, 1), 1);
        for j=1:size(q,1)
            if(round(q(j,2)) > size(labelMask, 1) || round(q(j,1)) > size(labelMask, 2) || round(q(j,2)) < 1 || round(q(j,1)) < 1)
                continue;
            end
            
            if(labelMask(round(q(j,2)), round(q(j,1))))
                pointMask(j) = true;
            end
        end
        
        if(sum(pointMask)) < 10
            continue;
        end
        
        % project 3D points onto local plane
        [~, sc, ~] = pca(Q(pointMask, :));
        Qlocal = sc(:, 1:2);
        
        % synthetic marker in high res. space
        m = zeros(151, 151);
        [x, y] = meshgrid(1:151, 1:151);
        m((x(:)-76).^2 + (y(:)-76).^2 <= 50^2) = 1.0;
        
        % relation between marker space (px) and true marker/local plane(mm)
        % true marker diameter is 1.75mm
        mScale = 101/1.8; %px/mm
        mShift = 76; %px
        
        % build homography from image to marker space
        H = fitgeotrans(q(pointMask, 1:2), mScale*Qlocal+mShift,  'projective');
        
        % bring image of marker into marker space
        imMarkerSpace = imwarp(frame, H, 'OutputView', imref2d(size(m)));
        imMarkerSpace = rgb2gray(im2double(imMarkerSpace));
        
        %figure; imshowpair(imMarkerSpace, m);
        
        % perform image registration
        % might be better off using subpixel image correlation
        [opt, met] = imregconfig('multimodal');
        T = imregtform(m, imMarkerSpace, 'translation', opt, met, 'DisplayOptimization', false);
        
        rege = imwarp(m, T, 'OutputView', imref2d(size(m)));
        %figure; imshowpair(imMarkerSpace, rege);
        
        % measure of correlation
        confI = sum(sum(imMarkerSpace .* rege))/sqrt(sum(sum(imMarkerSpace) * sum(sum(rege))));
        
        if confI<0.4
            continue;
        end
        
        fprintf('Found marker with confidence: %f\n', confI);
            
        % transform marker space coordinates (76,76) to frame space
        el = T.transformPointsForward([76, 76]);
        el = H.transformPointsInverse(el);
        
        nMarkersFound = nMarkersFound+1;
        e(nMarkersFound,:) = el;
        conf(nMarkersFound) = confI;
    end
    
    e = e(1:nMarkersFound, :);
    conf = conf(1:nMarkersFound);
end
 
function E = projectOntoPointCloud(e, P, pointCloud)
 
    q = [pointCloud ones(size(pointCloud,1),1)]*P;
    q = q(:,1:2)./[q(:,3) q(:,3)];
 
    E = nan(size(e,1), 3);
    
    for i=1:size(e, 1)
        sqDists = sum((q - repmat(e(i,:), size(q, 1), 1)).^2, 2);
        
        [sqDistsSorted, sortIdx] = sort(sqDists);
        
        neighbors = (sqDistsSorted < 4.0^2);
        
        distsSorted = sqrt(sqDistsSorted(neighbors));
        invDistsSorted = 1.0/distsSorted;
        sortIdx = sortIdx(neighbors);
        
        nNeighbors = sum(neighbors);
        
        if(nNeighbors >= 2)
            E(i, :) = 0;
            for j=1:nNeighbors
                E(i, :) = E(i, :) + invDistsSorted(j)/sum(invDistsSorted) * pointCloud(sortIdx(j), :);
            end
        end
            
    end    
end
 
 

