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Innovations for Shape Analysis pp 3–34Cite as

Modeling Three-Dimensional Morse and Morse-Smale Complexes

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Part of the book series: Mathematics and Visualization ((MATHVISUAL))

Abstract

Morse and Morse-Smale complexes have been recognized as a suitable tool for modeling the topology of a manifold M through a decomposition of M induced by a scalar field f defined over M. We consider here the problem of representing, constructing and simplifying Morse and Morse-Smale complexes in 3D. We first describe and compare two data structures for encoding 3D Morse and Morse-Smale complexes. We describe, analyze and compare algorithms for computing such complexes. Finally, we consider the simplification of Morse and Morse-Smale complexes by applying coarsening operators on them, and we discuss and compare the coarsening operators on Morse and Morse-Smale complexes described in the literature.

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Acknowledgements

This work has been partially supported by the Italian Ministry of Education and Research under the PRIN 2009 program, and by the National Science Foundation under grant number IIS-1116747.

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Authors and Affiliations

  1. Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovića 6, Novi Sad, Serbia

    Lidija Čomić

  2. Department of Computer Science, University of Genova, via Dodecaneso 35, Genova, Italy

    Leila De Floriani & Federico Iuricich

Authors
  1. Lidija Čomić
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  2. Leila De Floriani
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  3. Federico Iuricich
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Correspondence to Lidija Čomić .

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Editors and Affiliations

  1. , Inst. for Appl. Math.&Scient.Comp., Brandenburg Technical University, Platz der Deutschen Einheit 1, Cottbus, 03046, Germany

    Michael Breuß

  2. Department of Computer Science, Technion-Israel Institute of Technology, Haifa, 32000, Israel

    Alfred Bruckstein

  3. School of Electrical &, Computer Engineering, National Technical University of Athens, Athens, 15773, Greece

    Petros Maragos

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Čomić, L., De Floriani, L., Iuricich, F. (2013). Modeling Three-Dimensional Morse and Morse-Smale Complexes. In: Breuß, M., Bruckstein, A., Maragos, P. (eds) Innovations for Shape Analysis. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34141-0_1

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