% RANSACFITAFFINEFUND - fits affine fundamental matrix using RANSAC % % Usage: [F, inliers] = ransacfitaffinefund(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: % F - The 3x3 fundamental matrix such that x2'Fx1 = 0. % inliers - An array of indices of the elements of x1, x2 that were % the inliers for the best model. % % See Also: RANSAC, FUNDMATRIX AFFINEFUNDMATRIX % 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 % August 2005 Distance error function changed to match changes in RANSAC function [F, inliers] = ransacfitaffinefund(x1, x2, t, feedback) if ~all(size(x1)==size(x2)) error('Data sets x1 and x2 must have the same dimension'); end if nargin == 3 feedback = 0; end [rows,npts] = size(x1); if rows~=2 & rows~=3 error('x1 and x2 must have 2 or 3 rows'); 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 'fundmatrix' 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; % Number of points needed to fit an affine fundamental matrix. fittingfn = @affinefundmatrix; distfn = @funddist; degenfn = @isdegenerate; % x1 and x2 are 'stacked' to create a 6xN array for ransac [F, inliers] = ransac([x1; x2], fittingfn, distfn, degenfn, s, t, feedback); % Now do a final least squares fit on the data points considered to % be inliers. F = affinefundmatrix(x1(:,inliers), x2(:,inliers)); % Denormalise F = T2'*F*T1; %-------------------------------------------------------------------------- % Function to evaluate the first order approximation of the geometric error % (Sampson distance) of the fit of a fundamental matrix with respect to a % set of matched points as needed by RANSAC. See: Hartley and Zisserman, % 'Multiple View Geometry in Computer Vision', page 270. function [inliers, F] = funddist(F, x, t); x1 = x(1:3,:); % Extract x1 and x2 from x x2 = x(4:6,:); x2tFx1 = zeros(1,length(x1)); for n = 1:length(x1) x2tFx1(n) = x2(:,n)'*F*x1(:,n); end Fx1 = F*x1; Ftx2 = F'*x2; % Evaluate distances d = x2tFx1.^2 ./ ... (Fx1(1,:).^2 + Fx1(2,:).^2 + Ftx2(1,:).^2 + Ftx2(2,:).^2); inliers = find(abs(d) < t); % Indices of inlying points %---------------------------------------------------------------------- % (Degenerate!) function to determine if a set of matched points will result % in a degeneracy in the calculation of a fundamental matrix as needed by % RANSAC. This function assumes this cannot happen... function r = isdegenerate(x) r = 0;