ransacfitfundmatrix.m

MATLAB Functions for Multiple View Geometry

% RANSACFITFUNDMATRIX - fits fundamental matrix using RANSAC
%
% Usage:   [F, inliers] = ransacfitfundmatrix(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

% 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] = ransacfitfundmatrix(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 = 8;  % Number of points needed to fit a fundamental matrix. Note that
            % only 7 are needed but the function 'fundmatrix' only
            % implements the 8-point solution.
    
    fittingfn = @fundmatrix;
    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 = fundmatrix(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.
%
% Note that this code allows for F being a cell array of fundamental matrices of
% which we have to pick the best one. (A 7 point solution can return up to 3
% solutions)

function [bestInliers, bestF] = funddist(F, x, t);
    
    x1 = x(1:3,:);    % Extract x1 and x2 from x
    x2 = x(4:6,:);
    
    
    if iscell(F)  % We have several solutions each of which must be tested
		  
	nF = length(F);   % Number of solutions to test
	bestF = F{1};     % Initial allocation of best solution
	ninliers = 0;     % Number of inliers
	
	for k = 1:nF
	    x2tFx1 = zeros(1,length(x1));
	    for n = 1:length(x1)
		x2tFx1(n) = x2(:,n)'*F{k}*x1(:,n);
	    end
	    
	    Fx1 = F{k}*x1;
	    Ftx2 = F{k}'*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
	    
	    if length(inliers) > ninliers   % Record best solution
		ninliers = length(inliers);
		bestF = F{k};
		bestInliers = inliers;
	    end
	end
    
    else     % We just have one solution
	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);
	
	bestInliers = find(abs(d) < t);     % Indices of inlying points
	bestF = F;                          % Copy F directly to bestF
	
    end
	


%----------------------------------------------------------------------
% (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;