2 research outputs found
Local Rotation Invariant Patch Descriptors for 3D Vector Fields
Abstract—In this paper, we present two novel methods for the fast computation of local rotation invariant patch descriptors for 3D vectorial data. Patch based algorithms have recently become very popular approach for a wide range of 2D computer vision problems. Our local rotation invariant patch descriptors allow an extension of these methods to 3D vector fields. Our approaches are based on a harmonic representation for local spherical 3D vector field patches, which enables us to derive fast algorithms for the computation of rotation invariant power spectrum and bispectrum feature descriptors of such patches. Keywords-local feature; 3D vector field; invariance; I
The bispectrum as a source of phase-sensitive invariants for Fourier descriptors: a group-theoretic approach
This paper develops the theory behind the bispectrum, a concept that is well
established in statistical signal processing but not, until recently, extended
to computer vision as a source of frequency-domain invariants. Recent papers on
using the bispectrum in vision show good results when the bispectrum is applied
to spherical harmonic models of three-dimensional (3-D) shapes, in particular
by improving discrimination over previously-proposed magnitude invariants, and
also by allowing detection of neutral pose in human activity detection. The
bispectrum has also been formulated for vector spherical harmonics, which have
been used in medical imaging for 3-D anatomical modeling. In a paper published
in this journal, Smach {\it et al.} use duality theory to establish the
completeness of second-order invariants which, as shown here, are the same as
the bispectrum. This paper unifies earlier works of various researchers by
deriving the bispectrum formula for all compact groups. It also provides a
constructive algorithm for recovering functions from their bispectral values on
SO(3). The main theoretical result shows that the bispectrum serves as a
complete source of invariants for homogeneous spaces of compact groups,
including such important domains as the sphere