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2012 | OriginalPaper | Buchkapitel

Structure Tensor Estimation: Introducing Monomial Quadrature Filter Sets

verfasst von : Hans Knutsson, Carl-Fredrik Westin, Mats Andersson

Erschienen in: New Developments in the Visualization and Processing of Tensor Fields

Verlag: Springer Berlin Heidelberg

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Abstract

Description and 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. It has, however, a fairly broad and unspecific meaning. This chapter is intended to provide a framework for displaying the differences and similarities of existing structure estimation approaches. A new method for structure tensor estimation, which is a generalization of many of it’s predecessors, is presented. The method uses pairs of filter sets having Fourier directional responses in the form of monomials, one odd order set and one even order 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. In addition, we show that the chosen filter sets directly links order, scale and the gradient operator. 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.

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Titel: Structure Tensor Estimation: Introducing Monomial Quadrature Filter Sets
verfasst von: Hans Knutsson
Carl-Fredrik Westin
Mats Andersson
Verlag: Springer Berlin Heidelberg
Buch: New Developments in the Visualization and Processing of Tensor Fields
Print ISBN: 978-3-642-27342-1

Electronic ISBN: 978-3-642-27343-8

Copyright-Jahr: 2012
DOI: https://doi.org/10.1007/978-3-642-27343-8_1

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