Representing Local Structure Using Tensors II

  • Hans Knutsson
  • Carl-Fredrik Westin
  • Mats Andersson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6688)


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.


structure tensor higher order quadrature monomial filter 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Hans Knutsson
    • 1
    • 2
  • Carl-Fredrik Westin
    • 1
    • 3
  • Mats Andersson
    • 1
    • 2
  1. 1.Department of Biomedical EngineeringLinköping UniversitySweden
  2. 2.Center for Medical Image Science and Visualization (CMIV)LinköpingSweden
  3. 3.Laboratory of Mathematics in Imaging, Brigham and Women’s HospitalHarvard Medical SchoolBostonUSA

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