1 | % RANSACFITTRANSFUNDMATRIX - fits fundamental matrix using RANSAC |
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2 | % |
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3 | % Usage: [F, inliers] = ransacfitfundmatrix(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 |
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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] = ransacfitfundmatrix(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 | lx1 = size(x1,2); |
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69 | [points, T1] = normalise2dpts([x1,x2]); |
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70 | x1 = points(:,1:lx1); x2 = points(:,lx1+1:end); |
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71 | % [x1, T1] = normalise2dpts(x1); |
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72 | % [x2, T2] = normalise2dpts(x2); |
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73 | |
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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 | |
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78 | fittingfn = @transfundmatrix; |
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79 | distfn = @funddist; |
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80 | degenfn = @isdegenerate; |
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81 | % x1 and x2 are 'stacked' to create a 6xN array for ransac |
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82 | [F, inliers] = ransac([x1; x2], fittingfn, distfn, degenfn, s, t, feedback); |
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83 | |
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84 | % Now do a final least squares fit on the data points considered to |
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85 | % be inliers. |
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86 | F = transfundmatrix(x1(:,inliers), x2(:,inliers)); |
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87 | |
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88 | % Denormalise |
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89 | F = T1'*F*T1; |
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90 | |
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91 | |
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92 | %-------------------------------------------------------------------------- |
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93 | % Function to evaluate the first order approximation of the geometric error |
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94 | % (Sampson distance) of the fit of a fundamental matrix with respect to a |
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95 | % set of matched points as needed by RANSAC. See: Hartley and Zisserman, |
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96 | % 'Multiple View Geometry in Computer Vision', page 270. |
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97 | % |
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98 | % Note that this code allows for F being a cell array of fundamental matrices of |
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99 | % which we have to pick the best one. (A 7 point solution can return up to 3 |
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100 | % solutions) |
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101 | |
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102 | function [bestInliers, bestF] = funddist(F, x, t); |
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103 | |
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104 | x1 = x(1:3,:); % Extract x1 and x2 from x |
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105 | x2 = x(4:6,:); |
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106 | |
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107 | |
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108 | if iscell(F) % We have several solutions each of which must be tested |
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109 | |
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110 | nF = length(F); % Number of solutions to test |
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111 | bestF = F{1}; % Initial allocation of best solution |
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112 | ninliers = 0; % Number of inliers |
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113 | |
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114 | for k = 1:nF |
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115 | x2tFx1 = zeros(1,length(x1)); |
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116 | for n = 1:length(x1) |
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117 | x2tFx1(n) = x2(:,n)'*F{k}*x1(:,n); |
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118 | end |
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119 | |
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120 | Fx1 = F{k}*x1; |
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121 | Ftx2 = F{k}'*x2; |
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122 | |
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123 | % Evaluate distances |
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124 | d = x2tFx1.^2 ./ ... |
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125 | (Fx1(1,:).^2 + Fx1(2,:).^2 + Ftx2(1,:).^2 + Ftx2(2,:).^2); |
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126 | |
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127 | inliers = find(abs(d) < t); % Indices of inlying points |
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128 | |
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129 | if length(inliers) > ninliers % Record best solution |
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130 | ninliers = length(inliers); |
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131 | bestF = F{k}; |
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132 | bestInliers = inliers; |
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133 | end |
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134 | end |
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135 | |
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136 | else % We just have one solution |
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137 | x2tFx1 = zeros(1,length(x1)); |
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138 | for n = 1:length(x1) |
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139 | x2tFx1(n) = x2(:,n)'*F*x1(:,n); |
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140 | end |
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141 | |
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142 | Fx1 = F*x1; |
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143 | Ftx2 = F'*x2; |
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144 | |
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145 | % Evaluate distances |
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146 | d = x2tFx1.^2 ./ ... |
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147 | (Fx1(1,:).^2 + Fx1(2,:).^2 + Ftx2(1,:).^2 + Ftx2(2,:).^2); |
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148 | |
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149 | bestInliers = find(abs(d) < t); % Indices of inlying points |
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150 | bestF = F; % Copy F directly to bestF |
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151 | |
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152 | end |
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153 | |
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154 | |
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155 | |
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156 | %---------------------------------------------------------------------- |
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157 | % (Degenerate!) function to determine if a set of matched points will result |
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158 | % in a degeneracy in the calculation of a fundamental matrix as needed by |
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159 | % RANSAC. This function assumes this cannot happen... |
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160 | |
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161 | function r = isdegenerate(x) |
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162 | r = 0; |
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163 | |
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