W. Kropatsch, R. Casablanca, D. Batavia, R. Gonzalez-Diaz:

"Computing and Reducing Slope Complexes";

Talk: 7th intl. Workshop on Computational Topology in Image Context, Malaga; 2019-01-24 - 2019-01-25; in: "Proceedings 7th intl. Workshop on Computational Topology in Image Context", Springer, Berlin Heidelberg (2019), ISBN: 9783030108274; 12 - 25.

In this paper we provide a new characterization of cell de-composition (called slope complex) of a given 2-dimensional continuous surface. Each patch (cell) in the decomposition must satisfy that there exists a monotonic path for any two points in the cell. We prove that any triangulation of such surface is a slope complex and explain how to obtain new slope complexes with a smaller number of slope regions decomposing the surface. We give the minimal number of slope regions by counting certain bounding edges of a triangulation of the surface obtained from its critical points.

http://dx.doi.org/10.1007/978-3-030-10828-1_2

https://publik.tuwien.ac.at/files/publik_282000.pdf

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