Computing the projective distortion matrix


Points of reference

We know both Euclidean and projective coordinates of the points of reference:
tex2html_wrap_inline118  ; tex2html_wrap_inline120 ( tex2html_wrap_inline122 ).

Projective transformation matrix tex2html_wrap_inline124

Matrix tex2html_wrap_inline124 is a tex2html_wrap_inline128 matrix:

displaymath110

where tex2html_wrap_inline130 is an arbitrary scalar because tex2html_wrap_inline124 is defined up to a scale factor.

Equation

Letting tex2html_wrap_inline134 and eliminating tex2html_wrap_inline130 give

displaymath111

with

displaymath112

Solution

minimizing the following error function:

displaymath113

subject to tex2html_wrap_inline138 . The solution is the eigenvector of tex2html_wrap_inline140 associated to the smallest eigenvalue.



Author: Zhengyou Zhang
Email: zzhang@sophia.inria.fr

Thu Oct 10 15:42:44 MET DST 1996