% RANSAC - Robustly fits a model to data with the RANSAC algorithm%% Usage:%% [M, inliers] = ransac(x, fittingfn, distfn, degenfn s, t, feedback, ...%                       maxDataTrials, maxTrials)%% Arguments:%     x         - Data sets to which we are seeking to fit a model M%                 It is assumed that x is of size [d x Npts]%                 where d is the dimensionality of the data and Npts is%                 the number of data points.%%     fittingfn - Handle to a function that fits a model to s%                 data from x.  It is assumed that the function is of the%                 form: %                    M = fittingfn(x)%                 Note it is possible that the fitting function can return%                 multiple models (for example up to 3 fundamental matrices%                 can be fitted to 7 matched points).  In this case it is%                 assumed that the fitting function returns a cell array of%                 models.%                 If this function cannot fit a model it should return M as%                 an empty matrix.%%     distfn    - Handle to a function that evaluates the%                 distances from the model to data x.%                 It is assumed that the function is of the form:%                    [inliers, M] = distfn(M, x, t)%                 This function must evaluate the distances between points%                 and the model returning the indices of elements in x that%                 are inliers, that is, the points that are within distance%                 't' of the model.  Additionally, if M is a cell array of%                 possible models 'distfn' will return the model that has the%                 most inliers.  If there is only one model this function%                 must still copy the model to the output.  After this call M%                 will be a non-cell object representing only one model. %%     degenfn   - Handle to a function that determines whether a%                 set of datapoints will produce a degenerate model.%                 This is used to discard random samples that do not%                 result in useful models.%                 It is assumed that degenfn is a boolean function of%                 the form: %                    r = degenfn(x)%                 It may be that you cannot devise a test for degeneracy in%                 which case you should write a dummy function that always%                 returns a value of 1 (true) and rely on 'fittingfn' to return%                 an empty model should the data set be degenerate.%%     s         - The minimum number of samples from x required by%                 fittingfn to fit a model.%%     t         - The distance threshold between a data point and the model%                 used to decide whether the point is an inlier or not.%%     feedback  - An optional flag 0/1. If set to one the trial count and the%                 estimated total number of trials required is printed out at%                 each step.  Defaults to 0.%%     maxDataTrials - Maximum number of attempts to select a non-degenerate%                     data set. This parameter is optional and defaults to 100.%%     maxTrials - Maximum number of iterations. This parameter is optional and%                 defaults to 1000.%% Returns:%     M         - The model having the greatest number of inliers.%     inliers   - An array of indices of the elements of x that were%                 the inliers for the best model.%% For an example of the use of this function see RANSACFITHOMOGRAPHY or% RANSACFITPLANE % References:%    M.A. Fishler and  R.C. Boles. "Random sample concensus: A paradigm%    for model fitting with applications to image analysis and automated%    cartography". Comm. Assoc. Comp, Mach., Vol 24, No 6, pp 381-395, 1981%%    Richard Hartley and Andrew Zisserman. "Multiple View Geometry in%    Computer Vision". pp 101-113. Cambridge University Press, 2001% Copyright (c) 2003-2006 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% % 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.%% May      2003 - Original version% February 2004 - Tidied up.% August   2005 - Specification of distfn changed to allow model fitter to%                 return multiple models from which the best must be selected% Sept     2006 - Random selection of data points changed to ensure duplicate%                 points are not selected.% February 2007 - Jordi Ferrer: Arranged warning printout.%                               Allow maximum trials as optional parameters.%                               Patch the problem when non-generated data%                               set is not given in the first iteration.% August   2008 - 'feedback' parameter restored to argument list and other%                 breaks in code introduced in last update fixed.% function [M, inliers] = ransac(x, fittingfn, distfn, degenfn, s, t, feedback, ...                               maxDataTrials, MaxTrials)    % Test number of parameters    error ( nargchk ( 6, 9, nargin ) );    error ( nargoutchk ( 2, 2, nargout ) );        if nargin < 9; maxTrials = 1000;    end;     if nargin < 8; maxDataTrials = 100; end;     if nargin < 7; feedback = 0;        end;        [rows, npts] = size(x);                         p = 0.99;         % Desired probability of choosing at least one sample                      % free from outliers    bestM = NaN;      % Sentinel value allowing detection of solution failure.    trialcount = 0;    bestscore =  0;        N = 1;            % Dummy initialisation for number of trials.        while N > trialcount                % Select at random s datapoints to form a trial model, M.        % In selecting these points we have to check that they are not in        % a degenerate configuration.        degenerate = 1;        count = 1;        while degenerate            % Generate s random indicies in the range 1..npts            % (If you do not have the statistics toolbox, or are using Octave,            % use the function RANDOMSAMPLE from my webpage)            ind = randsample(npts, s);            % Test that these points are not a degenerate configuration.            degenerate = feval(degenfn, x(:,ind));                        if ~degenerate                 % Fit model to this random selection of data points.                % Note that M may represent a set of models that fit the data in                % this case M will be a cell array of models                M = feval(fittingfn, x(:,ind));                                % Depending on your problem it might be that the only way you                % can determine whether a data set is degenerate or not is to                % try to fit a model and see if it succeeds.  If it fails we                % reset degenerate to true.                if isempty(M)                    degenerate = 1;                end            end                        % Safeguard against being stuck in this loop forever            count = count + 1;            if count > maxDataTrials                warning('Unable to select a nondegenerate data set');                break            end        end                % Once we are out here we should have some kind of model...                % Evaluate distances between points and model returning the indices        % of elements in x that are inliers.  Additionally, if M is a cell        % array of possible models 'distfn' will return the model that has        % the most inliers.  After this call M will be a non-cell object        % representing only one model.        [inliers, M] = feval(distfn, M, x, t);%         [inliers, M] = feval(distfn, M, x);        % Find the number of inliers to this model.        ninliers = length(inliers);                if ninliers > bestscore    % Largest set of inliers so far...            bestscore = ninliers;  % Record data for this model            bestinliers = inliers;            bestM = M;                        % Update estimate of N, the number of trials to ensure we pick,             % with probability p, a data set with no outliers.            fracinliers =  ninliers/npts;            pNoOutliers = 1 -  fracinliers^s;            pNoOutliers = max(eps, pNoOutliers);  % Avoid division by -Inf            pNoOutliers = min(1-eps, pNoOutliers);% Avoid division by 0.            N = log(1-p)/log(pNoOutliers);        end                trialcount = trialcount+1;        if feedback            fprintf('trial %d out of %d         \r',trialcount, ceil(N));        end        % Safeguard against being stuck in this loop forever        if trialcount > maxTrials            warning( ...            sprintf('ransac reached the maximum number of %d trials',...                    maxTrials));            break        end         end    fprintf('\n');        if ~isnan(bestM)   % We got a solution         M = bestM;        inliers = bestinliers;    else                   M = [];        inliers = [];        error('ransac was unable to find a useful solution');    end