Affine rectification from fitted vp

perform an affine rectification of an image. Vanishing points are estimated from families of parallel lines.Then the line at infinity is fitted to the vanishing points. The homography that maps the line at infinity to its canonical form: (0: 0: 1) rectify the image up to an affinity transformation.

Luca Magri
Politecnico di Milano
2021

load the image
interactively select f families of segments that are images of 3D parallel lines
compute the vanishing points
compute the image of the line at infinity
build the rectification matrix
rectify the image and show the result

load the image

clear;
close all;
img = imread('images/img1.JPG');
figure; imshow(img);

interactively select f families of segments that are images of 3D parallel lines

f = 4; % number of families of parallel lines
numSegmentsPerFamily = 3;
parallelLines =cell(f,1); % store parallel lines
fprintf(['Draw ', num2str(f) , ' families of parallel segments\n']);
col = 'rgbm';
for i = 1:f
    count = 1;
    parallelLines{i} = nan(numSegmentsPerFamily,3);
    while(count <=numSegmentsPerFamily)
        figure(gcf);
        title(['Draw ', num2str(numSegmentsPerFamily),' segments: step ',num2str(count) ]);
        segment1 = drawline('Color',col(i));
        parallelLines{i}(count, :) = segToLine(segment1.Position);
        count = count +1;
    end
    fprintf('Press enter to continue\n');
    pause
end

Draw 4 families of parallel segments
Press enter to continue
Press enter to continue
Press enter to continue
Press enter to continue

compute the vanishing points

V = nan(2,f);
for i =1:f
    A = parallelLines{i}(:,1:2);
    B = -parallelLines{i}(:,3);
    V(:,i) = A\B;
end

compute the image of the line at infinity

imLinfty = fitline(V);
imLinfty = imLinfty./(imLinfty(3));

figure;
hold all;
for i = 1:f
    plot(V(1,i),V(2,i),'o','Color',col(i),'MarkerSize',20,'MarkerFaceColor',col(i));
end
hold all;
imshow(img);

build the rectification matrix

H = [eye(2),zeros(2,1); imLinfty(:)'];
% we can check that H^-T* imLinfty is the line at infinity in its canonical
% form:
fprintf('The vanishing line is mapped to:\n');
disp(inv(H)'*imLinfty);

The vanishing line is mapped to:
     0
     0
     1

rectify the image and show the result

tform = projective2d(H');
J = imwarp(img,tform);

figure;
imshow(J);
imwrite(J,'images/affRect_vp.JPG');




function [l] = segToLine(pts)
% convert the endpoints of a line segment to a line in homogeneous
% coordinates.
%
% pts are the endpoits of the segment: [x1 y1;
%                                       x2 y2]

% convert endpoints to cartesian coordinates
a = [pts(1,:)';1];
b = [pts(2,:)';1];
l = cross(a,b);
l = l./norm(l);
end