A geometric framework and a new criterion in optical flow modeling

We evaluate the dense optical flow between two frames via variational approach. In this paper, a new framework for deriving the regularization term is introduced giving a geometric insight into the action of a smoothing term. The framework is based on the Beltrami paradigm in image denoising. It includes a general formulation that unifies several previous methods. Using the proposed framework we also derive two novel anisotropic regularizers incorporating a new criterion that requires co-linearity between the gradients of optical flow components and possibly the intensity gradient. We call this criterion "alignment" and reveal its existence also in the celebrated Nagel and Enkelmann's formulation. It is shown that the physical model of rotational motion of a rigid body, pure divergent/convergent flow and irrotational fluid flow, satisfy the alignment criterion in the flow field. Experimental tests in comparison to a recently published method show the capability of the new criterion in improving the optical flow estimations.