Abstract
Ascending and descending Morse complexes, defined by a scalar function f over a manifold domain M, decompose M into regions of influence of the critical points of f, thus representing themorphology of the scalar function f over M in a compact way. Here, we introduce two simplification operators on Morse complexes which work in arbitrary dimensions and we discuss their interpretation as n-dimensional Euler operators. We consider a dual representation of the two Morse complexes in terms of an incidence graph and we describe how our simplification operators affect the graph representation. This provides the basis for defining a multi-scale graph-based model of Morse complexes in arbitrary dimensions.
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Acknowledgements
This work has been partially supported by the National Science Foundation under grant CCF-0541032, by the MIUR-FIRB project SHALOM under contract number RBIN04HWR8, and by the Ministry of Science of the Republic of Serbia through Project 23036.
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Čomić, L., De Floriani, L. (2011). Modeling and Simplifying Morse Complexes in Arbitrary Dimensions. In: Pascucci, V., Tricoche, X., Hagen, H., Tierny, J. (eds) Topological Methods in Data Analysis and Visualization. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15014-2_7
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DOI: https://doi.org/10.1007/978-3-642-15014-2_7
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