Rev 216	Rev 218
1	`function MSE = alignSubScansMarkers(calibrationFileName, alnFileName)`	1	`function MSE = alignSubScansMarkers(calibrationFileName, alnFileName)`
2	`%ALIGNSUBSCANSMARKERS Determines an exact alignment of sub scans (scans`	2	`%ALIGNSUBSCANSMARKERS Determines an exact alignment of sub scans (scans`
3	`% from e.g. one revolution of the rotation stage).`	3	`% from e.g. one revolution of the rotation stage).`
4	`% The method searches for circular white markers of a specific diameter.`	4	`% The method searches for circular white markers of a specific diameter.`
5	`% White frames corresponding to each sub scan must be available.`	5	`% White frames corresponding to each sub scan must be available.`
6	`% A coarse alignment in the form of an aln-file must be provided.`	6	`% A coarse alignment in the form of an aln-file must be provided.`
7	`%`	7	`%`
8	`% 2017 Jakob Wilm, DTU`	8	`% 2017 Jakob Wilm, DTU`
9		9
10	`initialAlign = readMeshLabALN(alnFileName);`	10	`initialAlign = readMeshLabALN(alnFileName);`
11		11
12	`calibration = readOpenCVXML(calibrationFileName);`	12	`calibration = readOpenCVXML(calibrationFileName);`
13		13
14	`% correct for Matlab 1-indexing in principle point coordinates`	14	`% correct for Matlab 1-indexing in principle point coordinates`
15	`calibration.K0(1:2, 3) = calibration.K0(1:2, 3)+1;`	15	`calibration.K0(1:2, 3) = calibration.K0(1:2, 3)+1;`
16	`calibration.K1(1:2, 3) = calibration.K1(1:2, 3)+1;`	16	`calibration.K1(1:2, 3) = calibration.K1(1:2, 3)+1;`
17		17
18	`% full projection matrices in Matlab convention`	18	`% full projection matrices in Matlab convention`
19	`P0 = transpose(calibration.K0*[eye(3) zeros(3,1)]);`	19	`P0 = transpose(calibration.K0*[eye(3) zeros(3,1)]);`
20	`P1 = transpose(calibration.K1*[calibration.R1 calibration.T1']);`	20	`P1 = transpose(calibration.K1*[calibration.R1 calibration.T1']);`
21		21
22	`% matlab cam params for undistortion`	22	`% matlab cam params for undistortion`
23	`camParams0 = cameraParameters('IntrinsicMatrix', calibration.K0', 'RadialDistortion', calibration.k0([1 2 5]), 'TangentialDistortion', calibration.k0([3 4]));`	23	`camParams0 = cameraParameters('IntrinsicMatrix', calibration.K0', 'RadialDistortion', calibration.k0([1 2 5]), 'TangentialDistortion', calibration.k0([3 4]));`
24	`camParams1 = cameraParameters('IntrinsicMatrix', calibration.K1', 'RadialDistortion', calibration.k1([1 2 5]), 'TangentialDistortion', calibration.k1([3 4]));`	24	`camParams1 = cameraParameters('IntrinsicMatrix', calibration.K1', 'RadialDistortion', calibration.k1([1 2 5]), 'TangentialDistortion', calibration.k1([3 4]));`
25		25
26	`% matlab struct for triangulation`	26	`% matlab struct for triangulation`
27	`camStereoParams = stereoParameters(camParams0, camParams1, calibration.R1', calibration.T1');`	27	`camStereoParams = stereoParameters(camParams0, camParams1, calibration.R1', calibration.T1');`
28		28
29	`nSubScans = length(initialAlign);`	29	`nSubScans = length(initialAlign);`
30		30
31	`% 3D coordinates of markers in local camera frame`	31	`% 3D coordinates of markers in local camera frame`
32	`E = cell(nSubScans, 1);`	32	`E = cell(nSubScans, 1);`
33		33
