[37] | 1 | % RANSACFITFUNDMATRIX - fits fundamental matrix using RANSAC |
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| 2 | % |
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| 3 | % Usage: [F, inliers, NewDist, fail] = ransacfitfundmatrix(defaultPara, x1, x2, t, Depth1, Depth2, dist, feedback, disp, FlagDist) |
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| 4 | % |
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| 5 | % Arguments: |
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| 6 | % defaultPara - useful default parameters (like, camera intrinsic matrix) |
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| 7 | % x1 - 2xN or 3xN set of homogeneous points. If the data is |
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| 8 | % 2xN it is assumed the homogeneous scale factor is 1. |
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| 9 | % x2 - 2xN or 3xN set of homogeneous points such that x1<->x2. |
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| 10 | % t - The distance threshold between data point and the model |
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| 11 | % used to decide whether a point is an inlier or not. |
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| 12 | % Note that point coordinates are normalised to that their |
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| 13 | % mean distance from the origin is sqrt(2). The value of |
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| 14 | % t should be set relative to this, say in the range |
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| 15 | % 0.001 - 0.01 |
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| 16 | % Depth1/2 - depth imformation to support more accurate ransac |
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| 17 | % distrib - initial distribution (default uniform dist) |
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| 18 | % feedback - An optional flag 0/1. If set to one the trial count and the |
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| 19 | % estimated total number of trials required is printed out at |
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| 20 | % each step. Defaults to 0. |
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| 21 | % disp - if true, display the matches found when done. |
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| 22 | % |
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| 23 | % FlagDist - if true, calculate the reprojection error |
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| 24 | % |
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| 25 | % Note that it is assumed that the matching of x1 and x2 are putative and it |
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| 26 | % is expected that a percentage of matches will be wrong. |
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| 27 | % |
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| 28 | % Returns: |
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| 29 | % F - The 3x3 fundamental matrix such that x2'Fx1 = 0. |
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| 30 | % inliers - An array of indices of the elements of x1, x2 that were |
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| 31 | % the inliers for the best model. |
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| 32 | % NewDist - New Distribution after Ransac (Outliers have zero distribution) |
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| 33 | % fail - true if Ransac fail to find any solution is not degenerated |
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| 34 | % |
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| 35 | % See Also: RANSAC, FUNDMATRIX |
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| 36 | |
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| 37 | % Copyright (c) 2004-2005 Peter Kovesi |
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| 38 | % School of Computer Science & Software Engineering |
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| 39 | % The University of Western Australia |
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| 40 | % http://www.csse.uwa.edu.au/ |
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| 41 | % |
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| 42 | % Permission is hereby granted, free of charge, to any person obtaining a copy |
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| 43 | % of this software and associated documentation files (the "Software"), to deal |
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| 44 | % in the Software without restriction, subject to the following conditions: |
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| 45 | % |
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| 46 | % The above copyright notice and this permission notice shall be included in |
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| 47 | % all copies or substantial portions of the Software. |
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| 48 | % |
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| 49 | % The Software is provided "as is", without warranty of any kind. |
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| 50 | |
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| 51 | % February 2004 Original version |
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| 52 | % August 2005 Distance error function changed to match changes in RANSAC |
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| 53 | % |
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| 54 | % additional parameter distrib is a vector of non-negative numbers that |
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| 55 | % specifies a (not necessarily normalized) probability distribution over |
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| 56 | % the different possible matches - passed to the ransac function to be |
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| 57 | % used during the sampling procedure. |
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| 58 | % (added by Jeff Michels) |
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| 59 | % Additional NewDist estimated after Ransac is formed by using Depth |
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| 60 | % information |
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| 61 | % (added by Min Sun) |
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| 62 | |
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| 63 | function [F, inliers, NewDist, fail] = ransacfitfundmatrix(defaultPara, x1, x2, t, Depth1, Depth2, distrib, feedback, disp, FlagDist, s) |
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| 64 | % [F, inliers, fail] = ransacfitfundmatrix(x1, x2, t, feedback, distrib) |
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| 65 | |
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| 66 | if ~all(size(x1)==size(x2)) |
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| 67 | error('Data sets x1 and x2 must have the same dimension'); |
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| 68 | end |
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| 69 | |
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| 70 | if nargin < 8 |
