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Next: 4 Constraining the rectifying Up: Rectification with unconstrained stereo Previous: 2 Notation and basics

 

3 The rectification transformation

We now show that, if tex2html_wrap_inline985 is the projection matrix which rectifies one of the two views, the linear transformation (in projective coordinates) that maps the retinal plane of tex2html_wrap_inline987 onto the rectified retinal plane is given by the matrix tex2html_wrap_inline989 . For any 3-D point w we can write

equation147

We know that the equation of the optical ray associated to tex2html_wrap_inline991 is

equation161

hence

equation168

Assuming that rectification does not alter the optical center ( tex2html_wrap_inline993 ), we obtain

equation211

This is a clearer and more compact result than the one reported in [1], in which tex2html_wrap_inline995 is not written as the inverse of a projection matrix.


next up previous
Next: 4 Constraining the rectifying Up: Rectification with unconstrained stereo Previous: 2 Notation and basics

Adrian F Clark
Wed Jul 23 16:48:44 BST 1997