Approximate model of fisheye camera based on the optical refraction

This paper proposes an approximate model of fisheye camera based on the optical refraction. The model of fisheye lens is firstly derived from the optical refraction and the structure of fisheye lenses. Secondly, a suitable linearization of the fisheye model is developed in order to obtain an approximate model, and the approximate model including two parameters is constructed from the linearization of the fisheye model. Finally, the estimation algorithm on the model parameters is presented using the epipolar constraint between two fisheye images. Furthermore, we provide lots of experiments with synthetic data and real fisheye images. To start with, the feasibility of the approximate model is tested through fitting the five common designed model of fisheye lens with synthetic data. Two groups of experiments with real fisheye image are then performed to estimate the model parameters. In practical situation, this method can automatically establish image correspondences using an improved random sample consensus algorithm without calibration objects.