34	`% 3D coordinates of markers in global initial alignment`	34	`% 3D coordinates of markers in global initial alignment`
35	`Eg = cell(size(E));`	35	`Eg = cell(size(E));`
36		36
37	`% find 3D markers coordinates`	37	`% find 3D markers coordinates`
38	`for i=1:nSubScans`	38	`for i=1:nSubScans`
39		39
40	`% load point cloud`	40	`% load point cloud`
41	`pc = pcread(initialAlign(i).FileName);`	41	`pc = pcread(initialAlign(i).FileName);`
42	`Q = pc.Location;`	42	`Q = pc.Location;`
43	`idString = strsplit(initialAlign(i).FileName, {'.ply', '_'});`	43	`idString = strsplit(initialAlign(i).FileName, {'.ply', '_'});`
44	`idString = idString{end-1};`	44	`idString = idString{end-1};`
45		45
46	`% load white frames`	46	`% load white frames`
47	`scanDir = strsplit(initialAlign(i).FileName, '/');`	47	`scanDir = strsplit(initialAlign(i).FileName, '/');`
48	`scanDir = fullfile(scanDir{1:end-1});`	48	`scanDir = fullfile(scanDir{1:end-1});`
49	`frame0 = imread(fullfile(scanDir, ['sequence_' idString], 'frames0_0.png'));`	49	`frame0 = imread(fullfile(scanDir, ['sequence_' idString], 'frames0_0.png'));`
50	`frame1 = imread(fullfile(scanDir, ['sequence_' idString], 'frames1_0.png'));`	50	`frame1 = imread(fullfile(scanDir, ['sequence_' idString], 'frames1_0.png'));`
51		51
52	`e0Coords = autoDetectMarkers(frame0, P0, Q);`	52	`e0Coords = autoDetectMarkers(frame0, P0, Q);`
53	`e1Coords = autoDetectMarkers(frame1, P1, Q);`	53	`e1Coords = autoDetectMarkers(frame1, P1, Q);`
54		54
55	`%e0Coords = manuallyDetectMarkers(frame0, P0, Q);`	55	`%e0Coords = manuallyDetectMarkers(frame0, P0, Q);`
56	`%e1Coords = manuallyDetectMarkers(frame1, P1, Q);`	56	`%e1Coords = manuallyDetectMarkers(frame1, P1, Q);`
57		57
58	`e0Coords = undistortPoints(e0Coords, camParams0);`	58	`%e0Coords = undistortPoints(e0Coords, camParams0);`
59	`e1Coords = undistortPoints(e1Coords, camParams1);`	59	`%e1Coords = undistortPoints(e1Coords, camParams1);`
60		60
61	`% match ellipse candidates between cameras based on projection`	61	`% match ellipse candidates between cameras based on projection`
62	`E0 = projectOntoPointCloud(e0Coords, P0, Q);`	62	`E0 = projectOntoPointCloud(e0Coords, P0, Q);`
63	`E1 = projectOntoPointCloud(e1Coords, P1, Q);`	63	`E1 = projectOntoPointCloud(e1Coords, P1, Q);`
64		64
65	`matchedPairs = nan(size(E0, 1), 2);`	65	`matchedPairs = nan(size(E0, 1), 2);`
66	`nMatchedPairs = 0;`	66	`nMatchedPairs = 0;`
67	`for j=1:size(E0, 1)`	67	`for j=1:size(E0, 1)`
68		68
69	`% should use pdist2 instead..`	69	`% should use pdist2 instead..`
70	`sqDists = sum((E1 - repmat(E0(j,:), size(E1, 1), 1)).^2, 2);`	70	`sqDists = sum((E1 - repmat(E0(j,:), size(E1, 1), 1)).^2, 2);`
71		71
72	`[minSqDist, minSqDistIdx] = min(sqDists);`	72	`[minSqDist, minSqDistIdx] = min(sqDists);`
73		73
74	`if(minSqDist < 1^2)`	74	`if(minSqDist < 1^2)`
75	`nMatchedPairs = nMatchedPairs + 1;`	75	`nMatchedPairs = nMatchedPairs + 1;`
76	`matchedPairs(nMatchedPairs, :) = [j, minSqDistIdx];`	76	`matchedPairs(nMatchedPairs, :) = [j, minSqDistIdx];`
77	`end`	77	`end`
78	`end`	78	`end`
79	`matchedPairs = matchedPairs(1:nMatchedPairs, :);`	79	`matchedPairs = matchedPairs(1:nMatchedPairs, :);`
80		80
