Rectification with unconstrained
stereo geometry

Andrea Fusiello
Dipartimento di Matematica e Informatica
Universitá di Udine, Italia
fusiello@dimi.uniud.it
- Emanuele Trucco
Department of Computing and Electrical Engineering
Heriot-Watt University, UK
mtc@cee.hw.ac.uk
- Alessandro Verri
Dipartimento di Fisica
Universitá di Genova, Italia
verri@infm.ge.it

Abstract:

We present a linear rectification algorithm for general, unconstrained stereo rigs. The algorithm requires the two projection matrices of the original cameras, and enforces explicitly all constraints necessary and sufficient to achieve a unique pair of rectified projection matrices. We report tests proving the correct behaviour of our method, as well as the negligible decrease of the accuracy of 3-D reconstruction if performed from the rectified images directly. To maximise reproducibility and usefulness, we give a working, 22-line Matlab code, and a URL where code, example data and a user guide can be found. Stereo reconstruction systems are very popular in vision research and applications, hence the usefulness of a general and easily accessible rectification algorithm.

• 1 Introduction and motivations
• 2 Notation and basics
• 3 The rectification transformation
• 4 Constraining the rectifying projection matrices
• 5 Solving for the rectifying projection matrices
• 6 Summary of the algorithm
• 7 Experimental Results
• 8 Discussion
• References