Open Access
A Fast Algorithm for Computing Reeb Graph of 2-Manifold
Jean-Baptiste Debard,Hu Shi Min +1 more
- 01 Jan 2006
TL;DR: An algorithm to compute the Reeb graph of a given Morse function over a compact connected oriented 2-manifold without boundary is presented and its complexity and its running time are discussed.
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Abstract: This paper presents an algorithm to compute the Reeb graph of a given Morse function over a compact connected oriented 2-manifold without boundary. After introducing the motivations for such a new algorithm, we will give the details of the algorithm for simplicial complex, prove its correctness and discuss its complexity and its running time.
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References
Surface coding based on Morse theory
TL;DR: In this paper, a Morse-based coding system for representing the hierarchical structure of contours is presented, and the resulting coding works interactively with a range of surface reconstruction systems.
385
Computational topology algorithms for discrete 2-manifolds
Peter Schröder,Zoë J. Wood +1 more
- 01 Jan 2003
TL;DR: Novel algorithms guaranteed to identify and isolate handles for various discrete surface representations and how geometric models can be greatly improved through topology simplification both for models represented by volume data or by triangle meshes are presented.
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Fair morse functions for extracting the topological structure of a surface mesh
Xinlai Ni,Michael Garland,John Hart +2 more
- 01 Aug 2004
TL;DR: This paper solves a relaxed form of Laplace's equation to find a "fair" Morse function with a user-controlled number and configuration of critical points, and devise a new "intermediate value propagation" multigrid solver for finding fair Morse functions that runs in provably linear time.
Topology matching for fully automatic similarity estimation of 3D shapes
Masaki Hilaga,Yoshihisa Shinagawa,Taku Kohmura,Tosiyasu L. Kunii +3 more
- 01 Aug 2001
TL;DR: A novel technique is proposed, called Topology Matching, in which similarity between polyhedral models is quickly, accurately, and automatically calculated by comparing Multiresolutional Reeb Graphs (MRGs), which operates well as a search key for 3D shape data sets.