Three Dimensional Orientation Signatures with Conic Kernel Filtering for Multiple Motion Analysis

We propose a new 3D kernel for the recovery of 3D orientation signatures. In the Cartesian coordinates, the kernel has a shape of a truncated cone with its axis in the radial direction and very small angular support. In the local spherical coordinates, the angular part of the kernel is a 2D Gaussian function. A set of such kernels is obtained by uniformly sampling the 2D space of azimuth and elevation angles. The projection of a local neighborhood on such a kernel set produces a local 3D orientation signature. In case of spatio-temporal analysis, such a kernel set can be applied either on the derivative space of a local neighborhood or on the local Fourier transform. The well known planes arising from one or multiple motions produce maxima in the orientation signature. The kernel's local support enables the resulting spatiotemporal signatures to possess higher orientation resolution than 3D steerable filters. Consequently, motion maxima can be detected and localized more accurately. We describe and show in experiments the superiority of the proposed kernels compared to Hough transformation or expectation -- maximization based multiple motion detection