Journal of Mathematical Imaging and Vision

, Volume 61, Issue 3, pp 252–268 | Cite as

Geometrical Analysis of Polynomial Lens Distortion Models

  • José I. RondaEmail author
  • Antonio Valdés


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.


Lens distortion Camera calibration Polynomial model 

Mathematics Subject Classification

51 78 



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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Grupo de Tratamiento de ImágenesUniversidad Politécnica de MadridMadridSpain
  2. 2.Departamento de Álgebra, Geometría y TopologíaUniversidad Complutense de MadridMadridSpain

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