The method of vector fields for catadioptric sensor design with applications to panoramic imaging

We present a design technique for realizing given projections as catadioptric sensors. In general, these problems do not have solutions, but approximate solutions may often be found that are visually acceptable. Our approach, which we call the "method of vector fields", reduces the problem to solving a linear system. A given transformation between the image plane object surface is shown to determine a vector field which is normal to the surface in the case where the vector field is a gradient. If the vector field is not a gradient, we present several functional that may be minimized to give approximate solutions.