Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Introduction to Solid Modeling
Introduction to Solid Modeling
Topological models for boundary representation: a comparison with n-dimensional generalized maps
Computer-Aided Design - Beyond solid modelling
The watershed transform: definitions, algorithms and parallelization strategies
Fundamenta Informaticae - Special issue on mathematical morphology
Topology preserving and controlled topology simplifying multiresolution isosurface extraction
Proceedings of the conference on Visualization '00
Hierarchical morse complexes for piecewise linear 2-manifolds
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Exploring scalar fields using critical isovalues
Proceedings of the conference on Visualization '02
Multiresolution Representation of Shapes Based on Cell Complexes (Invited Paper)
DCGI '99 Proceedings of the 8th International Conference on Discrete Geometry for Computer Imagery
Detecting critical regions in scalar fields
VISSYM '03 Proceedings of the symposium on Data visualisation 2003
Molecular shape analysis based upon the morse-smale complex and the connolly function
Proceedings of the nineteenth annual symposium on Computational geometry
Morse-smale complexes for piecewise linear 3-manifolds
Proceedings of the nineteenth annual symposium on Computational geometry
Applications of Forman's Discrete Morse Theory to Topology Visualization and Mesh Compression
IEEE Transactions on Visualization and Computer Graphics
Fair morse functions for extracting the topological structure of a surface mesh
ACM SIGGRAPH 2004 Papers
A Multi-resolution Data Structure for Two-dimensional Morse-Smale Functions
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Maximizing Adaptivity in Hierarchical Topological Models
SMI '05 Proceedings of the International Conference on Shape Modeling and Applications 2005
Persistence-sensitive simplification functions on 2-manifolds
Proceedings of the twenty-second annual symposium on Computational geometry
Vector Field Editing and Periodic Orbit Extraction Using Morse Decomposition
IEEE Transactions on Visualization and Computer Graphics
Efficient Computation of Morse-Smale Complexes for Three-dimensional Scalar Functions
IEEE Transactions on Visualization and Computer Graphics
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
A polyhedron representation for computer vision
AFIPS '75 Proceedings of the May 19-22, 1975, national computer conference and exposition
Ascending and descending regions of a discrete Morse function
Computational Geometry: Theory and Applications
Topological analysis and characterization of discrete scalar fields
Proceedings of the 11th international conference on Theoretical foundations of computer vision
Cancellation of critical points in 2D and 3D Morse and Morse-Smale complexes
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
A topological hierarchy for functions on triangulated surfaces
IEEE Transactions on Visualization and Computer Graphics
Simplifying morphological representations of 2D and 3D scalar fields
Proceedings of the 19th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
SMI 2012: Short Dimension-independent multi-resolution Morse complexes
Computers and Graphics
A primal/dual representation for discrete morse complexes on tetrahedral meshes
EuroVis '13 Proceedings of the 15th Eurographics Conference on Visualization
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Ascending and descending Morse complexes, determined by a scalar field f defined over a manifold M, induce a subdivision of M into regions associated with critical points of f, and compactly represent the topology of M. We define two simplification operators on Morse complexes, which work in arbitrary dimensions, and we define their inverse refinement operators. We describe how simplification and refinement operators affect Morse complexes on M, and we show that these operators form a complete set of atomic operators to create and update Morse complexes on M. Thus, any operator that modifies Morse complexes on M can be expressed as a suitable sequence of the atomic simplification and refinement operators we have defined. The simplification and refinement operators also provide a suitable basis for the construction of a multi-resolution representation of Morse complexes.