% parameters of projective (homographic) coordinate transformation % between six 1-D ``pictures'' (five successive pairs sequence) % just made up these numbers (e.g. from 2-D sciam sequence, took x-parameters p=[... 0.9985 -0.0135 -0.0008;... 0.9996 -0.0158 -0.0005;... 1.0033 -0.0162 0.0004;... 1.0045 -0.0203 0.0015;... 1.0055 -0.0256 0.0016... ]; % a little experiment: make a new p, based on a particular K: % K=[2 -.5;0,1] % % 10 degree pan... do various pan angles: % for thetaperdeg=-10:10 % pchirp(rand(1,10),thetaperdeg*o,K) % end % resulting in family of p values... p=[... 0.9155588 -0.3588750 0.0844412;... 0.9155588 -0.3588750 0.0844412;... 1.0922291 0.3919737 -0.0922291;... 1.0824572 0.3504431 -0.0824572;... 1.0728293 0.3095245 -0.0728293;... 1.0633365 0.2691800 -0.0633365;... 1.0539702 0.2293735 -0.0539702;... 1.0447225 0.1900707 -0.0447225;... 1.0355855 0.1512384 -0.0355855;... 1.0265518 0.1128450 -0.0265518;... 1.0176142 0.0748602 -0.0176142;... 1.0087658 0.0372546 -0.0087658;... 1.0000000 0.0000000 0.0000000;... 0.9913104 -0.0369309 0.0086896;... 0.9826907 -0.0735644 0.0173093;... 0.9741350 -0.1099263 0.0258650;... 0.9656373 -0.1460414 0.0343627;... 0.9571920 -0.1819341 0.0428080;... 0.9487934 -0.2176281 0.0512066;... 0.9404361 -0.2531466 0.0595639;... 0.9321147 -0.2885123 0.0678853;... 0.9238241 -0.3237478 0.0761759;... 0.9155588 -0.3588750 0.0844412;... ]; X=[]; % initialize the ``X'' of Hartley, page 8 for m=1:5 p11=p(m,1); p12=p(m,2); p21=p(m,3); p22=1; q=inv([p11,p12;p21,p22]); q=q/q(2,2); q11=q(1); q12=q(2); q21=q(3); q22=1; Xm=[q11-p11 q21-p12 0 ;... q12 q22-p11 -p12 ;... ... -p21 q11-p22 q21 ;... 0 q12-p21 q22-p22 ;... ]; X=[X;Xm]; end%for [v d]=eig(X'*X); d=diag(d); [trash location]=min(d); % choose least eigenvalue answer=v(:,location); C=[answer(1) answer(2);... answer(2) answer(3)... ]; K=chol(C); disp('still need to see why K(2,2) not equal to 1') K=K/K(2,2); % final result: %K = % 2.0471 -0.4579 % 0 1.0000 % is close to what it should be