This paper conducts a rigorous precision analysis of five classic camera distortion models—radial, division, FOV, polynomial, and rational—to determine their effectiveness in achieving high subpixel correction accuracy. Through extensive synthetic experiments using the Lensfun library and real-world validations with non-parametric distortion estimation and a plumb-line setup, the authors compare the models' simulation and inversion capabilities. While radially symmetric models can achieve high precision for ideal distortions, their non-linear optimization presents numerical risks. The study concludes that polynomial and rational models, though lacking direct physical interpretation, are more versatile as they are invariant to the distortion center and effectively model non-radially symmetric distortions. Particularly, the polynomial model, despite requiring higher degrees, is highlighted as the most secure and precise option due to its linear estimation process, achieving sub-pixel precision better than 0.1 pixels, especially for large distortions.
Precision Analysis of Camera Distortion Models
Introduction to Camera Distortion (Section I): Real cameras deviate from the ideal pinhole model due to lens geometric distortion and CCD shape, making accurate distortion correction critical for high-precision 3D metric reconstruction from photographs.
Five Models Evaluated (Section I): The paper investigates the radial, division, FOV, polynomial, and rational distortion models, evaluating their precision, especially at sub-pixel levels (up to 1/100 pixels).
Model Properties (Section I & II): Radially symmetric models are precise for radially symmetric distortions but require estimating a distortion center. Polynomial and rational models are more flexible, invariant to the distortion center, and can handle both radial and non-radially symmetric distortions.
Polynomial Model Advantage (Section I & II): The polynomial model stands out as the only linear model, allowing for secure and fast estimation through simple matrix inversion, which significantly reduces numerical risk compared to other models that require complex non-linear minimization.
Synthetic Experiments (Section III): Using the Lensfun library (over 3500 lens profiles), the models' abilities to simulate and invert distortions were tested. All models could achieve the target 10^-5 precision (equivalent to 1/100 pixel for typical images) for synthetic data if a sufficiently high order was used.
Known vs. Unknown Distortion Center (Section III.A & III.B): When the distortion center is known, radial models perform well. Even with an unknown distortion center, the results were very similar because accurate linear initialization methods exist, and polynomial/rational models are inherently invariant.
Radial vs. Division Models (Section III.C): Contrary to some previous claims, the paper found only marginal improvement of the division model over the radial model at the same number of parameters.
Realistic Distortion Simulation (Section III.D): When simulating a distortion based on a more complex radial+tangential model from a real camera, polynomial and rational models showed superior precision (1e-5 pixels) compared to radial-only or radial+tangential models.
Real Distortion Fitting (Section IV): Using a non-parametric method to estimate actual camera distortion from textured patterns, the polynomial and rational models consistently yielded smaller and more stable fitting errors than radially symmetric models, even when the latter accounted for homography and CCD slant.
Plumb-Line Validation (Section V): An objective physical test using tightly stretched strings confirmed the stability and quality of correction for all models. For large distortions (e.g., 18mm focal length), polynomial and rational models were twice as precise.
Key Takeaway: Polynomial Model for High Precision (Section VI): The paper concludes that for high-precision distortion correction (e.g., 1/100 pixels), the polynomial model is the best choice due to its numerical stability, linear estimation, and ability to handle various distortion types.
Methodological Implications (Section VI): For optimal results, distortion correction should be treated as an independent pre-processing step before camera calibration, and calibration patterns should include a high number of control points (e.g., >500) to support the parameter requirements of high-degree polynomial models.