Computation of 2D homography using RANSAC

Computation of 2D homography using RANSAC

Initial Images:

The first step of the algorithm is to compute interest points in each image. We are then faced with a "chicken and egg" problem: once the correspondence between the interest points is established the homography can be computed; conversely, given the homography the correspondence between the interest points can easily be established. This problem is resolved by using robust estimation, here RANSAC, as a "search engine".
The idea is first to obtain by some means a set of putative point correspondences. It is expected that a proportion of these correspondences will in fact be mismatches. RANSAC is designed to deal with exactly this situation - estimate the homography and also a set of inliers consistent with this estimate (the true correspondences), and outliers (the mismatches).



Initial Code:

thresh = 500; % Harris corner threshold
nonmaxrad = 3; % Non-maximal suppression radius
dmax = 100;
w = 11; % Window size for correlation matching

im1 = rgb2gray(imread('use1.jpg'));
im2 = rgb2gray(imread('use2.jpg'));

% Find Harris corners in image1 and image2
[cim1, r1, c1] = harris(im1, 1, thresh, 3);
show(im1,1), hold on, plot(c1,r1,'r+');

[cim2, r2, c2] = harris(im2, 1, thresh, 3);
show(im2,2), hold on, plot(c2,r2,'r+');

drawnow

tic
[m1,m2] = matchbycorrelation(im1, [r1';c1'], im2, [r2';c2'], w, dmax);
toc
% Display putative matches
show(im1,3), set(3,'name','Putative matches'), hold on 
for n = 1:length(m1);
line([m1(2,n) m2(2,n)], [m1(1,n) m2(1,n)])
end

% Assemble homogeneous feature coordinates for fitting of the
% homography matrix, note that [x,y] corresponds to [col, row]
x1 = [m1(2,:); m1(1,:); ones(1,length(m1))];
x2 = [m2(2,:); m2(1,:); ones(1,length(m1))]; 

t = .001; % Distance threshold for deciding outliers
[H, inliers] = ransacfithomography_vgg(x1, x2, t);

fprintf('Number of inliers was %d (%d%%) \n', ...
length(inliers),round(100*length(inliers)/length(m1)))
fprintf('Number of putative matches was %d \n', length(m1)) 

% Display both images overlayed with inlying matched feature points
show(double(im1)+double(im2),4), set(4,'name','Inlying matches'), hold on 
plot(m1(2,inliers),m1(1,inliers),'r+');
plot(m2(2,inliers),m2(1,inliers),'g+'); 

% Step through each matched pair of points and display the
% line linking the points on the overlayed images.

for n = inliers
line([m1(2,n) m2(2,n)], [m1(1,n) m2(1,n)],'color',[0 0 1])
end

return