On the Maximum Radius of Polynomial Lens Distortion

Polynomial radial lens distortion models are widely used in image processing and computer vision applications to compensate for when straight lines in the world appear curved in an image. While polynomial models are used pervasively in software ranging from PhotoShop to OpenCV to Blender, they have an often overlooked behavior: polynomial models can fold back onto themselves. This property often goes unnoticed when simply warping to undistort an image. However, in applications such as augmented reality where 3D scene geometry is projected and distorted to overlay an image, this folding can result in a surprising behavior. Points well outside the field of view can project into the middle of the image. The domain of a radial distortion model is only valid up to some (possibly infinite) maximum radius where this folding occurs. This paper derives the closed form expression for the maximum valid radius and demonstrates how this value can be used to filter invalid projections or validate the range of an estimated lens model. Experiments on the popular Lensfun database demonstrate that this folding problem exists on 30% of lens models used in the wild.