Projective reconstruction

Projective basis

Choose 5 points in the first image and their matches in the second (with the matrix tex2html_wrap_inline133 ). These points verify the epipolar constraints.

Camera projection matrices

Together with matrix tex2html_wrap_inline133 we can compute the camera projection matrices: tex2html_wrap_inline137 and tex2html_wrap_inline139 , w.r.t the chosen projective basis.

3D reconstruction

based on the classical triangulation principle:
Basic equations:
(Image points (u,v), (u',v') tex2html_wrap_inline145 3D projective point tex2html_wrap_inline147 )


Method 1:
eliminating s and s' gives


with tex2html_wrap_inline153 , the i-th row vector of tex2html_wrap_inline157 . Since the projective coordinates are defined up to a scale factor, we can impose the constraint: tex2html_wrap_inline159 . The solution is simply the eigenvector of tex2html_wrap_inline161 associated to the smallest eigenvalue.

Method 2:
a physically more meaningful criterion


3D reconstruction in projective space

The projective projection matrices are available HERE for the first image and THERE for the second image. The projective structure of the bi-plane object is available HERE for the first image.

Back projection of the projective reconstruction onto the first image


an orthographic projection of the projective reconstruction (not very meaningful in Euclidean sense)


Author: Zhengyou Zhang

Thu Oct 10 15:20:46 MET DST 1996