A Comparison of Isotropic and Anisotropic Second Order Regularisers for Optical Flow

In variational optical flow estimation, second order regularisation plays an important role, since it offers advantages in the context of non-fronto-parallel motion. However, in contrast to first order smoothness constraints, most second order regularisers are limited to isotropic concepts. Moreover, the few existing anisotropic concepts are lacking a comparison so far. Hence, our contribution is twofold. (i) First, we juxtapose general concepts for isotropic and anisotropic second order reglarisation based on direct second order methods, infimal convolution techniques, and indirect coupling models. For all the aforementioned strategies suitable optical flow regularisers are derived. (ii) Second, we show that modelling anisotropic second order smoothness terms gives an additional degree of freedom when penalising deviations from smoothness. This in turn allows us to propose a novel anisotropic strategy which we call double anisotropic regularisation. Experiments on the two KITTI benchmarks show the qualitative differences between the different strategies. Moreover, they demonstrate that the novel concept of double anisotropic regularisation is able to produce excellent results.