81	`% triangulate marker centers (lens correction has been performed)`	81	`% triangulate marker centers (lens correction has been performed)`
82	`[E{i}, e] = triangulate(e0Coords(matchedPairs(:, 1),:), e1Coords(matchedPairs(:, 2),:), camStereoParams);`	82	`[E{i}, e] = triangulate(e0Coords(matchedPairs(:, 1),:), e1Coords(matchedPairs(:, 2),:), camStereoParams);`
83	`E{i} = E{i}(e<1.0, :);`	83	`E{i} = E{i}(e<3.0, :);`
-		84	`display(e);`
84		85
85	`% write point cloud with marker (debugging)`	86	`% write point cloud with marker (debugging)`
86	`pcDebug = pointCloud([pc.Location; E{i}], 'Color', [pc.Color; repmat([255, 0, 0], size(E{i}, 1), 1)]);`	87	`pcDebug = pointCloud([pc.Location; E{i}], 'Color', [pc.Color; repmat([255, 0, 0], size(E{i}, 1), 1)]);`
87	`pcwrite(pcDebug, 'pcDebug.ply');`	88	`pcwrite(pcDebug, 'pcDebug.ply');`
88		89
89	`% bring markers into initial alignment`	90	`% bring markers into initial alignment`
90	`[U,~,V] = svd(initialAlign(i).Rotation);`	91	`[U,~,V] = svd(initialAlign(i).Rotation);`
91	`Ri = U*V';`	92	`Ri = U*V';`
92	`Ti = initialAlign(i).Translation;`	93	`Ti = initialAlign(i).Translation;`
93		94
94	`Eg{i} = E{i}*Ri' + repmat(Ti', size(E{i}, 1), 1);`	95	`Eg{i} = E{i}*Ri' + repmat(Ti', size(E{i}, 1), 1);`
95	`end`	96	`end`
96		97
97	`% show found markers in initial alignment`	98	`% show found markers in initial alignment`
98	`figure;`	99	`figure;`
99	`hold('on');`	100	`hold('on');`
100	`for i=1:nSubScans`	101	`for i=1:nSubScans`
101	`% fix Ri to be orthogonal`	102	`% fix Ri to be orthogonal`
102	`[U,~,V] = svd(initialAlign(i).Rotation);`	103	`[U,~,V] = svd(initialAlign(i).Rotation);`
103	`Ri = U*V';`	104	`Ri = U*V';`
104		105
105	`% bring point cloud into initial alignment`	106	`% bring point cloud into initial alignment`
106	`pc = pcread(initialAlign(i).FileName);`	107	`pc = pcread(initialAlign(i).FileName);`
107	`tform = affine3d([Ri' [0;0;0]; initialAlign(i).Translation' 1]);`	108	`tform = affine3d([Ri' [0;0;0]; initialAlign(i).Translation' 1]);`
108	`pcg = pctransform(pc, tform);`	109	`pcg = pctransform(pc, tform);`
109		110
110	`pcshow(pcg);`	111	`pcshow(pcg);`
111	`xlabel('x');`	112	`xlabel('x');`
112	`ylabel('y');`	113	`ylabel('y');`
113	`zlabel('z');`	114	`zlabel('z');`
114		115
115	`plot3(Eg{i}(:,1), Eg{i}(:,2), Eg{i}(:,3), '.', 'MarkerSize', 15);`	116	`plot3(Eg{i}(:,1), Eg{i}(:,2), Eg{i}(:,3), '.', 'MarkerSize', 15);`
116	`title('Initial Alignment');`	117	`title('Initial Alignment');`
117	`end`	118	`end`
118		119
119	`% match markers between poses using initial alignment`	120	`% match markers between poses using initial alignment`
120	`Pg = {};`	121	`Pg = {};`
121	`P = {};`	122	`P = {};`
122	`for i=1:nSubScans`	123	`for i=1:nSubScans`
123	`for j=1:size(Eg{i}, 1)`	124	`for j=1:size(Eg{i}, 1)`
124	`pg = Eg{i}(j,:);`	125	`pg = Eg{i}(j,:);`
125	`p = E{i}(j,:);`	126	`p = E{i}(j,:);`
126	`matched = false;`	127	`matched = false;`
127	`for k=1:size(Pg, 2)`	128	`for k=1:size(Pg, 2)`
128	`clusterCenter = mean(cat(1, Pg{:,k}), 1);`	129	`clusterCenter = mean(cat(1, Pg{:,k}), 1);`
129	`if(sum((pg - clusterCenter).^2) < 3^2)`	130	`if(sum((pg - clusterCenter).^2) < 3^2)`
130	`% store in global frame`	131	`% store in global frame`
