Epipolar rectification

with E. Trucco,  A. Verri,  L. Irsara

⚠ Disambiguation

The word rectification alone is used in the fields of Computer Vision, Photogrammetry and Image processing with several different meanings. For this reason I shall precede it with an adjective in order to disambiguate. This page is about epipolar (or stereoscopic) rectification. The removal of perspective effects on a single image is called perspective rectification (or control, or correction) and is implemented in this simple Perspective Rectification Toolkit

Description

Given a pair of stereo images, epipolar 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

1. 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)
2. Fusiello, A. and Irsara, L. Quasi-Euclidean epipolar rectification of uncalibrated images.  Machine Vision and Applications, 22 (4): 663-670, 2011.  (PDF)

^(*) These two matrices are obtained from calibration . You might want to download the Calibration Toolkit as well.