This paper presents radial distortion invariants and their application to lens evaluation under a single-optical-axis omnidirectional camera. Little work on geometric invariants of distorted images has been reported previously. We establish accurate geometric invariants from 2-dimensional/3-dimensional space points and their radially distorted image points. Based on the established invariants in a single image, we construct criterion functions and then design a feature vector for evaluating the camera lens, where the infinity norm of the feature vector is computed to indicate the tangent distortion amount. The evaluation is simple and convenient thanks to the feature vector that is analytical and straightforward on image points and space points without any other computations. In addition, the evaluation is flexible since the used invariants make any a coordinate system of measuring space or image points workable. Moreover, the constructed feature vector is free of point orders and resistant to noise. The established invariants in the paper have other potential applications such as camera calibration, image rectification, structure reconstruction, image matching, and object recognition. Extensive experiments, including on structure reconstruction, demonstrate the usefulness, higher accuracy, and higher stability of the present work. 
Radial distortion invariants and lens evaluation under a single-optical-axis omnidirectional camera