[926] | 1 | function [omckk,Tckk,Rckk] = compute_extrinsic_init(x_kk,X_kk,fc,cc,kc,alpha_c), |
---|
| 2 | |
---|
| 3 | %compute_extrinsic |
---|
| 4 | % |
---|
| 5 | %[omckk,Tckk,Rckk] = compute_extrinsic_init(x_kk,X_kk,fc,cc,kc,alpha_c) |
---|
| 6 | % |
---|
| 7 | %Computes the extrinsic parameters attached to a 3D structure X_kk given its projection |
---|
| 8 | %on the image plane x_kk and the intrinsic camera parameters fc, cc and kc. |
---|
| 9 | %Works with planar and non-planar structures. |
---|
| 10 | % |
---|
| 11 | %INPUT: x_kk: Feature locations on the images |
---|
| 12 | % X_kk: Corresponding grid coordinates |
---|
| 13 | % fc: Camera focal length |
---|
| 14 | % cc: Principal point coordinates |
---|
| 15 | % kc: Distortion coefficients |
---|
| 16 | % alpha_c: Skew coefficient |
---|
| 17 | % |
---|
| 18 | %OUTPUT: omckk: 3D rotation vector attached to the grid positions in space |
---|
| 19 | % Tckk: 3D translation vector attached to the grid positions in space |
---|
| 20 | % Rckk: 3D rotation matrices corresponding to the omc vectors |
---|
| 21 | % |
---|
| 22 | %Method: Computes the normalized point coordinates, then computes the 3D pose |
---|
| 23 | % |
---|
| 24 | %Important functions called within that program: |
---|
| 25 | % |
---|
| 26 | %normalize_pixel: Computes the normalize image point coordinates. |
---|
| 27 | % |
---|
| 28 | %pose3D: Computes the 3D pose of the structure given the normalized image projection. |
---|
| 29 | % |
---|
| 30 | %project_points.m: Computes the 2D image projections of a set of 3D points |
---|
| 31 | |
---|
| 32 | |
---|
| 33 | |
---|
| 34 | if nargin < 6, |
---|
| 35 | alpha_c = 0; |
---|
| 36 | if nargin < 5, |
---|
| 37 | kc = zeros(5,1); |
---|
| 38 | if nargin < 4, |
---|
| 39 | cc = zeros(2,1); |
---|
| 40 | if nargin < 3, |
---|
| 41 | fc = ones(2,1); |
---|
| 42 | if nargin < 2, |
---|
| 43 | error('Need 2D projections and 3D points (in compute_extrinsic.m)'); |
---|
| 44 | return; |
---|
| 45 | end; |
---|
| 46 | end; |
---|
| 47 | end; |
---|
| 48 | end; |
---|
| 49 | end; |
---|
| 50 | |
---|
| 51 | |
---|
| 52 | %keyboard; |
---|
| 53 | |
---|
| 54 | % Compute the normalized coordinates: |
---|
| 55 | |
---|
| 56 | xn = normalize_pixel(x_kk,fc,cc,kc,alpha_c); |
---|
| 57 | |
---|
| 58 | |
---|
| 59 | |
---|
| 60 | Np = size(xn,2); |
---|
| 61 | |
---|
| 62 | %% Check for planarity of the structure: |
---|
| 63 | %keyboard; |
---|
| 64 | |
---|
| 65 | X_mean = mean(X_kk')'; |
---|
| 66 | |
---|
| 67 | Y = X_kk - (X_mean*ones(1,Np)); |
---|
| 68 | |
---|
| 69 | YY = Y*Y'; |
---|
| 70 | |
---|
| 71 | [U,S,V] = svd(YY); |
---|
| 72 | |
---|
| 73 | r = S(3,3)/S(2,2); |
---|
| 74 | |
---|
| 75 | %keyboard; |
---|
| 76 | |
---|
| 77 | |
---|
| 78 | if (r < 1e-3)|(Np < 5), %1e-3, %1e-4, %norm(X_kk(3,:)) < eps, % Test of planarity |
---|
| 79 | |
---|
| 80 | %fprintf(1,'Planar structure detected: r=%f\n',r); |
---|
| 81 | |
---|
| 82 | % Transform the plane to bring it in the Z=0 plane: |
---|
| 83 | |
---|
| 84 | R_transform = V'; |
---|
| 85 | |
---|
| 86 | %norm(R_transform(1:2,3)) |
---|
| 87 | |
---|
| 88 | if norm(R_transform(1:2,3)) < 1e-6, |
---|
| 89 | R_transform = eye(3); |
---|
| 90 | end; |
---|
| 91 | |
---|
| 92 | if det(R_transform) < 0, R_transform = -R_transform; end; |
---|
| 93 | |
---|
| 94 | T_transform = -(R_transform)*X_mean; |
---|
| 95 | |
---|
| 96 | X_new = R_transform*X_kk + T_transform*ones(1,Np); |
---|
| 97 | |
---|
| 98 | |
---|
| 99 | % Compute the planar homography: |
---|
| 100 | |
---|
| 101 | H = compute_homography(xn,X_new(1:2,:)); |
---|
| 102 | |
---|
| 103 | % De-embed the motion parameters from the homography: |
---|
| 104 | |
---|
