Self-consistency and universality of camera lens distortion models.
Pré-print CMLA 2011-01 - version du 6 mai 2011
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Auteurs : R. Grompone von Gioi,P. Monasse, J.-M. Morel and Z. Tang
Abstract :
This paper introduces the concepts of "self-consistency'' and ``universality'' to evaluate the validity and precision of camera lens 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). 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 lens distortion models are reviewed and compared for their degree of self-consistency and universality. The study shows that radial symmetric models can be self-consistent, but cannot be used for non radial-symmetric distortion.
Among the evaluated models, the polynomial and the rational models are the only ones to be universal up to precisions of 1/100 pixel. However, the polynomial model, being linear, is much simpler and faster to estimate. Unusually high polynomial orders are required to reach a $1/100$ pixel precision. But our experiments show that such polynomials are easily computed, producing a precise lens 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.
Finally, our experiments show that in the polynomial model the residual errors stabilize for orders between 6 to 12, confirming that no over-fitting occurred. High order polynomials are unavoidable to obtain high precisions, and deliver accuracies hundred to thousand times higher than those obtained with classic models.
This paper introduces the concepts of "self-consistency'' and ``universality'' to evaluate the validity and precision of camera lens 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). 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 lens distortion models are reviewed and compared for their degree of self-consistency and universality. The study shows that radial symmetric models can be self-consistent, but cannot be used for non radial-symmetric distortion.
Among the evaluated models, the polynomial and the rational models are the only ones to be universal up to precisions of 1/100 pixel. However, the polynomial model, being linear, is much simpler and faster to estimate. Unusually high polynomial orders are required to reach a $1/100$ pixel precision. But our experiments show that such polynomials are easily computed, producing a precise lens 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.
Finally, our experiments show that in the polynomial model the residual errors stabilize for orders between 6 to 12, confirming that no over-fitting occurred. High order polynomials are unavoidable to obtain high precisions, and deliver accuracies hundred to thousand times higher than those obtained with classic models.
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