% RANSACFITHOMOGRAPHY - fits 2D homography using RANSAC%% Usage:   [H, inliers] = ransacfithomography_vgg(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% Peter Kovesi  % School of Computer Science & Software Engineering% The University of Western Australia% pk at csse uwa edu au% http://www.csse.uwa.edu.au/~pk%% February 2004 - original version% July     2004 - error in denormalising corrected (thanks to Andrew Stein)% Adapted to use vgg functions by Peter Kovesi and Andrew Zissermanfunction [H, inliers] = ransacfithomography_vgg(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 = @wrap_vgg_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.    Hlin = vgg_H_from_x_lin(x1(:,inliers), x2(:,inliers));    H = vgg_H_from_x_nonlin(Hlin,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 d2 = homogdist2d(H, x);        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);        %----------------------------------------------------------------------% 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));    function H = wrap_vgg_homography2d(x)     xs1 = x(1:3,:);     xs2 = x(4:6,:);      H = vgg_H_from_x_lin(xs1,xs2);