Geometrical analysis of polynomial lens distortion models
This work provides a geometric foundation for lens distortion modeling in computer vision, offering incremental improvements by systematizing model selection based on symmetry and isotropy.
The paper tackles the problem of selecting or designing polynomial lens distortion models by establishing desired geometrical properties a priori, resulting in the derivation of all possible isotropic linear models and axis-symmetric functions, which generalize classical models like decentering and thin prism distortion.
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.