Rectifying homographies for stereo vision: analytical solution for minimal distortion

TL;DR

This paper presents a closed-form solution for stereo rectification homographies that minimizes perspective distortion, improving accuracy and convergence over previous numerical methods, with an available Python implementation.

Contribution

It introduces an analytical method for stereo rectification that reduces distortion and enhances computational stability compared to prior numerical approaches.

Findings

The proposed solution effectively minimizes perspective distortion.

It outperforms previous methods in convergence reliability.

Python implementation is provided for practical use.

Abstract

Stereo rectification is the determination of two image transformations (or homographies) that map corresponding points on the two images, projections of the same point in the 3D space, onto the same horizontal line in the transformed images. Rectification is used to simplify the subsequent stereo correspondence problem and speeding up the matching process. Rectifying transformations, in general, introduce perspective distortion on the obtained images, which shall be minimised to improve the accuracy of the following algorithm dealing with the stereo correspondence problem. The search for the optimal transformations is usually carried out relying on numerical optimisation. This work proposes a closed-form solution for the rectifying homographies that minimise perspective distortion. The experimental comparison confirms its capability to solve the convergence issues of the previous formulation. Its Python implementation is provided.