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
%for i=5:5
    % 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
    g = rgb2gray(frame);
    g(g>254) = 0;
    bw = imbinarize(g, 'adaptive', 'Sensitivity', 10^(-50));
    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
    g = rgb2gray(frame);
    g(g>254) = 0;
    bw = imbinarize(g);
    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 = 101/1.4; %px/mm
        mShift = 76; %px
        
        % build homography from image to marker space
        H = fitgeotrans(q(pointMask, 1:2), mScale*Qlocal+mShift,  'projective');
        %Hdlt = Hest_DLT([mScale*Qlocal+mShift, ones(size(Qlocal, 1), 1)]', q(pointMask,:)');
        %H = projective2d(Hdlt');
        
        % 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))));
        %confI = 1.0;
        
        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
 
function H = Hest_DLT(q1, q2)
    % Estimate the homography between a set of point correspondences using the 
    % direct linear transform algorithm.
    %
    % Input:
    %           q1: 3xN matrix of homogenous point coordinates from camera 1. 
    %           q2: 3xN matrix of corresponding points from camera 2.
    % Output:
    %           H: 3x3 matrix. The Fundamental Matrix estimate. 
    %
    % Note that N must be at least 4.
    % See derivation in Aanaes, Lecture Notes on Computer Vision, 2011
 
    % Normalize points
    [T1,invT1] = normalizationMat(q1);
    q1_tilde = T1*q1;
 
    T2 = normalizationMat(q2);
    q2_tilde = T2*q2;
 
    % DLT estimation
    N = size(q1_tilde,2);
    assert(size(q2_tilde,2)==N);
 
    B = zeros(3*N,9);
 
    for i=1:N
        q1i = q1_tilde(:,i);
        q2i = q2_tilde(:,i);
        q1_x = [0 -q1i(3) q1i(2); q1i(3) 0 -q1i(1); -q1i(2) q1i(1) 0];
        biT = kron(q2i', q1_x); 
        B(3*(i-1)+1:3*i, :) = biT;
    end
 
    [U,S,~] = svd(B');
 
    [~,idx] = min(diag(S));
    h = U(:,idx);
 
    H_tilde = reshape(h, 3, 3);
 
    % Unnormalize H
    H = invT1*H_tilde*T2;
 
    % Arbitrarily chose scale
    H = H * 1/H(3,3);
end
 
function [T,invT] = normalizationMat(q)
    % Gives a normalization matrix for homogeneous coordinates
    % such that T*q will have zero mean and unit variance.
    % See Aanaes, Computer Vision Lecture Notes 2.8.2
    %
    % q: (M+1)xN matrix of N MD points in homogenous coordinates
    %
    % Extended to also efficiently compute the inverse matrix
    % DTU, 2013, Jakob Wilm
 
    [M,N] = size(q);
    M = M-1;
 
    mu = mean(q(1:M,:),2);
 
    q_bar = q(1:M,:)-repmat(mu,1,N);
 
    s = mean(sqrt(diag(q_bar'*q_bar)))/sqrt(2);
 
    T = [eye(M)/s, -mu/s; zeros(1,M) 1];
 
    invT = [eye(M)*s, mu; zeros(1,M) 1];
end
 
Generated by GNU Enscript 1.6.6.
 
 
 

