A cubic polynomial model for fisheye camera

In this paper, we present a kind of cubic polynomial model for fisheye camera by using the lifting strategy, which point coordinates in low dimension space is lifted to a vector in high dimension space. In contrast to existing the lifting strategies, our lifting strategy is to permit 3D point coordinates to appear in higher order polynomials. This paper demonstrates that the cubic polynomial model can effectively express the fisheye image points as the cubic polynomial function of world coordinates. Thus this allows a linear algorithm to estimate the nonlinear models, and in particular offers a simple solution to the estimation of the nonlinear relationship between 3D point and its corresponding fisheye image points. Experimental results with synthetic and real fisheye images are presented to show that the fisheye camera is accurately approximated by the explicit cubic polynomial model.