# Epipolar rectification

A. Fusiello with E. Trucco, A. Verri, L. Irsara

### Description

Given a pair of stereo images, **rectification **determines a
transformation of each image plane such that pairs of conjugate epipolar
lines become collinear and parallel to one of the image axes. The rectified
images can be thought of as acquired by a new stereo rig, obtained by
rotating the original cameras. The important advantage of rectification is
that computing **stereo correspondences **is reduced to a 1-D search
problem along the horizontal raster lines of the rectified images. Two
techniques are available:

**Calibrated:** The algorithm requires the two
perspective projection matrices of the original cameras, and enforces
explicitly all constraints necessary and sufficient to achieve a unique
pair of rectifying projection matrices.
**Uncalibrated:** This technique allows to rectify stereo
pairs when calibration data (perspective projection matrices) are not
available. The only required input are point correspondences.

### Code

The MATLAB Rectification
Toolkit includes both the calibrated and uncalibrated options. It
requires some functions contained in the MATLAB
Computer Vision Toolkit by A. Fusiello and
VLfeat toolbox by A. Vedaldi.
### Reference papers

- A. Fusiello, E. Trucco, and A. Verri.
**A compact
algorithm for rectification of stereo pairs**. Machine
Vision and Applications, 12(1):16-22, 2000. (PDF)
- Fusiello,
A. and
Irsara, L. Quasi-Euclidean
epipolar rectification of uncalibrated images.
*Machine
Vision and Applications*, 22 (4): 663-670, 2011.
(PDF)