A survey on variational optic flow methods for small displacements

Optic fow describes the displacement field in an image sequence. Its reliable computation constitutes one of the main challenges in computer vision, and variational methods belong to the most successful techniques for achieving this goal. Variational methods recover the optic flow field as a minimiser of a suitable energy functional that involves data and smoothness terms. In this paper we present a survey on different model assumptions for each of these terms and illustrate their impact by experiments. We restrict ourselves to rotationally invariant convex functionals with a linearised data term. Such models are appropriate for small displacements. Regarding the data term, constancy assumptions on the brightness, the gradient, the Hessian, the gradient magnitude, the Laplacian, and the Hessian determinant are investigated. Local integration and nonquadratic penalisation are considered in order to improve robustness under noise. With respect to the smoothness term, we review a recent taxonomy that links regularisers to diffusion processes. It allows to distinguish five types of regularisation strategies: homogeneous, isotropic image-driven, anisotropic image-driven, isotropic flow-driven, and anisotropic flow-driven. All these regularisations can be performed either in the spatial or the spatiotemporal domain. After discussing well-posedness results for convex optic flow functionals, we sketch some numerical ideas in order to achieve realtime performance on a standard PC by means of multigrid methods, and we survey a simple and intuitive confidence measure