Optic Flow Scale Space

Abstract

While image scale spaces are well understood, it is undeniable that the regularisation parameter in variational optic flow methods serves a similar role as the scale parameter in scale space evolutions. However, no thorough analysis of this optic flow scale-space exists to date. Our paper closes this gap by interpreting variational optic flow methods as Whittaker-Tikhonov regularisations of the normal flow, evaluated in a constraint-specific norm. The transition from this regularisation framework to an optic flow evolution creates novel vector-valued scale-spaces that are not in divergence form and act in a highly anisotropic way. From a practical viewpoint, the deep structure in optic flow scale space allows the automatic selection of the most accurate scale by means of an optimal prediction principle. Moreover, we show that our general class of optic flow scale-spaces incorporates novel methods that outperform classical variational approaches.