Rev 219	Rev 236
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	`%for i=5:5`
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<3.0, :);`	83	`E{i} = E{i}(e<3.0, :);`
84	`display(e);`	84	`display(e);`
85		85
86	`% write point cloud with marker (debugging)`	86	`% write point cloud with marker (debugging)`
87	`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)]);`
88	`pcwrite(pcDebug, 'pcDebug.ply');`	88	`pcwrite(pcDebug, 'pcDebug.ply');`
89		89
90	`% bring markers into initial alignment`	90	`% bring markers into initial alignment`
91	`[U,~,V] = svd(initialAlign(i).Rotation);`	91	`[U,~,V] = svd(initialAlign(i).Rotation);`
92	`Ri = U*V';`	92	`Ri = U*V';`
93	`Ti = initialAlign(i).Translation;`	93	`Ti = initialAlign(i).Translation;`
94		94
95	`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);`
96	`end`	96	`end`
97		97
98	`% show found markers in initial alignment`	98	`% show found markers in initial alignment`
99	`figure;`	99	`figure;`
100	`hold('on');`	100	`hold('on');`
101	`for i=1:nSubScans`	101	`for i=1:nSubScans`
102	`% fix Ri to be orthogonal`	102	`% fix Ri to be orthogonal`
103	`[U,~,V] = svd(initialAlign(i).Rotation);`	103	`[U,~,V] = svd(initialAlign(i).Rotation);`
104	`Ri = U*V';`	104	`Ri = U*V';`
105		105
106	`% bring point cloud into initial alignment`	106	`% bring point cloud into initial alignment`
107	`pc = pcread(initialAlign(i).FileName);`	107	`pc = pcread(initialAlign(i).FileName);`
108	`tform = affine3d([Ri' [0;0;0]; initialAlign(i).Translation' 1]);`	108	`tform = affine3d([Ri' [0;0;0]; initialAlign(i).Translation' 1]);`
109	`pcg = pctransform(pc, tform);`	109	`pcg = pctransform(pc, tform);`
110		110
111	`pcshow(pcg);`	111	`pcshow(pcg);`
112	`xlabel('x');`	112	`xlabel('x');`
113	`ylabel('y');`	113	`ylabel('y');`
114	`zlabel('z');`	114	`zlabel('z');`
115		115
116	`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);`
117	`title('Initial Alignment');`	117	`title('Initial Alignment');`
118	`end`	118	`end`
119		119
120	`% match markers between poses using initial alignment`	120	`% match markers between poses using initial alignment`
121	`Pg = {};`	121	`Pg = {};`
122	`P = {};`	122	`P = {};`
123	`for i=1:nSubScans`	123	`for i=1:nSubScans`
124	`for j=1:size(Eg{i}, 1)`	124	`for j=1:size(Eg{i}, 1)`
125	`pg = Eg{i}(j,:);`	125	`pg = Eg{i}(j,:);`
126	`p = E{i}(j,:);`	126	`p = E{i}(j,:);`
127	`matched = false;`	127	`matched = false;`
128	`for k=1:size(Pg, 2)`	128	`for k=1:size(Pg, 2)`
129	`clusterCenter = mean(cat(1, Pg{:,k}), 1);`	129	`clusterCenter = mean(cat(1, Pg{:,k}), 1);`
130	`if(sum((pg - clusterCenter).^2) < 3^2)`	130	`if(sum((pg - clusterCenter).^2) < 3^2)`
131	`% store in global frame`	131	`% store in global frame`
132	`Pg{i,k} = pg;`	132	`Pg{i,k} = pg;`
133	`% store in local frame`	133	`% store in local frame`
134	`P{i,k} = p;`	134	`P{i,k} = p;`
135	`matched = true;`	135	`matched = true;`
136	`break;`	136	`break;`
137	`end`	137	`end`
138	`end`	138	`end`
139	`% create new cluster`	139	`% create new cluster`
140	`if(not(matched))`	140	`if(not(matched))`
141	`Pg{i,end+1} = pg;`	141	`Pg{i,end+1} = pg;`
142	`P{i,end+1} = p;`	142	`P{i,end+1} = p;`
143	`end`	143	`end`
144	`end`	144	`end`
145	`end`	145	`end`
146		146
147	`% run optimization`	147	`% run optimization`
