% RANSACFITHOMOGRAPHY - fits 2D homography using RANSAC % % Usage: [H, inliers] = ransacfithomography(x1, x2, t) % % Arguments: % x1 - 2xN or 3xN set of homogeneous points. If the data is % 2xN it is assumed the homogeneous scale factor is 1. % x2 - 2xN or 3xN set of homogeneous points such that x1<->x2. % t - The distance threshold between data point and the model % used to decide whether a point is an inlier or not. % Note that point coordinates are normalised to that their % mean distance from the origin is sqrt(2). The value of % t should be set relative to this, say in the range % 0.001 - 0.01 % % Note that it is assumed that the matching of x1 and x2 are putative and it % is expected that a percentage of matches will be wrong. % % Returns: % H - The 3x3 homography such that x2 = H*x1. % inliers - An array of indices of the elements of x1, x2 that were % the inliers for the best model. % % See Also: ransac, homography2d, homography1d % Copyright (c) 2004-2005 Peter Kovesi % School of Computer Science & Software Engineering % The University of Western Australia % http://www.csse.uwa.edu.au/ % % Permission is hereby granted, free of charge, to any person obtaining a copy % of this software and associated documentation files (the "Software"), to deal % in the Software without restriction, subject to the following conditions: % % The above copyright notice and this permission notice shall be included in % all copies or substantial portions of the Software. % % The Software is provided "as is", without warranty of any kind. % February 2004 - original version % July 2004 - error in denormalising corrected (thanks to Andrew Stein) % August 2005 - homogdist2d modified to fit new ransac specification. function [H, inliers] = ransacfithomography(x1, x2, t) if ~all(size(x1)==size(x2)) error('Data sets x1 and x2 must have the same dimension'); end [rows,npts] = size(x1); if rows~=2 & rows~=3 error('x1 and x2 must have 2 or 3 rows'); end if npts < 4 error('Must have at least 4 points to fit homography'); end if rows == 2 % Pad data with homogeneous scale factor of 1 x1 = [x1; ones(1,npts)]; x2 = [x2; ones(1,npts)]; end % Normalise each set of points so that the origin is at centroid and % mean distance from origin is sqrt(2). normalise2dpts also ensures the % scale parameter is 1. Note that 'homography2d' will also call % 'normalise2dpts' but the code in 'ransac' that calls the distance % function will not - so it is best that we normalise beforehand. [x1, T1] = normalise2dpts(x1); [x2, T2] = normalise2dpts(x2); s = 4; % Minimum No of points needed to fit a homography. fittingfn = @homography2d; distfn = @homogdist2d; degenfn = @isdegenerate; % x1 and x2 are 'stacked' to create a 6xN array for ransac [H, inliers] = ransac([x1; x2], fittingfn, distfn, degenfn, s, t); % Now do a final least squares fit on the data points considered to % be inliers. H = homography2d(x1(:,inliers), x2(:,inliers)); % Denormalise H = T2\H*T1; %---------------------------------------------------------------------- % Function to evaluate the symmetric transfer error of a homography with % respect to a set of matched points as needed by RANSAC. function [inliers, H] = homogdist2d(H, x, t); x1 = x(1:3,:); % Extract x1 and x2 from x x2 = x(4:6,:); % Calculate, in both directions, the transfered points Hx1 = H*x1; invHx2 = H\x2; % Normalise so that the homogeneous scale parameter for all coordinates % is 1. x1 = hnormalise(x1); x2 = hnormalise(x2); Hx1 = hnormalise(Hx1); invHx2 = hnormalise(invHx2); d2 = sum((x1-invHx2).^2) + sum((x2-Hx1).^2); inliers = find(abs(d2) < t); %---------------------------------------------------------------------- % Function to determine if a set of 4 pairs of matched points give rise % to a degeneracy in the calculation of a homography as needed by RANSAC. % This involves testing whether any 3 of the 4 points in each set is % colinear. function r = isdegenerate(x) x1 = x(1:3,:); % Extract x1 and x2 from x x2 = x(4:6,:); r = ... iscolinear(x1(:,1),x1(:,2),x1(:,3)) | ... iscolinear(x1(:,1),x1(:,2),x1(:,4)) | ... iscolinear(x1(:,1),x1(:,3),x1(:,4)) | ... iscolinear(x1(:,2),x1(:,3),x1(:,4)) | ... iscolinear(x2(:,1),x2(:,2),x2(:,3)) | ... iscolinear(x2(:,1),x2(:,2),x2(:,4)) | ... iscolinear(x2(:,1),x2(:,3),x2(:,4)) | ... iscolinear(x2(:,2),x2(:,3),x2(:,4));