# Geometrical analysis of polynomial lens distortion models

arXiv: https://arxiv.org/abs/1804.03584 · HTML: https://mlsanity.com/paper/1804.03584/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Apr 2018.

## Built on by (most cited first, 1 of 1)

- [Automatic camera orientation estimation for a partially calibrated camera above a plane with a line at known planar distance](https://mlsanity.com/paper/2507.20689/) (2025)

## Abstract (arXiv)

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.