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The Laplace-Beltrami Operator: A Ubiquitous Tool for Image and Shape Processing

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Mathematical Morphology and Its Applications to Signal and Image Processing (ISMM 2013)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 7883))

Abstract

The ubiquity of the Laplace-Beltrami operator in shape analysis can be seen by observing the wide variety of applications where it has been found to be useful. Here we demonstrate a small subset of such uses with their latest developments including a scale invariant transform for general triangulated meshes, an effective and efficient method for denoising meshes using Beltrami flows via high dimensional embeddings of 2D manifolds and finally the possibility of viewing the framework of geodesic active contours as a surface minimization having the Laplace-Beltrami operator as its main ingredient.

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Author information

Authors and Affiliations

  1. Technion - Israel Institute of Technology, Haifa, Israel

    Aaron Wetzler, Yonathan Aflalo, Anastasia Dubrovina & Ron Kimmel

Authors
  1. Aaron Wetzler
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  2. Yonathan Aflalo
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  3. Anastasia Dubrovina
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  4. Ron Kimmel
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Editor information

Editors and Affiliations

  1. Centre for Image Analysis, Swedish University of Agricultural Sciences and Uppsala University, Box 337, 751 05, Uppsala, Sweden

    Cris L. Luengo Hendriks , Gunilla Borgefors  & Robin Strand ,  & 

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Wetzler, A., Aflalo, Y., Dubrovina, A., Kimmel, R. (2013). The Laplace-Beltrami Operator: A Ubiquitous Tool for Image and Shape Processing. In: Hendriks, C.L.L., Borgefors, G., Strand, R. (eds) Mathematical Morphology and Its Applications to Signal and Image Processing. ISMM 2013. Lecture Notes in Computer Science, vol 7883. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38294-9_26

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  • DOI: https://doi.org/10.1007/978-3-642-38294-9_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38293-2

  • Online ISBN: 978-3-642-38294-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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