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