Computer Aided Geometric Design - Special issue: Applications of geometric modeling in the life sciences
Describing shapes by geometrical-topological properties of real functions
ACM Computing Surveys (CSUR)
Ascending and descending regions of a discrete Morse function
Computational Geometry: Theory and Applications
Computer Aided Geometric Design - Special issue: Applications of geometric modeling in the life sciences
On the search of optimal reconstruction resolution
Pattern Recognition Letters
SMI 2013: Steepest descent paths on simplicial meshes of arbitrary dimensions
Computers and Graphics
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The 3D Morse-Smale complex is a fundamental topological construct that partitions the domain of a real-valued function into regions having uniform gradient flow behavior. In this paper, we consider the construction and selective presentation of cells of the Morse-Smale complex and their use in the analysis and visualization of scientific datasets. We take advantage of the fact that cells of different dimension often characterize different types of features present in the data. For example, critical points pinpoint changes in topology by showing where components of the level sets are created, destroyed or modified in genus. Edges of the Morse-Smale complex extract filament-like features that are not explicitly modeled in the original data. Interactive selection and rendering of portions of the Morse-Smale complex introduces fundamental data management challenges due to the unstructured nature of the complex even for structured inputs. We describe a data structure that stores the Morse-Smale complex and allows efficient selective traversal of regions of interest. Finally, we illustrate the practical use of this approach by applying it to cryo-electron microscopy data of protein molecules.