148	`alignment = groupwiseOrthogonalProcrustes(P, initialAlign);`	148	`alignment = groupwiseOrthogonalProcrustes(P, initialAlign);`
149		149
150	`% show found markers in optimized alignment`	150	`% show found markers in optimized alignment`
151	`figure;`	151	`figure;`
152	`hold('on');`	152	`hold('on');`
153	`for i=1:nSubScans`	153	`for i=1:nSubScans`
154	`% fix Ri to be orthogonal`	154	`% fix Ri to be orthogonal`
155	`[U,~,V] = svd(alignment(i).Rotation);`	155	`[U,~,V] = svd(alignment(i).Rotation);`
156	`Ri = U*V';`	156	`Ri = U*V';`
157	`Ti = alignment(i).Translation;`	157	`Ti = alignment(i).Translation;`
158		158
159	`Ea = E{i}*Ri' + repmat(Ti', size(E{i}, 1), 1);`	159	`Ea = E{i}*Ri' + repmat(Ti', size(E{i}, 1), 1);`
160		160
161	`% bring point cloud into optimized alignment`	161	`% bring point cloud into optimized alignment`
162	`pc = pcread(initialAlign(i).FileName);`	162	`pc = pcread(initialAlign(i).FileName);`
163	`tform = affine3d([Ri' [0;0;0]; initialAlign(i).Translation' 1]);`	163	`tform = affine3d([Ri' [0;0;0]; initialAlign(i).Translation' 1]);`
164	`pcg = pctransform(pc, tform);`	164	`pcg = pctransform(pc, tform);`
165		165
166	`pcshow(pcg);`	166	`pcshow(pcg);`
167	`xlabel('x');`	167	`xlabel('x');`
168	`ylabel('y');`	168	`ylabel('y');`
169	`zlabel('z');`	169	`zlabel('z');`
170		170
171	`plot3(Ea(:,1), Ea(:,2), Ea(:,3), '.', 'MarkerSize', 15);`	171	`plot3(Ea(:,1), Ea(:,2), Ea(:,3), '.', 'MarkerSize', 15);`
172	`title('Optimized Alignment');`	172	`title('Optimized Alignment');`
173	`end`	173	`end`
174		174
175	`% write to ALN file`	175	`% write to ALN file`
176	`for i=1:length(alignment)`	176	`for i=1:length(alignment)`
177	`alignment(i).FileName = initialAlign(i).FileName;`	177	`alignment(i).FileName = initialAlign(i).FileName;`
178	`end`	178	`end`
179		179
180	`writeMeshLabALN(alignment, strrep(alnFileName, '.aln', 'Optimized.aln'));`	180	`writeMeshLabALN(alignment, strrep(alnFileName, '.aln', 'Optimized.aln'));`
181		181
182	`end`	182	`end`
183		183
184	`function e = autoDetectMarkers(frame, P, pointCloud)`	184	`function e = autoDetectMarkers(frame, P, pointCloud)`
185		185
186	`% create mask based on morphology`	186	`% create mask based on morphology`
187	`bw = imbinarize(rgb2gray(frame));`	187	`g = rgb2gray(frame);`
-		188	`g(g>254) = 0;`
-		189	`bw = imbinarize(g, 'adaptive', 'Sensitivity', 10^(-50));`
188	`cc = bwconncomp(bw);`	190	`cc = bwconncomp(bw);`
189	`rp = regionprops(cc, 'Area', 'Solidity', 'Eccentricity', 'Centroid');`	191	`rp = regionprops(cc, 'Area', 'Solidity', 'Eccentricity', 'Centroid');`
190	`idx = ([rp.Area] > 100 & [rp.Area] < 1000 & [rp.Solidity] > 0.9);`	192	`idx = ([rp.Area] > 100 & [rp.Area] < 1000 & [rp.Solidity] > 0.9);`
191		193
192	`initialGuesses = cat(1, rp(idx).Centroid);`	194	`initialGuesses = cat(1, rp(idx).Centroid);`
193		195
194	`[e, ~] = detectMarkersSubpix(frame, initialGuesses, P, pointCloud);`	196	`[e, ~] = detectMarkersSubpix(frame, initialGuesses, P, pointCloud);`
195		197
196	`figure;`	198	`figure;`
197	`imshow(frame);`	199	`imshow(frame);`
198	`hold('on');`	200	`hold('on');`
199	`plot(e(:,1), e(:,2), 'rx', 'MarkerSize', 15);`	201	`plot(e(:,1), e(:,2), 'rx', 'MarkerSize', 15);`
200	`drawnow;`	202	`drawnow;`
201	`end`	203	`end`
202		204
203	`function e = manuallyDetectMarkers(frame, P, pointCloud)`	205	`function e = manuallyDetectMarkers(frame, P, pointCloud)`
