Hierarchical morse complexes for piecewise linear 2-manifolds
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Morse-smale complexes for piecewise linear 3-manifolds
Proceedings of the nineteenth annual symposium on Computational geometry
External Memory Management and Simplification of Huge Meshes
IEEE Transactions on Visualization and Computer Graphics
Applications of Forman's Discrete Morse Theory to Topology Visualization and Mesh Compression
IEEE Transactions on Visualization and Computer Graphics
Foundations of Multidimensional and Metric Data Structures (The Morgan Kaufmann Series in Computer Graphics and Geometric Modeling)
Describing shapes by geometrical-topological properties of real functions
ACM Computing Surveys (CSUR)
A Practical Approach to Morse-Smale Complex Computation: Scalability and Generality
IEEE Transactions on Visualization and Computer Graphics
Incremental construction of the delaunay triangulation and the delaunay graph in medium dimension
Proceedings of the twenty-fifth annual symposium on Computational geometry
Spatial indexing on tetrahedral meshes
Proceedings of the 18th SIGSPATIAL International Conference on Advances in Geographic Information Systems
Theory and Algorithms for Constructing Discrete Morse Complexes from Grayscale Digital Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
The PR-star octree: a spatio-topological data structure for tetrahedral meshes
Proceedings of the 19th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
Direct Feature Visualization Using Morse-Smale Complexes
IEEE Transactions on Visualization and Computer Graphics
A primal/dual representation for discrete morse complexes on tetrahedral meshes
EuroVis '13 Proceedings of the 15th Eurographics Conference on Visualization
Hi-index | 0.00 |
Several algorithms have recently been introduced for morphological analysis of scalar fields (terrains, static and dynamic volume data) based on a discrete version of Morse theory. However, despite the applicability of the theory to very general discretized domains, memory constraints have limited its practical usage to scalar fields defined on regular grids, or to relatively small simplicial complexes. We propose an efficient and effective data structure for the extraction of morphological features, such as critical points and their regions of influence, based on the PR-star octree data structure [24], which uses a spatial index over the embedding space of the complex to locally reconstruct the connectivity among its cells. We demonstrate the effectiveness and scalability of our approach over irregular simplicial meshes in 2D and in 3D with a set of streaming algorithms which extract topological features of the associated scalar field from its locally computed discrete gradient field. Specifically, we extract the critical points of the scalar field, their corresponding regions in the Morse decomposition of the field domain induced by the gradient field, and their connectivity.