131	`Pg{i,k} = pg;`	132	`Pg{i,k} = pg;`
132	`% store in local frame`	133	`% store in local frame`
133	`P{i,k} = p;`	134	`P{i,k} = p;`
134	`matched = true;`	135	`matched = true;`
135	`break;`	136	`break;`
136	`end`	137	`end`
137	`end`	138	`end`
138	`% create new cluster`	139	`% create new cluster`
139	`if(not(matched))`	140	`if(not(matched))`
140	`Pg{i,end+1} = pg;`	141	`Pg{i,end+1} = pg;`
141	`P{i,end+1} = p;`	142	`P{i,end+1} = p;`
142	`end`	143	`end`
143	`end`	144	`end`
144	`end`	145	`end`
145		146
146	`% run optimization`	147	`% run optimization`
147	`alignment = groupwiseOrthogonalProcrustes(P, initialAlign);`	148	`alignment = groupwiseOrthogonalProcrustes(P, initialAlign);`
148		149
149	`% show found markers in optimized alignment`	150	`% show found markers in optimized alignment`
150	`figure;`	151	`figure;`
151	`hold('on');`	152	`hold('on');`
152	`for i=1:nSubScans`	153	`for i=1:nSubScans`
-		154	`% fix Ri to be orthogonal`
153	`Ri = alignment(i).Rotation;`	155	`[U,~,V] = svd(alignment(i).Rotation);`
-		156	`Ri = U*V';`
154	`Ti = alignment(i).Translation;`	157	`Ti = alignment(i).Translation;`
155		158
156	`Ea = E{i}*Ri' + repmat(Ti', size(E{i}, 1), 1);`	159	`Ea = E{i}*Ri' + repmat(Ti', size(E{i}, 1), 1);`
157		160
158	`% bring point cloud into optimized alignment`	161	`% bring point cloud into optimized alignment`
159	`pc = pcread(initialAlign(i).FileName);`	162	`pc = pcread(initialAlign(i).FileName);`
160	`tform = affine3d([Ri' [0;0;0]; initialAlign(i).Translation' 1]);`	163	`tform = affine3d([Ri' [0;0;0]; initialAlign(i).Translation' 1]);`
161	`pcg = pctransform(pc, tform);`	164	`pcg = pctransform(pc, tform);`
162		165
163	`pcshow(pcg);`	166	`pcshow(pcg);`
164	`xlabel('x');`	167	`xlabel('x');`
165	`ylabel('y');`	168	`ylabel('y');`
166	`zlabel('z');`	169	`zlabel('z');`
167		170
168	`plot3(Ea(:,1), Ea(:,2), Ea(:,3), '.', 'MarkerSize', 15);`	171	`plot3(Ea(:,1), Ea(:,2), Ea(:,3), '.', 'MarkerSize', 15);`
169	`title('Optimized Alignment');`	172	`title('Optimized Alignment');`
170	`end`	173	`end`
171		174
172	`% write to ALN file`	175	`% write to ALN file`
173	`for i=1:length(alignment)`	176	`for i=1:length(alignment)`
174	`alignment(i).FileName = initialAlign(i).FileName;`	177	`alignment(i).FileName = initialAlign(i).FileName;`
175	`end`	178	`end`
176		179
177	`writeMeshLabALN(alignment, strrep(alnFileName, '.aln', 'Optimized.aln'));`	180	`writeMeshLabALN(alignment, strrep(alnFileName, '.aln', 'Optimized.aln'));`
178		181
179	`end`	182	`end`
180		183
181	`function e = autoDetectMarkers(frame, P, pointCloud)`	184	`function e = autoDetectMarkers(frame, P, pointCloud)`
182		185
183	`% create mask based on morphology`	186	`% create mask based on morphology`
184	`bw = imbinarize(rgb2gray(frame));`	187	`bw = imbinarize(rgb2gray(frame));`
185	`cc = bwconncomp(bw);`	188	`cc = bwconncomp(bw);`
186	`rp = regionprops(cc, 'Area', 'Solidity', 'Eccentricity', 'Centroid');`	189	`rp = regionprops(cc, 'Area', 'Solidity', 'Eccentricity', 'Centroid');`
187	`idx = ([rp.Area] > 100 & [rp.Area] < 1000 & [rp.Solidity] > 0.9);`	190	`idx = ([rp.Area] > 100 & [rp.Area] < 1000 & [rp.Solidity] > 0.9);`
188		191
189	`initialGuesses = cat(1, rp(idx).Centroid);`	192	`initialGuesses = cat(1, rp(idx).Centroid);`
