A Precision Analysis of Camera Distortion Models

Abstract

This paper addresses the question of identifying the right camera direct or inverse distortion model, permitting a high subpixel precision to fit to real camera distortion. Five classic camera distortion models are reviewed and their precision is compared for direct or inverse distortion. By definition, the three radially symmetric models can only model a distortion radially symmetric around some distortion center. They can be extended to deal with non-radially symmetric distortions by adding tangential distortion components, but still may be too simple for very accurate modeling of real cameras. The polynomial and the rational models instead miss a physical or optical interpretation, but can cope equally with radially and non-radially symmetric distortions. Indeed, they do not require the evaluation of a distortion center. When requiring high precisions, we found that the distortion modeling must also be evaluated primarily as a numerical problem. Indeed, all models except the polynomial involve a non-linear minimization, which increases the numerical risk. The estimation of a polynomial distortion model leads instead to a linear problem, which is secure and much faster. We concluded by extensive numerical experiments that, although high degree polynomials were required to reach a high precision of 1/100 pixels, such polynomials were easily estimated and produced a precise distortion modeling without overfitting. Our conclusion is validated by three independent experimental setups: the models were compared first on the lens distortion database of the Lensfun library by their distortion simulation and inversion power; second by fitting real camera distortions estimated by a non parametric algorithm; and finally by the absolute correction measurement provided by the photographs of tightly stretched strings, warranting a high straightness.

Hyperbolic Distortion Model for Radial Distortion Correction

“…Table1 presents the distortion coefficients' estimates computed from the set of points extracted from the panorama imagery. An analysis of the table shows that the imagery exhibits 'moustache' distortion profile described by apposite signs of both the distortion coefficients 1 k and 2 k (Tang et al, 2017). In terms of accuracy of the first distortion coefficient 1 k the line based method was the less efficient for the lenses used in this study while the best results were obtained by the proposed hyperbolic and rational models as illustrated in figure1.…”

Optical Camera Communications: Principles, Modulations, Potential and Challenges

“…The use of a lens in a camera with a focal length not matching to the size of the IS, introduces optical distortions in the captured image [137][138][139]. These distortions can be barrel, pincushion, and mustache distortions, as illustrated in Figure 38.…”

Out-of-Focus Projector Calibration Method with Distortion Correction on the Projection Plane in the Structured Light Three-Dimensional Measurement System

“…The lens distortion of the camera should be corrected to improve the calibration accuracy. Several models exist for lens distortion, such as a radial and tangential distortion model [ 30 , 31 ], rational function distortion model [ 32 , 33 ], division distortion model [ 31 , 34 ], and so on [ 35 ]. In this paper, a typical radial and tangential distortion model was used due to its simplicity and sufficient accuracy, formulated as: where represents the imaging point on the imaging plane of camera with radial and tangential correction, is the imaging point before correction, and is the absolute distance between the imaging point and the original point .…”