[37] | 1 | % By Philip Torr 2002
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| 2 | % copyright Microsoft Corp.
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| 3 | %MAPSAC is the Bayesian version of MLESAC, and it is easier to pronounce!
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| 4 | %
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| 5 | % %designed for the good of the world by Philip Torr based on ideas contained in
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| 6 | % copyright Philip Torr and Microsoft Corp 2002
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| 7 | %
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| 8 | % [f,f_sq_errors, n_inliers,inlier_matches] = torr_mapsac_F(x1,y1,x2,y2, no_matches, m3, no_samp, T)
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| 9 | % f is fundamentalmatrix in 9 vector
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| 10 | % f_sq_errors are non robust errors on each match
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| 11 | % n_inliers is the no of inliers
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| 12 | % inlier_index is a vector with index no of each inlier
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| 13 | %
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| 14 | % x1,y1,x2,y2 are column vectors of the data no_matches by 4
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| 15 | % m3 is the 3rd homogeneous coordinate (256)
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| 16 | % no_samp is the number of samples to be taken (set to 0 if jump out required, at the moment jump out not implemented
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| 17 | % T is the threshold on the residuals, derived from MLESAC?MAPSAC paper
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| 18 | %
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| 19 | % at the moment it is assumed all is normalized so that Gaussian noise has sigma 1
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| 20 |
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| 21 | % /*
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| 22 | %
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| 23 | % @inproceedings{Torr93b,
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| 24 | % author = "Torr, P. H. S. and Murray, D. W.",
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| 25 | % title = "Outlier Detection and Motion Segmentation",
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| 26 | % booktitle = "Sensor Fusion VI",
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| 27 | % editor = "Schenker, P. S.",
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| 28 | % publisher = "SPIE volume 2059",
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| 29 | % note = "Boston",
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| 30 | % pages = {432-443},
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| 31 | % year = 1993 }
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| 32 | %
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| 33 | %
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| 34 | % @phdthesis{Torr:thesis,
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| 35 | % author="Torr, P. H. S.",
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| 36 | % title="Outlier Detection and Motion Segmentation",
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| 37 | % school=" Dept. of Engineering Science, University of Oxford",
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| 38 | % year=1995}
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| 39 | %
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| 40 | %
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| 41 | %
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| 42 | % @article{Torr97c,
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| 43 | % author="Torr, P. H. S. and Murray, D. W. ",
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| 44 | % title="The Development and Comparison of Robust Methods for Estimating the Fundamental Matrix",
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| 45 | % journal="IJCV",
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| 46 | % volume = 24,
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| 47 | % number = 3,
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| 48 | % pages = {271--300},
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| 49 | % year=1997
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| 50 | % }
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| 51 | %
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| 52 | %
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| 53 | %
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| 54 | %
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| 55 | % @article{Torr99c,
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| 56 | % author = "Torr, P. H. S. and Zisserman, A",
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| 57 | % title ="MLESAC: A New Robust Estimator with Application to Estimating Image Geometry ",
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| 58 | % journal = "CVIU",
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| 59 | % Volume = {78},
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| 60 | % number = 1,
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| 61 | % pages = {138-156},
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| 62 | % year = 2000}
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| 63 | %
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| 64 | % %MAPSAC is the Bayesian version of MLESAC, and it is easier to pronounce!
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| 65 | % it is described in:
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| 66 | %
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| 67 | % @article{Torr02d,
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| 68 | % author = "Torr, P. H. S.",
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| 69 | % title ="Bayesian Model Estimation and Selection for Epipolar Geometry and
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| 70 | % Generic Manifold Fitting",
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| 71 | % journal = "IJCV",
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| 72 | % Volume = {?},
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| 73 | % number = ?,
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| 74 | % pages = {?},
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| 75 | % url = "http://research.microsoft.com/~philtorr/",
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| 76 | % year = 2002}
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| 77 | %
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| 78 |
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| 79 | %threshold is the maximum squared value of the residuals
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| 80 | %no_matches is the number of matches
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| 81 | %no_samp is the number of random samples to be taken
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| 82 | %m3 is the estimate of the 3rf projective coordinate (f in pixels)
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| 83 |
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| 84 | %the F matrix is defined like:
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| 85 | % (nx2, ny2, m3) f(1 2 3) nx1
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| 86 | % (4 5 6) ny1
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| 87 | % (7 8 9) m3
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| 88 |
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| 89 |
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| 90 |
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| 91 | %we minimize a robust function min(e^2,T) see mapsac paper.
