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On the Equivariance of the Orientation and the Tensor Field Representation
Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-9091-4724
Linköping University, Department of Electrical Engineering, Computer Vision. Linköping University, The Institute of Technology.
1993 (English)Report (Other academic)
Abstract [en]

The tensor representation has proven a successful tool as a mean to describe local multi-dimensional orientation. In this respect, the tensor representation is a map from the local orientation to a second order tensor. This paper investigates how variations of the orientation are mapped to variation of the tensor, thereby giving an explicit equivariance relation. The results may be used in order to design tensor based algorithms for extraction of image features defined in terms of local variations of the orientation, e.g. multi-dimensional curvature or circular symmetries. It is assumed that the variation of the local orientation can be described in terms of an orthogonal transformation group. Under this assumption a corresponding orthogonal transformation group, acting on the tensor, is constructed. Several correspondences between the two groups are demonstrated.

Place, publisher, year, edition, pages
Linköping, Sweden: Linköping University, Department of Electrical Engineering , 1993. , 8 p.
Series
LiTH-ISY-R, ISSN 1400-3902 ; 1530
Keyword [en]
Image analysis, Tensor representation, Orientation
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:liu:diva-53305ISRN: LiTH-ISY-R-1530OAI: oai:DiVA.org:liu-53305DiVA: diva2:288623
Available from: 2010-01-21 Created: 2010-01-20 Last updated: 2014-10-08Bibliographically approved

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Nordberg, KlasKnutsson, HansGranlund, Gösta

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CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf