Approximate Regularization for Structural Optical Flow Estimation

We address the problem of maximum a posteriori (MAP) estimation of optical flow with a geometric prior from gray-value images. We estimate simultaneously the optical flow and the corresponding surface - the structural optical flow (SOF) - subject to three types of constraints: intensity constancy, geometric, and smoothness constraints. Our smoothness constraints restrict the unknowns to locally coincide with a set of finitely parameterized admissible functions. The geometric constraints locally enforce consistency between the optical flow and the corresponding surface. Our theory amounts to a discrete generalization of regularization defined in terms of partial derivatives. The point-wise regularizers are efficiently implemented with linear run-time complexity in the number of discretization points. We demonstrate the applicability of our method by example computations of SOF from photographs of human faces.