204		206
205	`e = [];`	207	`e = [];`
206	`%edges = edge(rgb2gray(frame), 'Canny', [0.08 0.1], 2);`	208	`%edges = edge(rgb2gray(frame), 'Canny', [0.08 0.1], 2);`
207		209
208	`figure;`	210	`figure;`
209	`hold('on');`	211	`hold('on');`
210	`imshow(frame);`	212	`imshow(frame);`
211	`title('Close figure to end.');`	213	`title('Close figure to end.');`
212	`set(gcf, 'pointer', 'crosshair');`	214	`set(gcf, 'pointer', 'crosshair');`
213	`set(gcf, 'WindowButtonDownFcn', @clickCallback);`	215	`set(gcf, 'WindowButtonDownFcn', @clickCallback);`
214		216
215	`uiwait;`	217	`uiwait;`
216		218
217	`function clickCallback(caller, ~)`	219	`function clickCallback(caller, ~)`
218		220
219	`p = get(gca, 'CurrentPoint');`	221	`p = get(gca, 'CurrentPoint');`
220	`p = p(1, 1:2);`	222	`p = p(1, 1:2);`
221		223
222	`[el, ~] = detectMarkersSubpix(frame, p, P, pointCloud);`	224	`[el, ~] = detectMarkersSubpix(frame, p, P, pointCloud);`
223	`e = [e; el(:, 1:2)];`	225	`e = [e; el(:, 1:2)];`
224		226
225	`if(not(isempty(el)))`	227	`if(not(isempty(el)))`
226	`figure(caller);`	228	`figure(caller);`
227	`hold('on');`	229	`hold('on');`
228	`plot(el(1), el(2), 'rx', 'MarkerSize', 15);`	230	`plot(el(1), el(2), 'rx', 'MarkerSize', 15);`
229	`end`	231	`end`
230	`end`	232	`end`
231		233
232	`end`	234	`end`
233		235
234	`function [e, conf] = detectMarkersSubpix(frame, initGuesses, P, Q)`	236	`function [e, conf] = detectMarkersSubpix(frame, initGuesses, P, Q)`
235		237
236	`% create mask based on morphology`	238	`% create mask based on morphology`
237	`bw = imbinarize(rgb2gray(frame));`	239	`g = rgb2gray(frame);`
-		240	`g(g>254) = 0;`
-		241	`bw = imbinarize(g);`
238	`cc = bwconncomp(bw);`	242	`cc = bwconncomp(bw);`
239	`labels = labelmatrix(cc);`	243	`labels = labelmatrix(cc);`
240		244
241	`% project point cloud into image`	245	`% project point cloud into image`
242	`q = [Q ones(size(Q,1),1)]*P;`	246	`q = [Q ones(size(Q,1),1)]*P;`
243	`q = q./[q(:,3) q(:,3) q(:,3)];`	247	`q = q./[q(:,3) q(:,3) q(:,3)];`
244		248
245	`e = zeros(size(initGuesses));`	249	`e = zeros(size(initGuesses));`
246	`conf = zeros(size(initGuesses, 1), 1);`	250	`conf = zeros(size(initGuesses, 1), 1);`
247		251
248	`nMarkersFound = 0;`	252	`nMarkersFound = 0;`
249		253
250	`for i=1:size(initGuesses, 1)`	254	`for i=1:size(initGuesses, 1)`
251		255
252	`labelId = labels(round(initGuesses(i,2)), round(initGuesses(i,1)));`	256	`labelId = labels(round(initGuesses(i,2)), round(initGuesses(i,1)));`
253	`labelMask = (labels == labelId);`	257	`labelMask = (labels == labelId);`
254	`labelMask = imdilate(labelMask, strel('disk', 3, 0));`	258	`labelMask = imdilate(labelMask, strel('disk', 3, 0));`
255		259
256	`if(sum(sum(labelMask)) < 10 \|\| sum(sum(labelMask)) > 1000)`	260	`if(sum(sum(labelMask)) < 10 \|\| sum(sum(labelMask)) > 1000)`
257	`continue;`	261	`continue;`
258	`end`	262	`end`
259		263
260	`% determine 3D points that are part of the marker`	264	`% determine 3D points that are part of the marker`
261	`% note: we should probably undistort labelMask`	265	`% note: we should probably undistort labelMask`
262	`pointMask = false(size(q, 1), 1);`	266	`pointMask = false(size(q, 1), 1);`
263	`for j=1:size(q,1)`	267	`for j=1:size(q,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)`	268	`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)`
