Multidimensional steerable filters and 3D flow estimation

In this work, the 3D flow estimation problem is formulated in the 4D spatiotemporal frequency domain, and it is shown that 3D motion manifests itself as energy concentration along hyper-planes in that domain. Based on this, the construction and use of appropriate directional multidimensional “steerable” filters, which can extract directional energy in spacetime, is proposed. Steerable filters have been constructed for up to 3 dimensions. We extend the relevant mathematical definitions to multiple dimensions and formulate filter-based algorithms for 3D flow estimation. Experimental results on simulated and real data verify the efficiency of the algorithms.