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Stratified metric promotion after affine rectification

perform metric rectification of an image, after affine rectification. Given two pairs of image of orthogonal lines, the script finds the image of the dual conic to circular points and computes the homography that brings it back to its canonical form

Luca Magri
Politecnico di Milano
2020

close all;
clear all;
clc;
imgAffRect = imread('images/affRect_vp.JPG');


figure;
imshow(imgAffRect);
numConstraints = 5; % 2 is the minimum number

hold all;
fprintf('Draw pairs of orthogonal segments\n');
count = 1;
A = zeros(numConstraints,3);
% select pairs of orthogonal segments
while (count <=numConstraints)
    figure(gcf);
    title('Select pairs of orthogonal segments')
    col = 'rgbcmykwrgbcmykw';
    segment1 = drawline('Color',col(count));
    segment2 = drawline('Color',col(count));

    l = segToLine(segment1.Position);
    m = segToLine(segment2.Position);

    % each pair of orthogonal lines gives rise to a constraint on s
    % [l(1)*m(1),l(1)*m(2)+l(2)*m(1), l(2)*m(2)]*s = 0
    % store the constraints in a matrix A
     A(count,:) = [l(1)*m(1),l(1)*m(2)+l(2)*m(1), l(2)*m(2)];

    count = count+1;
end

Draw pairs of orthogonal segments

solve the system

%S = [x(1) x(2); x(2) 1];
[~,~,v] = svd(A);
s = v(:,end); %[s11,s12,s22];
S = [s(1),s(2); s(2),s(3)];

compute the rectifying homography

imDCCP = [S,zeros(2,1); zeros(1,3)]; % the image of the circular points
[U,D,V] = svd(S);
A = U*sqrt(D)*V';
H = eye(3);
H(1,1) = A(1,1);
H(1,2) = A(1,2);
H(2,1) = A(2,1);
H(2,2) = A(2,2);

Hrect = inv(H);
Cinfty = [eye(2),zeros(2,1);zeros(1,3)];

tform = projective2d(Hrect');
J = imwarp(imgAffRect,tform);

figure;
imshow(J);

Published with MATLAB® R2021a