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https://open.uns.ac.rs/handle/123456789/16249
Title: | Smale-like decomposition and Forman theory for discrete scalar fields | Authors: | Čomić, Lidija Mesmoudi M. De Floriani L. |
Issue Date: | 18-Apr-2011 | Journal: | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Abstract: | Forman theory, which is a discrete alternative for cell complexes to the well-known Morse theory, is currently finding several applications in areas where the data to be handled are discrete, such as image processing and computer graphics. Here, we show that a discrete scalar field f, defined on the vertices of a triangulated multidimensional domain ∑, and its gradient vector field Grad f through the Smale-like decomposition of f [6], are both the restriction of a Forman function F and its gradient field Grad F that extends f over all the simplexes of ∑. We present an algorithm that gives an explicit construction of such an extension. Hence, the scalar field f inherits the properties of Forman gradient vector fields and functions from field Grad F and function F. © 2011 Springer-Verlag. | URI: | https://open.uns.ac.rs/handle/123456789/16249 | ISBN: | 9783642198663 | ISSN: | 3029743 | DOI: | 10.1007/978-3-642-19867-0_40 |
Appears in Collections: | FTN Publikacije/Publications |
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