265	`continue;`	269	`continue;`
266	`end`	270	`end`
267		271
268	`if(labelMask(round(q(j,2)), round(q(j,1))))`	272	`if(labelMask(round(q(j,2)), round(q(j,1))))`
269	`pointMask(j) = true;`	273	`pointMask(j) = true;`
270	`end`	274	`end`
271	`end`	275	`end`
272		276
273	`if(sum(pointMask)) < 10`	277	`if(sum(pointMask)) < 10`
274	`continue;`	278	`continue;`
275	`end`	279	`end`
276		280
277	`% project 3D points onto local plane`	281	`% project 3D points onto local plane`
278	`[~, sc, ~] = pca(Q(pointMask, :));`	282	`[~, sc, ~] = pca(Q(pointMask, :));`
279	`Qlocal = sc(:, 1:2);`	283	`Qlocal = sc(:, 1:2);`
280		284
281	`% synthetic marker in high res. space`	285	`% synthetic marker in high res. space`
282	`m = zeros(151, 151);`	286	`m = zeros(151, 151);`
283	`[x, y] = meshgrid(1:151, 1:151);`	287	`[x, y] = meshgrid(1:151, 1:151);`
284	`m((x(:)-76).^2 + (y(:)-76).^2 <= 50^2) = 1.0;`	288	`m((x(:)-76).^2 + (y(:)-76).^2 <= 50^2) = 1.0;`
285		289
286	`% relation between marker space (px) and true marker/local plane(mm)`	290	`% relation between marker space (px) and true marker/local plane(mm)`
287	`% true marker diameter is 1.75mm`	291	`% true marker diameter is 1.75mm`
288	`mScale = 101/1.8; %px/mm`	292	`mScale = 101/1.4; %px/mm`
289	`mShift = 76; %px`	293	`mShift = 76; %px`
290		294
291	`% build homography from image to marker space`	295	`% build homography from image to marker space`
292	`%H = fitgeotrans(q(pointMask, 1:2), mScale*Qlocal+mShift, 'projective');`	296	`H = fitgeotrans(q(pointMask, 1:2), mScale*Qlocal+mShift, 'projective');`
293	`Hdlt = Hest_DLT([mScale*Qlocal+mShift, ones(size(Qlocal, 1), 1)]', q(pointMask,:)');`	297	`%Hdlt = Hest_DLT([mScale*Qlocal+mShift, ones(size(Qlocal, 1), 1)]', q(pointMask,:)');`
294	`H = projective2d(Hdlt');`	298	`%H = projective2d(Hdlt');`
295		299
296	`% bring image of marker into marker space`	300	`% bring image of marker into marker space`
297	`imMarkerSpace = imwarp(frame, H, 'OutputView', imref2d(size(m)));`	301	`imMarkerSpace = imwarp(frame, H, 'OutputView', imref2d(size(m)));`
298	`imMarkerSpace = rgb2gray(im2double(imMarkerSpace));`	302	`imMarkerSpace = rgb2gray(im2double(imMarkerSpace));`
299		303
300	`%figure; imshowpair(imMarkerSpace, m);`	304	`%figure; imshowpair(imMarkerSpace, m);`
301		305
302	`% perform image registration`	306	`% perform image registration`
303	`% might be better off using subpixel image correlation`	307	`% might be better off using subpixel image correlation`
304	`[opt, met] = imregconfig('multimodal');`	308	`[opt, met] = imregconfig('multimodal');`
305	`T = imregtform(m, imMarkerSpace, 'translation', opt, met, 'DisplayOptimization', false);`	309	`T = imregtform(m, imMarkerSpace, 'translation', opt, met, 'DisplayOptimization', false);`
306		310
307	`rege = imwarp(m, T, 'OutputView', imref2d(size(m)));`	311	`rege = imwarp(m, T, 'OutputView', imref2d(size(m)));`
308	`%figure; imshowpair(imMarkerSpace, rege);`	312	`%figure; imshowpair(imMarkerSpace, rege);`
309		313
310	`% measure of correlation`	314	`% measure of correlation`
311	`confI = sum(sum(imMarkerSpace .* rege))/sqrt(sum(sum(imMarkerSpace) * sum(sum(rege))));`	315	`confI = sum(sum(imMarkerSpace .* rege))/sqrt(sum(sum(imMarkerSpace) * sum(sum(rege))));`
