The Cubic Rational Polynomial Camera Model

This paper describes an implementation of the Cubic Rational Polynomial Camera model developed as part of the FOCUS project. FOCUS ([1]) is on ongoing “shared vision” IR&D project jointly sponsored by Lockheed Martin Missiles and Space (LMMSS/Sunnyvale) and General Electric CR&D. A cubic camera has the advantage that all cameras, such as projective, affine and the linear pushbroom, which map the image points as rational polynomial functions (of degree no greater than 3) of the coordinates of a world point, can be treated as special cases of the cubic camera. This paper demonstrates that the cubic camera can very effectively model even those cameras which express the image points as complicated functions of world coordinates, such as radicals. In particular, it is empirically demonstrated that a SAR sensor is very accurately approximated by a cubic camera, but not by any linear camera model. The paper also outlines an algorithm for estimating the parameters of the cubic camera, given a set of image to world correspondences. The non-linear nature of this camera can make parameter estimation a very unstable process. The slightest noise in the coefficients of the nonlinear terms can lead to a completely unrealistic model of the camera. This paper discusses some refinements such as avoiding degeneracies, data normalization, and regularization which are necessary for accurate estimation of the cubic camera parameters and minimization of noise in the coefficients of the higher degree terms.