3D-orientation signatures with conic kernel filtering for multiple motion analysis

In this paper we propose a new 3D kernel for the recovery of 3D-orientation signatures. The kernel is a Gaussian function defined in local spherical coordinates and its Cartesian support has the shape of a truncated cone with its axis in the radial direction and very small angular support. A set of such kernels is obtained by uniformly sampling the 2D space of polar and azimuth angles. The projection of a local neighborhood on such a kernel set produces a local 3D-orientation signature. In the case of spatiotemporal 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 single or multiple motion produce maxima in the orientation signature. Due to the kernel's local support spatiotemporal signatures possess higher orientation resolution than 3D steerable filters and 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 EM-based multiple motion detection.