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The rectifying transformation

Now that - for each camera - the rectifying PPM is known, we want to compute the linear transformation (in projective coordinates) that maps the retinal plane of the old PPM, tex2html_wrap_inline1289 , onto the retinal plane of tex2html_wrap_inline1291 .

We will see that this transformation is the tex2html_wrap_inline1135 matrix tex2html_wrap_inline1295 .

For any 3-D point w we can write


We know from Eq. (10) that the equation of the optical ray associated to tex2html_wrap_inline1297 is




Assuming that rectification does not alter the optical centre ( tex2html_wrap_inline1299 ), we obtain:


The transformation tex2html_wrap_inline1301 is then applied to the original image to produce a rectified image, as in Fig. 3. Note that the pixels (integer-coordinate positions) of the rectified image correspond, in general, to non-integer positions on the original image plane. Therefore, the gray levels of the rectified image are computed by bilinear interpolation.

Andrea Fusiello
Tue Feb 3 17:18:41 MET 1998