2009/02/01 by Ramakrishna Kakarala, Kakarala, Ramakrishna · 2 citations
Chemistry · Computer Science · Engineering · #14L24 #43A77 #68T10 #Blind Source Separation Techniques #FOS: Mathematics #Group Theory (math.GR) #Image and Signal Denoising Methods #Representation Theory (math.RT) #Sparse and Compressive Sensing Techniques #Spectroscopy and Chemometric Analyses
paper · pdf · doi:10.48550/arxiv.0902.0196
openalex publication_date 2009/02/01 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
This paper develops the theory behind the bispectrum, a concept that is well\nestablished in statistical signal processing but not, until recently, extended\nto computer vision as a source of frequency-domain invariants. Recent papers on\nusing the bispectrum in vision show good results when the bispectrum is applied\nto spherical harmonic models of three-dimensional (3-D) shapes, in particular\nby improving discrimination over previously-proposed magnitude invariants, and\nalso by allowing detection of neutral pose in human activity detection. The\nbispectrum has also been formulated for vector spherical harmonics, which have\nbeen used in medical imaging for 3-D anatomical modeling. In a paper published\nin this journal, Smach it et al. use duality theory to establish the\ncompleteness of second-order invariants which, as shown here, are the same as\nthe bispectrum. This paper unifies earlier works of various researchers by\nderiving the bispectrum formula for all compact groups. It also provides a\nconstructive algorithm for recovering functions from their bispectral values on\nSO(3). The main theoretical result shows that the bispectrum serves as a\ncomplete source of invariants for homogeneous spaces of compact groups,\nincluding such important domains as the sphere S2.\n