Representing local structure using tensors II

Authors:
Hans Knutsson;Carl-Fredrik Westin;Mats Andersson
Affiliations:
Department of Biomedical Engineering, Linköping University, Sweden and Center for Medical Image Science and Visualization (CMIV), Linköping, Sweden;Department of Biomedical Engineering, Linköping University, Sweden and Laboratory of Mathematics in Imaging, Brigham and Women's Hospital, Harvard Medical School, Boston, MA;Department of Biomedical Engineering, Linköping University, Sweden and Center for Medical Image Science and Visualization (CMIV), Linköping, Sweden
Venue:
SCIA'11 Proceedings of the 17th Scandinavian conference on Image analysis
Year:
2011

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Abstract

Estimation of local spatial structure has a long history and numerous analysis tools have been developed. A concept that is widely recognized as fundamental in the analysis is the structure tensor. However, precisely what it is taken to mean varies within the research community. We present a new method for structure tensor estimation which is a generalization of many of it's predecessors. The method uses filter sets having Fourier directional responses being monomials of the normalized frequency vector, one odd order sub-set and one even order sub-set. It is shown that such filter sets allow for a particularly simple way of attaining phase invariant, positive semi-definite, local structure tensor estimates. We continue to compare a number of known structure tensor algorithms by formulating them in monomial filter set terms. In conclusion we show how higher order tensors can be estimated using a generalization of the same simple formulation.