190		193
191	`[e, ~] = detectMarkersSubpix(frame, initialGuesses, P, pointCloud);`	194	`[e, ~] = detectMarkersSubpix(frame, initialGuesses, P, pointCloud);`
192		195
193	`figure;`	196	`figure;`
194	`imshow(frame);`	197	`imshow(frame);`
195	`hold('on');`	198	`hold('on');`
196	`plot(e(:,1), e(:,2), 'rx', 'MarkerSize', 15);`	199	`plot(e(:,1), e(:,2), 'rx', 'MarkerSize', 15);`
197	`drawnow;`	200	`drawnow;`
198	`end`	201	`end`
199		202
200	`function e = manuallyDetectMarkers(frame, P, pointCloud)`	203	`function e = manuallyDetectMarkers(frame, P, pointCloud)`
201		204
202	`e = [];`	205	`e = [];`
203	`%edges = edge(rgb2gray(frame), 'Canny', [0.08 0.1], 2);`	206	`%edges = edge(rgb2gray(frame), 'Canny', [0.08 0.1], 2);`
204		207
205	`figure;`	208	`figure;`
206	`hold('on');`	209	`hold('on');`
207	`imshow(frame);`	210	`imshow(frame);`
208	`title('Close figure to end.');`	211	`title('Close figure to end.');`
209	`set(gcf, 'pointer', 'crosshair');`	212	`set(gcf, 'pointer', 'crosshair');`
210	`set(gcf, 'WindowButtonDownFcn', @clickCallback);`	213	`set(gcf, 'WindowButtonDownFcn', @clickCallback);`
211		214
212	`uiwait;`	215	`uiwait;`
213		216
214	`function clickCallback(caller, ~)`	217	`function clickCallback(caller, ~)`
215		218
216	`p = get(gca, 'CurrentPoint');`	219	`p = get(gca, 'CurrentPoint');`
217	`p = p(1, 1:2);`	220	`p = p(1, 1:2);`
218		221
219	`[el, ~] = detectMarkersSubpix(frame, p, P, pointCloud);`	222	`[el, ~] = detectMarkersSubpix(frame, p, P, pointCloud);`
220	`e = [e; el(:, 1:2)];`	223	`e = [e; el(:, 1:2)];`
221		224
222	`if(not(isempty(el)))`	225	`if(not(isempty(el)))`
223	`figure(caller);`	226	`figure(caller);`
224	`hold('on');`	227	`hold('on');`
225	`plot(el(1), el(2), 'rx', 'MarkerSize', 15);`	228	`plot(el(1), el(2), 'rx', 'MarkerSize', 15);`
226	`end`	229	`end`
227	`end`	230	`end`
228		231
229	`end`	232	`end`
230		233
231	`function [e, conf] = detectMarkersSubpix(frame, initGuesses, P, Q)`	234	`function [e, conf] = detectMarkersSubpix(frame, initGuesses, P, Q)`
232		235
233	`% create mask based on morphology`	236	`% create mask based on morphology`
234	`bw = imbinarize(rgb2gray(frame));`	237	`bw = imbinarize(rgb2gray(frame));`
235	`cc = bwconncomp(bw);`	238	`cc = bwconncomp(bw);`
236	`labels = labelmatrix(cc);`	239	`labels = labelmatrix(cc);`
237		240
238	`% project point cloud into image`	241	`% project point cloud into image`
239	`q = [Q ones(size(Q,1),1)]*P;`	242	`q = [Q ones(size(Q,1),1)]*P;`
240	`q = q./[q(:,3) q(:,3) q(:,3)];`	243	`q = q./[q(:,3) q(:,3) q(:,3)];`
241		244
242	`e = zeros(size(initGuesses));`	245	`e = zeros(size(initGuesses));`
243	`conf = zeros(size(initGuesses, 1), 1);`	246	`conf = zeros(size(initGuesses, 1), 1);`
244		247
245	`nMarkersFound = 0;`	248	`nMarkersFound = 0;`
246		249
247	`for i=1:size(initGuesses, 1)`	250	`for i=1:size(initGuesses, 1)`
248		251
249	`labelId = labels(round(initGuesses(i,2)), round(initGuesses(i,1)));`	252	`labelId = labels(round(initGuesses(i,2)), round(initGuesses(i,1)));`
250	`labelMask = (labels == labelId);`	253	`labelMask = (labels == labelId);`
251	`labelMask = imdilate(labelMask, strel('disk', 3, 0));`	254	`labelMask = imdilate(labelMask, strel('disk', 3, 0));`
