Decomposing and regularizing sparse/non-sparse components for motion field estimation

Regularizing motion field is critical to achieve accurate estimation of the motion field. As the motion field may include discontinuity (e.g., at the motion boundaries), traditional smoothness regularization may not work well. Among many approaches to handling motion discontinuity, recent attempts pursued a sparse representation of the motion field for regularization, and achieved quite encouraging results. However, statistics show that these methods tend to over-sparsify the motion field, and thus confronted by the non-sparse noise in practice. In this paper, we propose to decompose the motion field into sparse and non-sparse components for the motion boundaries and small universal noises, respectively. This separation approach regularizes these two sources differently. We propose a novel and efficient optimization algorithm to solve this problem. In addition, our study reveals the in-depth connection between this noise separation approach and the influence function approach in robust statistics. We validate and evaluate our new approach on the Middlebury benchmark, and have achieved outstanding testing performance.