Morse Set Classification and Hierarchical Refinement Using Conley Index

—Morse decomposition provides a numerically stable topological representation of vector fields that is crucial for their rigorous interpretation. However, Morse decomposition is not unique, and its granularity directly impacts its computational cost. In this paper, we propose an automatic refinement scheme to construct the Morse Connection Graph (MCG) of a given vector field in a hierarchical fashion. Our framework allows a Morse set to be refined through a local update of the flow combinatorialization graph, as well as the connection regions between Morse sets. The computation is fast because the most expensive computation is concentrated on a small portion of the domain. Furthermore, the present work allows the generation of a topologically consistent hierarchy of MCGs, which cannot be obtained using a global method. The classification of the extracted Morse sets is a crucial step for the construction of the MCG, for which the Poincare´ index is inadequate. We make use of an upper...

• Type: Journal
• Year: 2012
• Where: TVCG
• Authors: Guoning Chen, Qingqing Deng, Andrzej Szymczak, Robert S. Laramee, Eugene Zhang
• Keywords: Connection Graph, Hardware, TVCG 2012, Vector Fields, Visualization Technique