312	`confI = 1.0;`	316	`%confI = 1.0;`
313		317
314	`if confI<0.4`	318	`if confI<0.4`
315	`continue;`	319	`continue;`
316	`end`	320	`end`
317		321
318	`fprintf('Found marker with confidence: %f\n', confI);`	322	`fprintf('Found marker with confidence: %f\n', confI);`
319		323
320	`% transform marker space coordinates (76,76) to frame space`	324	`% transform marker space coordinates (76,76) to frame space`
321	`el = T.transformPointsForward([76, 76]);`	325	`el = T.transformPointsForward([76, 76]);`
322	`el = H.transformPointsInverse(el);`	326	`el = H.transformPointsInverse(el);`
323		327
324	`nMarkersFound = nMarkersFound+1;`	328	`nMarkersFound = nMarkersFound+1;`
325	`e(nMarkersFound,:) = el;`	329	`e(nMarkersFound,:) = el;`
326	`conf(nMarkersFound) = confI;`	330	`conf(nMarkersFound) = confI;`
327	`end`	331	`end`
328		332
329	`e = e(1:nMarkersFound, :);`	333	`e = e(1:nMarkersFound, :);`
330	`conf = conf(1:nMarkersFound);`	334	`conf = conf(1:nMarkersFound);`
331	`end`	335	`end`
332		336
333	`function E = projectOntoPointCloud(e, P, pointCloud)`	337	`function E = projectOntoPointCloud(e, P, pointCloud)`
334		338
335	`q = [pointCloud ones(size(pointCloud,1),1)]*P;`	339	`q = [pointCloud ones(size(pointCloud,1),1)]*P;`
336	`q = q(:,1:2)./[q(:,3) q(:,3)];`	340	`q = q(:,1:2)./[q(:,3) q(:,3)];`
337		341
338	`E = nan(size(e,1), 3);`	342	`E = nan(size(e,1), 3);`
339		343
340	`for i=1:size(e, 1)`	344	`for i=1:size(e, 1)`
341	`sqDists = sum((q - repmat(e(i,:), size(q, 1), 1)).^2, 2);`	345	`sqDists = sum((q - repmat(e(i,:), size(q, 1), 1)).^2, 2);`
342		346
343	`[sqDistsSorted, sortIdx] = sort(sqDists);`	347	`[sqDistsSorted, sortIdx] = sort(sqDists);`
344		348
345	`neighbors = (sqDistsSorted < 4.0^2);`	349	`neighbors = (sqDistsSorted < 4.0^2);`
346		350
347	`distsSorted = sqrt(sqDistsSorted(neighbors));`	351	`distsSorted = sqrt(sqDistsSorted(neighbors));`
348	`invDistsSorted = 1.0/distsSorted;`	352	`invDistsSorted = 1.0/distsSorted;`
349	`sortIdx = sortIdx(neighbors);`	353	`sortIdx = sortIdx(neighbors);`
350		354
351	`nNeighbors = sum(neighbors);`	355	`nNeighbors = sum(neighbors);`
352		356
353	`if(nNeighbors >= 2)`	357	`if(nNeighbors >= 2)`
354	`E(i, :) = 0;`	358	`E(i, :) = 0;`
355	`for j=1:nNeighbors`	359	`for j=1:nNeighbors`
356	`E(i, :) = E(i, :) + invDistsSorted(j)/sum(invDistsSorted) * pointCloud(sortIdx(j), :);`	360	`E(i, :) = E(i, :) + invDistsSorted(j)/sum(invDistsSorted) * pointCloud(sortIdx(j), :);`
357	`end`	361	`end`
358	`end`	362	`end`
359		363
360	`end`	364	`end`
361	`end`	365	`end`
362		366
363	`function H = Hest_DLT(q1, q2)`	367	`function H = Hest_DLT(q1, q2)`
364	`% Estimate the homography between a set of point correspondences using the`	368	`% Estimate the homography between a set of point correspondences using the`
365	`% direct linear transform algorithm.`	369	`% direct linear transform algorithm.`
366	`%`	370	`%`
367	`% Input:`	371	`% Input:`
368	`% q1: 3xN matrix of homogenous point coordinates from camera 1.`	372	`% q1: 3xN matrix of homogenous point coordinates from camera 1.`
369	`% q2: 3xN matrix of corresponding points from camera 2.`	373	`% q2: 3xN matrix of corresponding points from camera 2.`
370	`% Output:`	374	`% Output:`
371	`% H: 3x3 matrix. The Fundamental Matrix estimate.`	375	`% H: 3x3 matrix. The Fundamental Matrix estimate.`
