function [ pto Tinv pn ] = back_projection( v, imgpt )
% [PTO TINV PN] = BAC_PROJECTION(V, IMGPT)
%   Projects image points back to plane [a b c d] = [0 0 1 0];
%   V is camera description
%   IMGPT are the image points (N, 2) array
%   PTO are the output projected points
%   TINV is the projection matrix
%   PN is the plane (as seen by camera)
%
%

R = rotation_matrix(v);
Ty = [R [0 0  -v(4)]'; [0 0 0 1]];
pw = [0 0 1 0];
pn = pw*Ty;
d = -pn(4);
M = [d 0 0 0; 0 d 0 0; 0 0 d 0; pn(1:3) 0];
Tn = Ty*M;
Tinv = Tn';
sz = size(imgpt);
N = sz(1);
k = [imgpt ones(N,2)];
pth = k*Tinv;
pto = pth(:,1:3)./repmat(pth(:,4),[1 3]);
end

Published with MATLAB® 7.9