[37] | 1 | % RANSACFITAFFINEFUND - fits affine fundamental matrix using RANSAC |
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| 2 | % |
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| 3 | % Usage: [F, inliers] = ransacfitaffinefund(x1, x2, t) |
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| 4 | % |
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| 5 | % Arguments: |
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| 6 | % x1 - 2xN or 3xN set of homogeneous points. If the data is |
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| 7 | % 2xN it is assumed the homogeneous scale factor is 1. |
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| 8 | % x2 - 2xN or 3xN set of homogeneous points such that x1<->x2. |
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| 9 | % t - The distance threshold between data point and the model |
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| 10 | % used to decide whether a point is an inlier or not. |
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| 11 | % Note that point coordinates are normalised to that their |
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| 12 | % mean distance from the origin is sqrt(2). The value of |
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| 13 | % t should be set relative to this, say in the range |
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| 14 | % 0.001 - 0.01 |
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| 15 | % |
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| 16 | % Note that it is assumed that the matching of x1 and x2 are putative and it |
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| 17 | % is expected that a percentage of matches will be wrong. |
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| 18 | % |
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| 19 | % Returns: |
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| 20 | % F - The 3x3 fundamental matrix such that x2'Fx1 = 0. |
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| 21 | % inliers - An array of indices of the elements of x1, x2 that were |
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| 22 | % the inliers for the best model. |
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| 23 | % |
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| 24 | % See Also: RANSAC, FUNDMATRIX AFFINEFUNDMATRIX |
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| 25 | |
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| 26 | % Copyright (c) 2004-2005 Peter Kovesi |
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| 27 | % School of Computer Science & Software Engineering |
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| 28 | % The University of Western Australia |
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| 29 | % http://www.csse.uwa.edu.au/ |
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| 30 | % |
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| 31 | % Permission is hereby granted, free of charge, to any person obtaining a copy |
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| 32 | % of this software and associated documentation files (the "Software"), to deal |
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| 33 | % in the Software without restriction, subject to the following conditions: |
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| 34 | % |
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| 35 | % The above copyright notice and this permission notice shall be included in |
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| 36 | % all copies or substantial portions of the Software. |
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| 37 | % |
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| 38 | % The Software is provided "as is", without warranty of any kind. |
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| 39 | |
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| 40 | % February 2004 Original version |
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| 41 | % August 2005 Distance error function changed to match changes in RANSAC |
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| 42 | |
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| 43 | function [F, inliers] = ransacfitaffinefund(x1, x2, t, feedback) |
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| 44 | |
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| 45 | if ~all(size(x1)==size(x2)) |
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| 46 | error('Data sets x1 and x2 must have the same dimension'); |
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| 47 | end |
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| 48 | |
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| 49 | if nargin == 3 |
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| 50 | feedback = 0; |
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| 51 | end |
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| 52 | |
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| 53 | [rows,npts] = size(x1); |
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| 54 | if rows~=2 & rows~=3 |
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| 55 | error('x1 and x2 must have 2 or 3 rows'); |
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| 56 | end |
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| 57 | |
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| 58 | if rows == 2 % Pad data with homogeneous scale factor of 1 |
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| 59 | x1 = [x1; ones(1,npts)]; |
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| 60 | x2 = [x2; ones(1,npts)]; |
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| 61 | end |
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| 62 | |
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| 63 | % Normalise each set of points so that the origin is at centroid and |
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| 64 | % mean distance from origin is sqrt(2). normalise2dpts also ensures the |
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| 65 | % scale parameter is 1. Note that 'fundmatrix' will also call |
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| 66 | % 'normalise2dpts' but the code in 'ransac' that calls the distance |
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| 67 | % function will not - so it is best that we normalise beforehand. |
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| 68 | [x1, T1] = normalise2dpts(x1); |
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| 69 | [x2, T2] = normalise2dpts(x2); |
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| 70 | |
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| 71 | s = 4; % Number of points needed to fit an affine fundamental matrix. |
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| 72 | |
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| 73 | fittingfn = @affinefundmatrix; |
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| 74 | distfn = @funddist; |
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| 75 | degenfn = @isdegenerate; |
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| 76 | % x1 and x2 are 'stacked' to create a 6xN array for ransac |
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| 77 | [F, inliers] = ransac([x1; x2], fittingfn, distfn, degenfn, s, t, feedback); |
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| 78 | |
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| 79 | % Now do a final least squares fit on the data points considered to |
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| 80 | % be inliers. |
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| 81 | F = affinefundmatrix(x1(:,inliers), x2(:,inliers)); |
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| 82 | |
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| 83 | % Denormalise |
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| 84 | F = T2'*F*T1; |
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| 85 | |
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| 86 | %-------------------------------------------------------------------------- |
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| 87 | % Function to evaluate the first order approximation of the geometric error |
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| 88 | % (Sampson distance) of the fit of a fundamental matrix with respect to a |
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| 89 | % set of matched points as needed by RANSAC. See: Hartley and Zisserman, |
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| 90 | % 'Multiple View Geometry in Computer Vision', page 270. |
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| 91 | |
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| 92 | function [inliers, F] = funddist(F, x, t); |
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| 93 | |
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| 94 | x1 = x(1:3,:); % Extract x1 and x2 from x |
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| 95 | x2 = x(4:6,:); |
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| 96 | |
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| 97 | x2tFx1 = zeros(1,length(x1)); |
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| 98 | for n = 1:length(x1) |
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| 99 | x2tFx1(n) = x2(:,n)'*F*x1(:,n); |
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| 100 | end |
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| 101 | |
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| 102 | Fx1 = F*x1; |
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| 103 | Ftx2 = F'*x2; |
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| 104 | |
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| 105 | % Evaluate distances |
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| 106 | d = x2tFx1.^2 ./ ... |
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| 107 | (Fx1(1,:).^2 + Fx1(2,:).^2 + Ftx2(1,:).^2 + Ftx2(2,:).^2); |
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| 108 | |
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| 109 | inliers = find(abs(d) < t); % Indices of inlying points |
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| 110 | |
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| 111 | |
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| 112 | %---------------------------------------------------------------------- |
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| 113 | % (Degenerate!) function to determine if a set of matched points will result |
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| 114 | % in a degeneracy in the calculation of a fundamental matrix as needed by |
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| 115 | % RANSAC. This function assumes this cannot happen... |
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| 116 | |
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| 117 | function r = isdegenerate(x) |
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| 118 | r = 0; |
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| 119 | |
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