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| 71 | feedback = 0; |
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| 72 | disp = 0; |
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| 73 | FlagDist = 0; |
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| 74 | s = 8; % Number of points needed to fit a fundamental matrix. Note that |
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| 75 | % only 7 are needed but the function 'fundmatrix' only |
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| 76 | % implements the 8-point solution. |
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| 77 | elseif nargin < 11 |
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| 78 | s = 8; % Number of points needed to fit a fundamental matrix. Note that |
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| 79 | % only 7 are needed but the function 'fundmatrix' only |
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| 80 | % implements the 8-point solution. |
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| 81 | end |
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| 82 | |
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| 83 | [rows,npts] = size(x1); |
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| 84 | if rows~=2 & rows~=3 |
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| 85 | error('x1 and x2 must have 2 or 3 rows'); |
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| 86 | end |
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| 87 | |
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| 88 | if rows == 2 % Pad data with homogeneous scale factor of 1 |
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| 89 | x1 = [x1; ones(1,npts)]; |
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| 90 | x2 = [x2; ones(1,npts)]; |
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| 91 | end |
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| 92 | |
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| 93 | % Normalise each set of points so that the origin is at centroid and |
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| 94 | % mean distance from origin is sqrt(2). normalise2dpts also ensures the |
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| 95 | % scale parameter is 1. Note that 'fundmatrix' will also call |
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| 96 | % 'normalise2dpts' but the code in 'ransac' that calls the distance |
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| 97 | % function will not - so it is best that we normalise beforehand. |
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| 98 | [x1, T1] = normalise2dpts(x1); |
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| 99 | [x2, T2] = normalise2dpts(x2); |
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| 100 | |
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| 101 | |
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| 102 | fittingfn = @fundmatrix; |
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| 103 | distfn = @funddist; % funciton handler below |
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| 104 | degenfn = @isdegenerate; % function handler below |
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| 105 | % x1 and x2 are 'stacked' to create a 6xN array for ransac |
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| 106 | [F, inliers, NewDist, fail] = ... |
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| 107 | ransac(defaultPara, [x1; x2], [Depth1; Depth2], fittingfn, distfn, degenfn, s, t, distrib, [T1; T2], feedback, disp, FlagDist); |
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| 108 | |
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| 109 | % Now do a final least squares fit on the data points considered to |
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| 110 | % be inliers. |
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| 111 | F = fundmatrix(x1(:,inliers), x2(:,inliers)); |
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| 112 | |
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| 113 | % Denormalise |
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| 114 | F = T2'*F*T1; |
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| 115 | |
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| 116 | %-------------------------------------------------------------------------- |
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| 117 | % Function to evaluate the first order approximation of the geometric error |
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| 118 | % (Sampson distance) of the fit of a fundamental matrix with respect to a |
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| 119 | % set of matched points as needed by RANSAC. See: Hartley and Zisserman, |
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| 120 | % 'Multiple View Geometry in Computer Vision', page 270. |
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| 121 | % |
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| 122 | % Note that this code allows for F being a cell array of fundamental matrices of |
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| 123 | % which we have to pick the best one. (A 7 point solution can return up to 3 |
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| 124 | % solutions) |
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| 125 | % |
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| 126 | % Min add to calculate ReProjection Error from Depth information (4/22, 2007) |
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| 127 | |
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| 128 | function [bestInliers, bestF, ReProjError] = funddist(F, x, t, defaultPara, Depth, T, FlagDist); |
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| 129 | %[bestInliers, bestF] = funddist(F, x, t); |
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| 130 | |
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| 131 | x1 = x(1:3,:); % Extract x1 and x2 from x |
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| 132 | x2 = x(4:6,:); |
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| 133 | T1 = T(1:3,:); |
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| 134 | T2 = T(4:6,:); |
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| 135 | |
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| 136 | if iscell(F) % We have several solutions each of which must be tested |
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| 137 | |
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| 138 | nF = length(F); % Number of solutions to test |
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| 139 | bestF = F{1}; % Initial allocation of best solution |
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| 140 | ninliers = 0; % Number of inliers |
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| 141 | |
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| 142 | for k = 1:nF |
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| 143 | t |
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| 144 | x2tFx1 = zeros(1,length(x1)); |
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| 145 | for n = 1:length(x1) |