| 105 | sc = mean([norm(H(:,1));norm(H(:,2))]); |
---|
| 106 | |
---|
| 107 | H = H/sc; |
---|
| 108 | |
---|
| 109 | % Extra normalization for some reasons... |
---|
| 110 | %H(:,1) = H(:,1)/norm(H(:,1)); |
---|
| 111 | %H(:,2) = H(:,2)/norm(H(:,2)); |
---|
| 112 | |
---|
| 113 | if 0, %%% Some tests for myself... the opposite sign solution leads to negative depth!!! |
---|
| 114 | |
---|
| 115 | % Case#1: no opposite sign: |
---|
| 116 | |
---|
| 117 | omckk1 = rodrigues([H(:,1:2) cross(H(:,1),H(:,2))]); |
---|
| 118 | Rckk1 = rodrigues(omckk1); |
---|
| 119 | Tckk1 = H(:,3); |
---|
| 120 | |
---|
| 121 | Hs1 = [Rckk1(:,1:2) Tckk1]; |
---|
| 122 | xn1 = Hs1*[X_new(1:2,:);ones(1,Np)]; |
---|
| 123 | xn1 = [xn1(1,:)./xn1(3,:) ; xn1(2,:)./xn1(3,:)]; |
---|
| 124 | e1 = xn1 - xn; |
---|
| 125 | |
---|
| 126 | % Case#2: opposite sign: |
---|
| 127 | |
---|
| 128 | omckk2 = rodrigues([-H(:,1:2) cross(H(:,1),H(:,2))]); |
---|
| 129 | Rckk2 = rodrigues(omckk2); |
---|
| 130 | Tckk2 = -H(:,3); |
---|
| 131 | |
---|
| 132 | Hs2 = [Rckk2(:,1:2) Tckk2]; |
---|
| 133 | xn2 = Hs2*[X_new(1:2,:);ones(1,Np)]; |
---|
| 134 | xn2 = [xn2(1,:)./xn2(3,:) ; xn2(2,:)./xn2(3,:)]; |
---|
| 135 | e2 = xn2 - xn; |
---|
| 136 | |
---|
| 137 | if 1, %norm(e1) < norm(e2), |
---|
| 138 | omckk = omckk1; |
---|
| 139 | Tckk = Tckk1; |
---|
| 140 | Rckk = Rckk1; |
---|
| 141 | else |
---|
| 142 | omckk = omckk2; |
---|
| 143 | Tckk = Tckk2; |
---|
| 144 | Rckk = Rckk2; |
---|
| 145 | end; |
---|
| 146 | |
---|
| 147 | else |
---|
| 148 | |
---|
| 149 | u1 = H(:,1); |
---|
| 150 | u1 = u1 / norm(u1); |
---|
| 151 | u2 = H(:,2) - dot(u1,H(:,2)) * u1; |
---|
| 152 | u2 = u2 / norm(u2); |
---|
| 153 | u3 = cross(u1,u2); |
---|
| 154 | RRR = [u1 u2 u3]; |
---|
| 155 | omckk = rodrigues(RRR); |
---|
| 156 | |
---|
| 157 | %omckk = rodrigues([H(:,1:2) cross(H(:,1),H(:,2))]); |
---|
| 158 | Rckk = rodrigues(omckk); |
---|
| 159 | Tckk = H(:,3); |
---|
| 160 | |
---|
| 161 | end; |
---|
| 162 | |
---|
| 163 | |
---|
| 164 | |
---|
| 165 | %If Xc = Rckk * X_new + Tckk, then Xc = Rckk * R_transform * X_kk + Tckk + T_transform |
---|
| 166 | |
---|
| 167 | Tckk = Tckk + Rckk* T_transform; |
---|
| 168 | Rckk = Rckk * R_transform; |
---|
| 169 | |
---|
| 170 | omckk = rodrigues(Rckk); |
---|
| 171 | Rckk = rodrigues(omckk); |
---|
| 172 | |
---|
| 173 | |
---|
| 174 | else |
---|
| 175 | |
---|
| 176 | %fprintf(1,'Non planar structure detected: r=%f\n',r); |
---|
| 177 | |
---|
| 178 | % Computes an initial guess for extrinsic parameters (works for general 3d structure, not planar!!!): |
---|
| 179 | % The DLT method is applied here!! |
---|
| 180 | |
---|
| 181 | J = zeros(2*Np,12); |
---|
| 182 | |
---|
| 183 | xX = (ones(3,1)*xn(1,:)).*X_kk; |
---|
| 184 | yX = (ones(3,1)*xn(2,:)).*X_kk; |
---|
| 185 | |
---|
| 186 | J(1:2:end,[1 4 7]) = -X_kk'; |
---|
| 187 | J(2:2:end,[2 5 8]) = X_kk'; |
---|
| 188 | J(1:2:end,[3 6 9]) = xX'; |
---|
| 189 | J(2:2:end,[3 6 9]) = -yX'; |
---|
| 190 | J(1:2:end,12) = xn(1,:)'; |
---|
| 191 | J(2:2:end,12) = -xn(2,:)'; |
---|
| 192 | J(1:2:end,10) = -ones(Np,1); |
---|
| 193 | J(2:2:end,11) = ones(Np,1); |
---|
| 194 | |
---|
| 195 | JJ = J'*J; |
---|
| 196 | [U,S,V] = svd(JJ); |
---|
| 197 | |
---|
| 198 | RR = reshape(V(1:9,12),3,3); |
---|
| 199 | |
---|
| 200 | if det(RR) < 0, |
---|
| 201 | V(:,12) = -V(:,12); |
---|
| 202 | RR = -RR; |
---|
| 203 | end; |
---|
| 204 | |
---|
| 205 | [Ur,Sr,Vr] = svd(RR); |
---|
| 206 | |
---|
| 207 | Rckk = Ur*Vr'; |
---|
| 208 | |
---|
| 209 | sc = norm(V(1:9,12)) / norm(Rckk(:)); |
---|
| 210 | Tckk = V(10:12,12)/sc; |
---|
| 211 | |
---|
| 212 | omckk = rodrigues(Rckk); |
---|
| 213 | Rckk = rodrigues(omckk); |
---|
| 214 | |
---|
| 215 | end; |
---|