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Extracting 3D Objects from Volume Data Using Digital Morse Theory

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Computer Vision, Virtual Reality and Robotics in Medicine (CVRMed 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 905))

Abstract

Algorithms that tile isovalued surfaces should produce “correctly” tiled orientable manifold surfaces. Rigorous evaluation of different algorithms or case tables has been impossible up to now because of the lack of a clear and comprehensive theoretical framework. We propose and develop an extension of continuous Morse theory, called Digital Morse Theory. In contrast to applications of Morse theory for a single isovalued surface, we seek to apprehend the data as a whole, independent of isovalue. DMT provides a heuristic to correctly disambiguate tiling decisions. DMT gives insight into topologically correct simplification of a volume data set independent of isovalue. We discuss our preliminary implementation of these ideas, with applications to imaging, segmentation, and navigation of a volume while dynamically changing resolution scale and/or isovalue.

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Author information

Authors and Affiliations

  1. Department of Surgery, New York University Medical Center, 560 First Avenue, New York, New York, 10016

    Daniel B. Karron

  2. Department of Computer Science, Brooklyn College of the City University Of New York, USA

    James Cox

Authors
  1. Daniel B. Karron
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  2. James Cox
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Editor information

Editors and Affiliations

  1. INRIA, B. P. 93, F-06902, Sophia-Antipolis, France

    Nicholas Ayache

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© 1995 Springer-Verlag Berlin Heidelberg

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Karron, D.B., Cox, J. (1995). Extracting 3D Objects from Volume Data Using Digital Morse Theory. In: Ayache, N. (eds) Computer Vision, Virtual Reality and Robotics in Medicine. CVRMed 1995. Lecture Notes in Computer Science, vol 905. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-49197-2_64

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  • DOI: https://doi.org/10.1007/978-3-540-49197-2_64

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-59120-7

  • Online ISBN: 978-3-540-49197-2

  • eBook Packages: Springer Book Archive

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