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| 146 | x2tFx1(n) = x2(:,n)'*F{k}*x1(:,n); |
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| 147 | end |
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| 148 | |
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| 149 | Fx1 = F{k}*x1; |
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| 150 | Ftx2 = F{k}'*x2; |
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| 151 | |
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| 152 | % Evaluate distances |
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| 153 | d = x2tFx1.^2 ./ ... |
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| 154 | (Fx1(1,:).^2 + Fx1(2,:).^2 + Ftx2(1,:).^2 + Ftx2(2,:).^2); |
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| 155 | |
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| 156 | inliers = find(abs(d) < t); % Indices of inlying points |
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| 157 | |
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| 158 | if length(inliers) > ninliers % Record best solution |
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| 159 | ninliers = length(inliers); |
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| 160 | bestF = F{k}; |
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| 161 | bestInliers = inliers; |
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| 162 | end |
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| 163 | end |
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| 164 | |
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| 165 | else % We just have one solution |
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| 166 | x2tFx1 = zeros(1,length(x1)); |
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| 167 | for n = 1:length(x1) |
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| 168 | x2tFx1(n) = x2(:,n)'*F*x1(:,n); |
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| 169 | end |
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| 170 | |
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| 171 | Fx1 = F*x1; |
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| 172 | Ftx2 = F'*x2; |
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| 173 | |
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| 174 | % Evaluate distances |
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| 175 | d = x2tFx1.^2 ./ ... |
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| 176 | (Fx1(1,:).^2 + Fx1(2,:).^2 + Ftx2(1,:).^2 + Ftx2(2,:).^2); |
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| 177 | figure(1);hist(d(d<t)); |
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| 178 | bestInliers = find(abs(d) < t); % Indices of inlying points |
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| 179 | bestF = F; % Copy F directly to bestF |
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| 180 | |
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| 181 | end |
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| 182 | |
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| 183 | % calculate ReProError ------------------------------------------------ |
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| 184 | if FlagDist |
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| 185 | Depth1 = Depth(1,:); |
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| 186 | Depth2 = Depth(2,:); |
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| 187 | X1 = inv(defaultPara.InrinsicK1)*inv(T1)*x1.*repmat(Depth1,3,1); |
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| 188 | X2 = inv(defaultPara.InrinsicK2)*inv(T2)*x2.*repmat(Depth2,3,1); |
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| 189 | E = (defaultPara.InrinsicK2'*T2'*bestF*T1*defaultPara.InrinsicK1); |
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| 190 | [U S V] =svd(E); |
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| 191 | Rz_pos = [ [0 -1 0];... |
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| 192 | [1 0 0];... |
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| 193 | [0 0 1]]; |
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| 194 | Rz_neg = Rz_pos'; |
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| 195 | T_hat1 = U*Rz_pos*diag([1 1 0])*U'; |
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| 196 | T1 = [-T_hat1(2,3); T_hat1(1,3); -T_hat1(1,2)]; |
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| 197 | R1 = U*Rz_pos'*V'; |
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| 198 | T_hat2 = U*Rz_neg*diag([1 1 0])*U'; |
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| 199 | T2 = [-T_hat2(2,3); T_hat2(1,3); -T_hat2(1,2)]; |
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| 200 | R2 = U*Rz_neg'*V'; |
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| 201 | X1_2_1 = R1*X1; |
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| 202 | X1_2_2 = R2*X1; |
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| 203 | ops = sdpsettings('solver','sedumi','verbose',1); |
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| 204 | a = sdpvar(1,1); |
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| 205 | b = sdpvar(1,1); |
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| 206 | F = set(a>=0)+set(b>=0); |
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| 207 | sol = solvesdp(F,norm(X1_2_1(:)*a + b*repmat(T1, size(X1,2),1)- X2(:),1),ops); |
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| 208 | sol = solvesdp(F,norm(X1_2_2(:)*a + b*repmat(T2, size(X1,2),1)- X2(:),1),ops); |
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| 209 | a = double(a); |
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| 210 | b = double(b); |
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| 211 | ReProjError = sum(abs(X2_1*a - X1),1) + sum(abs(X1_2*b - X2),1); |
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| 212 | ReProjError(setdiff(1:size(ReProjError,2), bestInliers)) = Inf; |
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| 213 | else |
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| 214 | ReProjError = []; |
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| 215 | end |
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| 216 | % ---------------------------------------------------------------------` |
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| 217 | |
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| 218 | %---------------------------------------------------------------------- |
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| 219 | % (Degenerate!) function to determine if a set of matched points will result |
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| 220 | % in a degeneracy in the calculation of a fundamental matrix as needed by |
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| 221 | % RANSAC. This function assumes this cannot happen... |
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| 222 | |
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| 223 | function r = isdegenerate(x) |
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| 224 | r = 0; |
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| 225 | |
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| 226 | |
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