Image Rectification for Stereo Vision. Charles Loop Zhengyou Zhang Microsoft Research. Problem Statement. Compute a pair of 2D projective transforms ( homographies ). rectification. Original images. Rectified images. Motivations. To simplify stereo matching:
Instead of comparing pixels on skew lines, we now only compare pixels on the same scan lines.
Rectifying homographies are not unique
geometrically well-defined criteria minimizing image distortion due to rectification
F: a 3x3 rank-2 matrix
H and H’ are not unique.
Lines v and v’, and lines w and w’ must be corresponding epipolar lines.
Lines w and w’ define the rectifying plane.
How to do it?
If all weights are equal, then there is no distortion.
minimize the variation of wi over all pixels
Preserve original image resolution as close as possible.