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
Maximizing Adaptivity in Hierarchical Topological Models
SMI '05 Proceedings of the International Conference on Shape Modeling and Applications 2005
A Topological Approach to Simplification of Three-Dimensional Scalar Functions
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)
Theory and Algorithms for Constructing Discrete Morse Complexes from Grayscale Digital Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
The persistent morse complex segmentation of a 3-manifold
3DPH'09 Proceedings of the 2009 international conference on Modelling the Physiological Human
A topological hierarchy for functions on triangulated surfaces
IEEE Transactions on Visualization and Computer Graphics
Topology-based smoothing of 2D scalar fields with C1-continuity
EuroVis'10 Proceedings of the 12th Eurographics / IEEE - VGTC conference on Visualization
SMI 2013: Generalized extrinsic distortion and applications
Computers and Graphics
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Morse and Morse-Smale complexes have been recognized as a suitable model for representing topological information extracted from discrete scalar fields. Here, we propose a dimension-independent multi-resolution model for Morse complexes built on a graph representation of the complexes, that we call a Multi-Resolution Morse Incidence Graph (MMIG). We define data structures for encoding the MMIG and we discuss how to extract from an MMIG topological representations of the scalar field over its domain M at both uniform and variable resolutions. We present experimental results evaluating the storage cost of the data structures encoding the MMIG, and timings for building and querying an MMIG.