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Practical and Intuitive Basis for Tensor Field Processing with Invariant Gradients and Rotation Tangents

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Book cover Tensors in Image Processing and Computer Vision

Part of the book series: Advances in Pattern Recognition ((ACVPR))

Abstract

Abstract Recent work has outlined a framework for analyzing diffusion tensor gradient and covariance tensors in terms of invariant gradient and rotation tangents, which span local variations in tensor shape and orientation, respectively. This chapter hopes to increase the adoption of this framework by giving it a more intuitive conceptual description, as well as providing practical advice for its numeric implementation. Example applications are described, with an emphasis on decomposing the third-order gradient of a diffusion tensor field.

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Author information

Authors and Affiliations

  1. Laboratory of Mathematics in Imaging, Brigham and Women’s Hospital, Boston, Massachusetts

    Gordon L. Kindlmann & Carl-Fredrik Westin

Authors
  1. Gordon L. Kindlmann
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  2. Carl-Fredrik Westin
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Corresponding author

Correspondence to Gordon L. Kindlmann .

Editor information

Editors and Affiliations

  1. Escuela Técnica Superior de Ingenieros de Telecomunicacíon, Universidad de Valladolid, Campus Miguel Delibes, 47011 Valladolid, Spain

    Santiago Aja-Fernández  & Rodrigo de Luis García  & 

  2. Dept. Computing, HongKong Polytechnic University, Hong Kong

    Dacheng Tao

  3. University of London Birkbeck College School of Computer Science & Information Systems, Malet Street, London, WC1E 7HX, UK

    Xuelong Li

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© 2009 Springer-Verlag London Limited

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Kindlmann, G.L., Westin, CF. (2009). Practical and Intuitive Basis for Tensor Field Processing with Invariant Gradients and Rotation Tangents. In: Aja-Fernández, S., de Luis García, R., Tao, D., Li, X. (eds) Tensors in Image Processing and Computer Vision. Advances in Pattern Recognition. Springer, London. https://doi.org/10.1007/978-1-84882-299-3_14

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  • DOI: https://doi.org/10.1007/978-1-84882-299-3_14

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-84882-298-6

  • Online ISBN: 978-1-84882-299-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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