# Epipolar rectification

A. Fusiello, E. Trucco and A. Verri

### 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. We present a linear rectification
algorithm for general, unconstrained stereo rigs. 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.

### Reference paper

- 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)

## _Uncalibrated_ epipolar rectification

This technique allows to rectify stereo pairs when calibration data
(perspective projection matrices) are not available. The only required
input are point correspondences. The code for image matching can be
downloaded
here (it depends on functions from other authors).

### Reference paper

- A. Fusiello and L. Irsara.
Quasi-euclidean Uncalibrated Epipolar Rectification. International
Conference on Pattern Recognition (ICPR), 2008, Tampa, FL
(PDF)
(PDF
extended version)