Self-consistency and universality of camera lens distortion models

This paper introduces the concepts of "self-consistency" and "universality" to evaluate high precision camera distortion models. Self-consistency is evaluated by the residual error when the distortion generated with a certain model is corrected by the best parameters for the same model (used in reverse way, which is common practice). Analogously, universality is measured by the residual error when a model is used to correct distortions generated by a family of other models. Five classic camera distortion models are reviewed and compared for their degree of self-consistency and universality. Among the evaluated models, it is concluded that only the polynomial and the rational models are universal up to precisions of 1/100 pixel. However, the polynomial model, being linear, is much simpler and faster to estimate. Unusually high polynomial degrees are required to reach this strong precision. Nevertheless, extensive numerical experiments show that such distortion polynomials are easily estimated and produce a precise distortion correction without over-fitting. Our conclusions are validated by three independent experimental setups: The models are compared first in synthetic experiments by their approximation power; second by fitting a real camera distortion estimated by a non parametric algorithm; and finally by the absolute correction measurement provided by photographs of tightly stretched strings, warranting a high straightness.