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A Fully Implicit Framework for Sobolev Active Contours and Surfaces

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Pattern Recognition (DAGM 2011)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 6835))

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Abstract

We present a convenient framework for Sobolev active contours and surfaces, which uses an implicit representation on purpose, in contrast to related approaches which use an implicit representation only for the computation of Sobolev gradients. Another difference to related approaches is that we use a Sobolev type inner product, which has a better geometric interpretation, such as the ones proposed for Sobolev active contours. Since the computation of Sobolev gradients for surface evolutions requires the solution of partial differential equations on surfaces, we derive a numerical scheme which allows the user to obtain approximative Sobolev gradients even in linear complexity, if desired. Finally, we perform several experiments to demonstrate that the resulting curve and surface evolutions enjoy the same regularity properties as the original Sobolev active contours and show the whole potential of our method by tracking the left ventricular cavity acquired with 4D MRI.

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Author information

Authors and Affiliations

  1. Computer Aided Medical Procedures and Augmented Reality (CAMPAR), Technische Universität München, Germany

    Maximilian Baust & Nassir Navab

Authors
  1. Maximilian Baust
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  2. Nassir Navab
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Editor information

Editors and Affiliations

  1. Visual Sensorics and Information Processing Lab, Johann-Wolfgang Goethe University, 60054, Frankfurt/Main, Germany

    Rudolf Mester

  2. Computer Vision Laboratory, Linköping University, 58183, Linköping, Sweden

    Michael Felsberg

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© 2011 Springer-Verlag Berlin Heidelberg

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Baust, M., Navab, N. (2011). A Fully Implicit Framework for Sobolev Active Contours and Surfaces. In: Mester, R., Felsberg, M. (eds) Pattern Recognition. DAGM 2011. Lecture Notes in Computer Science, vol 6835. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23123-0_3

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  • DOI: https://doi.org/10.1007/978-3-642-23123-0_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-23122-3

  • Online ISBN: 978-3-642-23123-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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