252		255
253	`if(sum(sum(labelMask)) < 10 \|\| sum(sum(labelMask)) > 1000)`	256	`if(sum(sum(labelMask)) < 10 \|\| sum(sum(labelMask)) > 1000)`
254	`continue;`	257	`continue;`
255	`end`	258	`end`
256		259
257	`% determine 3D points that are part of the marker`	260	`% determine 3D points that are part of the marker`
258	`% note: we should probably undistort labelMask`	261	`% note: we should probably undistort labelMask`
259	`pointMask = false(size(q, 1), 1);`	262	`pointMask = false(size(q, 1), 1);`
260	`for j=1:size(q,1)`	263	`for j=1:size(q,1)`
261	`if(round(q(j,2)) > size(labelMask, 1) \|\| round(q(j,1)) > size(labelMask, 2) \|\| round(q(j,2)) < 1 \|\| round(q(j,1)) < 1)`	264	`if(round(q(j,2)) > size(labelMask, 1) \|\| round(q(j,1)) > size(labelMask, 2) \|\| round(q(j,2)) < 1 \|\| round(q(j,1)) < 1)`
262	`continue;`	265	`continue;`
263	`end`	266	`end`
264		267
265	`if(labelMask(round(q(j,2)), round(q(j,1))))`	268	`if(labelMask(round(q(j,2)), round(q(j,1))))`
266	`pointMask(j) = true;`	269	`pointMask(j) = true;`
267	`end`	270	`end`
268	`end`	271	`end`
269		272
270	`if(sum(pointMask)) < 10`	273	`if(sum(pointMask)) < 10`
271	`continue;`	274	`continue;`
272	`end`	275	`end`
273		276
274	`% project 3D points onto local plane`	277	`% project 3D points onto local plane`
275	`[~, sc, ~] = pca(Q(pointMask, :));`	278	`[~, sc, ~] = pca(Q(pointMask, :));`
276	`Qlocal = sc(:, 1:2);`	279	`Qlocal = sc(:, 1:2);`
277		280
278	`% synthetic marker in high res. space`	281	`% synthetic marker in high res. space`
279	`m = zeros(151, 151);`	282	`m = zeros(151, 151);`
280	`[x, y] = meshgrid(1:151, 1:151);`	283	`[x, y] = meshgrid(1:151, 1:151);`
281	`m((x(:)-76).^2 + (y(:)-76).^2 <= 50^2) = 1.0;`	284	`m((x(:)-76).^2 + (y(:)-76).^2 <= 50^2) = 1.0;`
282		285
283	`% relation between marker space (px) and true marker/local plane(mm)`	286	`% relation between marker space (px) and true marker/local plane(mm)`
284	`% true marker diameter is 1.75mm`	287	`% true marker diameter is 1.75mm`
285	`mScale = 101/1.8; %px/mm`	288	`mScale = 101/1.8; %px/mm`
286	`mShift = 76; %px`	289	`mShift = 76; %px`
287		290
288	`% build homography from image to marker space`	291	`% build homography from image to marker space`
289	`H = fitgeotrans(q(pointMask, 1:2), mScale*Qlocal+mShift, 'projective');`	292	`H = fitgeotrans(q(pointMask, 1:2), mScale*Qlocal+mShift, 'projective');`
290		293
291	`% bring image of marker into marker space`	294	`% bring image of marker into marker space`
292	`imMarkerSpace = imwarp(frame, H, 'OutputView', imref2d(size(m)));`	295	`imMarkerSpace = imwarp(frame, H, 'OutputView', imref2d(size(m)));`
293	`imMarkerSpace = rgb2gray(im2double(imMarkerSpace));`	296	`imMarkerSpace = rgb2gray(im2double(imMarkerSpace));`
294		297
295	`%figure; imshowpair(imMarkerSpace, m);`	298	`%figure; imshowpair(imMarkerSpace, m);`
296		299
297	`% perform image registration`	300	`% perform image registration`
298	`% might be better off using subpixel image correlation`	301	`% might be better off using subpixel image correlation`
299	`[opt, met] = imregconfig('multimodal');`	302	`[opt, met] = imregconfig('multimodal');`
