Geometrical analysis of polynomial lens distortion models

TL;DR

This paper provides a geometric framework for designing polynomial lens distortion models, identifying all isotropic and axis-symmetric models, and relating classical models to these families for improved understanding and generalization.

Contribution

It introduces a comprehensive geometric approach to classify and extend polynomial lens distortion models based on their symmetry properties.

Findings

Classical distortion models are special cases of the geometric families identified.

All isotropic linear models for lens distortion are characterized.

The approach aids in designing models with desired geometric properties.

Abstract

Polynomial functions are a usual choice to model the nonlinearity of lenses. Typically, these models are obtained through physical analysis of the lens system or on purely empirical grounds. The aim of this work is to facilitate an alternative approach to the selection or design of these models based on establishing a priori the desired geometrical properties of the distortion functions. With this purpose we obtain all the possible isotropic linear models and also those that are formed by functions with symmetry with respect to some axis. In this way, the classical models (decentering, thin prism distortion) are found to be particular instances of the family of models found by geometric considerations. These results allow to find generalizations of the most usually employed models while preserving the desired geometrical properties. Our results also provide a better understanding of the geometric properties of the models employed in the most usual computer vision software libraries.