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| 92 |
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| 93 |
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| 94 | function [f,f_sq_errors, n_inliers,inlier_index] = torr_napsac_F(x1,y1,x2,y2, no_matches, m3, no_samp, T)
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| 95 | %disp('This just does calculation of perfect data,for test')
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| 96 | %disp('Use estf otherwise')
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| 97 | %f = rand(9);
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| 98 |
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| 99 |
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| 100 | %%%%%%%%%%debug
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| 101 | %used for debugging:
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| 102 | no_trials = 1;
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| 103 | max_inliers = 0;
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| 104 | %%%%%%%%%%end debug
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| 105 |
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| 106 | for(i = 1:no_samp)
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| 107 |
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| 108 | %NAPSAC frenzyoid! first pick one point then take 6 nearest, described in thesis/china paper
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| 109 | choice = randperm(no_matches);
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| 110 | %set up local design matrix, here we estimate from 7 matches
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| 111 | distance_xyxy = (x1 - x1(choice(1))).^2 + (x2 - x2(choice(1))).^2 + (y1 - y1(choice(1))).^2 + (y2 - y2(choice(1))).^2;
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| 112 | [sorted_distance_xyxy, index_distance_xyxy] = sort(distance_xyxy);
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| 113 |
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| 114 |
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| 115 | %next randomly permute the best 50 matches
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| 116 | choice2 = randperm(60);
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| 117 |
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| 118 | for (j = 1:7)
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| 119 | tx1(j) = x1( index_distance_xyxy(choice2(j)));
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| 120 | tx2(j) = x2( index_distance_xyxy(choice2(j)));
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| 121 | ty1(j) = y1( index_distance_xyxy(choice2(j)));
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| 122 | ty2(j) = y2( index_distance_xyxy(choice2(j)));
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| 123 | end % for (j = 1:7)
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| 124 |
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| 125 | % tx1 = x1( index_distance_xyxy(1:7));
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| 126 | % tx2 = x2( index_distance_xyxy(1:7));
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| 127 | % ty1 = y1( index_distance_xyxy(1:7));
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| 128 | % ty2 = y2( index_distance_xyxy(1:7));
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| 129 |
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| 130 | %produces 1 or 3 solutions.
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| 131 | [no_F big_result]= torr_F_constrained_fit(tx1,ty1,tx2,ty2,m3);
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| 132 |
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| 133 | for j = 1:no_F
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| 134 | ft = big_result(j,:);
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| 135 |
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| 136 | %get squared errors
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| 137 | et = torr_errf2(ft,x1,y1,x2,y2, no_matches, m3);
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| 138 |
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| 139 |
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| 140 |
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| 141 |
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| 142 | %capped residuals
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| 143 | cet = min(et,T);
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| 144 | sse = cet' * cet;
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| 145 | % use sse 0 to bring it to a reasonable value
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| 146 | if ((i ==1) & (j ==1))
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| 147 | f = ft;
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| 148 | bestsse = sse;
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| 149 | elseif bestsse > sse
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| 150 | f = ft;
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| 151 | bestsse = sse;
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| 152 | bestcet = cet; %store best set of residuals
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| 153 | end %if
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| 154 |
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| 155 |
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| 156 | %monitor progress %debug
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| 157 | inlier_index = find((et < T) == 1);
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| 158 | mapsac_inliers(no_trials) = length(inlier_index);
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| 159 | if mapsac_inliers(no_trials) > max_inliers
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| 160 | max_inliers = mapsac_inliers(no_trials);
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| 161 | else
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| 162 | mapsac_inliers(no_trials) = max_inliers;
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| 163 | end
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| 164 | no_trials = no_trials + 1;
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| 165 | %%%%%%%%end debug
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| 166 |
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| 167 |
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| 168 |
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| 169 | end
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| 170 |
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| 171 |
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| 172 |
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| 173 | end %for(i = 1:no_samp)
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| 174 |
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| 175 |
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| 176 | %calculate squared errors (distance to manifold of F)
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| 177 | f_sq_errors = torr_errf2(f,x1,y1,x2,y2, no_matches, m3);
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| 178 | %next generate index set of inliers
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| 179 | inlier_index = find((f_sq_errors < T) == 1);
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| 180 | n_inliers = length(inlier_index);
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| 181 |
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| 182 |
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| 183 |
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| 184 | %%%%%%%%%%debug
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| 185 | %for NAPSAC paper
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| 186 | no_matches
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| 187 | n_inliers
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| 188 | no_trials
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| 189 |
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| 190 | mapsac_inliers(1:30)
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| 191 | %find out how many it took to get to n_inliers
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| 192 | perc = n_inliers;
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| 193 | map_index = find((mapsac_inliers < perc) == 1);
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| 194 | perc100 = length(map_index)+1
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| 195 | %find out how many it took to get to n_inliers
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| 196 |
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| 197 | perc = n_inliers * 0.9;
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| 198 | map_index = find((mapsac_inliers < perc) == 1);
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| 199 | perc90 = length(map_index)+1
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| 200 |
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| 201 | perc = n_inliers * 0.8;
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| 202 | map_index = find((mapsac_inliers < perc) == 1);
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| 203 | perc80 = length(map_index)+1
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| 204 |
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| 205 |
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| 206 |
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| 207 | perc = n_inliers * 0.7;
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| 208 | map_index = find((mapsac_inliers < perc) == 1);
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| 209 | perc70 = length(map_index)+1
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| 210 |
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| 211 |
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| 212 |
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| 213 | perc = n_inliers * 0.6;
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| 214 | map_index = find((mapsac_inliers < perc) == 1);
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| 215 | perc60 = length(map_index)+1
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| 216 |
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| 217 |
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| 218 | n_inliers
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| 219 |
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| 220 | disp('Napsac');
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| 221 | %
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| 222 | % figure
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| 223 | % hold on
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| 224 | % for i = 1:no_trials-1
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| 225 | % plot(i, mapsac_inliers(i),'rs');
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| 226 | % end
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| 227 | % hold off
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| 228 | % %%%%%%%%%%%%end debug
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| 229 |
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| 230 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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| 231 |
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| 232 | |
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