300	`T = imregtform(m, imMarkerSpace, 'translation', opt, met, 'DisplayOptimization', true);`	303	`T = imregtform(m, imMarkerSpace, 'translation', opt, met, 'DisplayOptimization', false);`
301		304
302	`rege = imwarp(m, T, 'OutputView', imref2d(size(m)));`	305	`rege = imwarp(m, T, 'OutputView', imref2d(size(m)));`
303	`%figure; imshowpair(imMarkerSpace, rege);`	306	`%figure; imshowpair(imMarkerSpace, rege);`
304		307
305	`% measure of correlation`	308	`% measure of correlation`
306	`confI = sum(sum(imMarkerSpace .* rege))/sqrt(sum(sum(imMarkerSpace) * sum(sum(rege))));`	309	`confI = sum(sum(imMarkerSpace .* rege))/sqrt(sum(sum(imMarkerSpace) * sum(sum(rege))));`
307		310
308	`if confI<0.4`	311	`if confI<0.4`
309	`continue;`	312	`continue;`
310	`end`	313	`end`
311		314
312	`fprintf('Found marker with confidence: %f\n', confI);`	315	`fprintf('Found marker with confidence: %f\n', confI);`
313		316
314	`% transform marker space coordinates (76,76) to frame space`	317	`% transform marker space coordinates (76,76) to frame space`
315	`el = T.transformPointsForward([76, 76]);`	318	`el = T.transformPointsForward([76, 76]);`
316	`el = H.transformPointsInverse(el);`	319	`el = H.transformPointsInverse(el);`
317		320
318	`nMarkersFound = nMarkersFound+1;`	321	`nMarkersFound = nMarkersFound+1;`
319	`e(nMarkersFound,:) = el;`	322	`e(nMarkersFound,:) = el;`
320	`conf(nMarkersFound) = confI;`	323	`conf(nMarkersFound) = confI;`
321	`end`	324	`end`
322		325
323	`e = e(1:nMarkersFound, :);`	326	`e = e(1:nMarkersFound, :);`
324	`conf = conf(1:nMarkersFound);`	327	`conf = conf(1:nMarkersFound);`
325	`end`	328	`end`
326		329
327	`function E = projectOntoPointCloud(e, P, pointCloud)`	330	`function E = projectOntoPointCloud(e, P, pointCloud)`
328		331
329	`q = [pointCloud ones(size(pointCloud,1),1)]*P;`	332	`q = [pointCloud ones(size(pointCloud,1),1)]*P;`
330	`q = q(:,1:2)./[q(:,3) q(:,3)];`	333	`q = q(:,1:2)./[q(:,3) q(:,3)];`
331		334
332	`E = nan(size(e,1), 3);`	335	`E = nan(size(e,1), 3);`
333		336
334	`for i=1:size(e, 1)`	337	`for i=1:size(e, 1)`
335	`sqDists = sum((q - repmat(e(i,:), size(q, 1), 1)).^2, 2);`	338	`sqDists = sum((q - repmat(e(i,:), size(q, 1), 1)).^2, 2);`
336		339
337	`[sqDistsSorted, sortIdx] = sort(sqDists);`	340	`[sqDistsSorted, sortIdx] = sort(sqDists);`
338		341
339	`neighbors = (sqDistsSorted < 4.0^2);`	342	`neighbors = (sqDistsSorted < 4.0^2);`
340		343
341	`distsSorted = sqrt(sqDistsSorted(neighbors));`	344	`distsSorted = sqrt(sqDistsSorted(neighbors));`
342	`invDistsSorted = 1.0/distsSorted;`	345	`invDistsSorted = 1.0/distsSorted;`
343	`sortIdx = sortIdx(neighbors);`	346	`sortIdx = sortIdx(neighbors);`
344		347
345	`nNeighbors = sum(neighbors);`	348	`nNeighbors = sum(neighbors);`
346		349
347	`if(nNeighbors >= 2)`	350	`if(nNeighbors >= 2)`
348	`E(i, :) = 0;`	351	`E(i, :) = 0;`
349	`for j=1:nNeighbors`	352	`for j=1:nNeighbors`
350	`E(i, :) = E(i, :) + invDistsSorted(j)/sum(invDistsSorted) * pointCloud(sortIdx(j), :);`	353	`E(i, :) = E(i, :) + invDistsSorted(j)/sum(invDistsSorted) * pointCloud(sortIdx(j), :);`
351	`end`	354	`end`
352	`end`	355	`end`
353		356
354	`end`	357	`end`
355	`end`	358	`end`
356		359
357		360

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