372	`%`	376	`%`
373	`% Note that N must be at least 4.`	377	`% Note that N must be at least 4.`
374	`% See derivation in Aanaes, Lecture Notes on Computer Vision, 2011`	378	`% See derivation in Aanaes, Lecture Notes on Computer Vision, 2011`
375		379
376	`% Normalize points`	380	`% Normalize points`
377	`[T1,invT1] = normalizationMat(q1);`	381	`[T1,invT1] = normalizationMat(q1);`
378	`q1_tilde = T1*q1;`	382	`q1_tilde = T1*q1;`
379		383
380	`T2 = normalizationMat(q2);`	384	`T2 = normalizationMat(q2);`
381	`q2_tilde = T2*q2;`	385	`q2_tilde = T2*q2;`
382		386
383	`% DLT estimation`	387	`% DLT estimation`
384	`N = size(q1_tilde,2);`	388	`N = size(q1_tilde,2);`
385	`assert(size(q2_tilde,2)==N);`	389	`assert(size(q2_tilde,2)==N);`
386		390
387	`B = zeros(3*N,9);`	391	`B = zeros(3*N,9);`
388		392
389	`for i=1:N`	393	`for i=1:N`
390	`q1i = q1_tilde(:,i);`	394	`q1i = q1_tilde(:,i);`
391	`q2i = q2_tilde(:,i);`	395	`q2i = q2_tilde(:,i);`
392	`q1_x = [0 -q1i(3) q1i(2); q1i(3) 0 -q1i(1); -q1i(2) q1i(1) 0];`	396	`q1_x = [0 -q1i(3) q1i(2); q1i(3) 0 -q1i(1); -q1i(2) q1i(1) 0];`
393	`biT = kron(q2i', q1_x);`	397	`biT = kron(q2i', q1_x);`
394	`B(3(i-1)+1:3i, :) = biT;`	398	`B(3(i-1)+1:3i, :) = biT;`
395	`end`	399	`end`
396		400
397	`[U,S,~] = svd(B');`	401	`[U,S,~] = svd(B');`
398		402
399	`[~,idx] = min(diag(S));`	403	`[~,idx] = min(diag(S));`
400	`h = U(:,idx);`	404	`h = U(:,idx);`
401		405
402	`H_tilde = reshape(h, 3, 3);`	406	`H_tilde = reshape(h, 3, 3);`
403		407
404	`% Unnormalize H`	408	`% Unnormalize H`
405	`H = invT1H_tildeT2;`	409	`H = invT1H_tildeT2;`
406		410
407	`% Arbitrarily chose scale`	411	`% Arbitrarily chose scale`
408	`H = H * 1/H(3,3);`	412	`H = H * 1/H(3,3);`
409	`end`	413	`end`
410		414
411	`function [T,invT] = normalizationMat(q)`	415	`function [T,invT] = normalizationMat(q)`
412	`% Gives a normalization matrix for homogeneous coordinates`	416	`% Gives a normalization matrix for homogeneous coordinates`
413	`% such that T*q will have zero mean and unit variance.`	417	`% such that T*q will have zero mean and unit variance.`
414	`% See Aanaes, Computer Vision Lecture Notes 2.8.2`	418	`% See Aanaes, Computer Vision Lecture Notes 2.8.2`
415	`%`	419	`%`
416	`% q: (M+1)xN matrix of N MD points in homogenous coordinates`	420	`% q: (M+1)xN matrix of N MD points in homogenous coordinates`
417	`%`	421	`%`
418	`% Extended to also efficiently compute the inverse matrix`	422	`% Extended to also efficiently compute the inverse matrix`
419	`% DTU, 2013, Jakob Wilm`	423	`% DTU, 2013, Jakob Wilm`
420		424
421	`[M,N] = size(q);`	425	`[M,N] = size(q);`
422	`M = M-1;`	426	`M = M-1;`
423		427
424	`mu = mean(q(1:M,:),2);`	428	`mu = mean(q(1:M,:),2);`
425		429
426	`q_bar = q(1:M,:)-repmat(mu,1,N);`	430	`q_bar = q(1:M,:)-repmat(mu,1,N);`
427		431
428	`s = mean(sqrt(diag(q_bar'*q_bar)))/sqrt(2);`	432	`s = mean(sqrt(diag(q_bar'*q_bar)))/sqrt(2);`
429		433
430	`T = [eye(M)/s, -mu/s; zeros(1,M) 1];`	434	`T = [eye(M)/s, -mu/s; zeros(1,M) 1];`
431		435
432	`invT = [eye(M)*s, mu; zeros(1,M) 1];`	436	`invT = [eye(M)*s, mu; zeros(1,M) 1];`
433	`end`	437	`end`
434		438
435	`Generated by GNU Enscript 1.6.6.`	439	`Generated by GNU Enscript 1.6.6.`
436		440
437		441
438		442

Subversion Repositories seema-scanner

(root)/matlab/alignSubScansMarkers.m – Rev 219 → 236