Topographic distance and watershed lines
Signal Processing - Special issue on mathematical morphology and its applications to signal processing
Visualization of scalar topology for structural enhancement
Proceedings of the conference on Visualization '98
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
Non-manifold Decomposition in Arbitrary Dimensions
DGCI '02 Proceedings of the 10th International Conference on Discrete Geometry for Computer Imagery
Using the CW-complex to represent the topological structure of implicit surfaces and solids
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
A new approach for a topographic feature-based characterization of digital elevation data
Proceedings of the 12th annual ACM international workshop on Geographic information systems
Multi-scale dual morse complexes for representing terrain morphology
Proceedings of the 15th annual ACM international symposium on Advances in geographic information systems
Describing shapes by geometrical-topological properties of real functions
ACM Computing Surveys (CSUR)
Tree-Based Encoding for Cancellations on Morse Complexes
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
Discrete distortion in triangulated 3-manifolds
SGP '08 Proceedings of the Symposium on Geometry Processing
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
Smale-like decomposition and forman theory for discrete scalar fields
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
Computing morse decompositions for triangulated terrains: an analysis and an experimental evaluation
ICIAP'11 Proceedings of the 16th international conference on Image analysis and processing: Part I
Morse-Smale decompositions for modeling terrain knowledge
COSIT'05 Proceedings of the 2005 international conference on Spatial Information Theory
A multi-resolution representation for terrain morphology
GIScience'06 Proceedings of the 4th international conference on Geographic Information Science
Morphologically-aware elimination of flat edges from a TIN
Proceedings of the 21st ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
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In this paper, we address the problem of analyzing the topology of discrete scalar fields defined on triangulated domains. To this aim, we introduce the notions of discrete gradient vector field and of Smale-like decomposition for the domain of a d-dimensional scalar field. We use such notions to extract the most relevant features representing the topology of the field.We describe a decomposition algorithm, which is independent of the dimension of the scalar field, and, based on it, methods for extracting the critical net of a scalar field. A complete classification of the critical points of a 2-dimensional field that corresponds to a piecewise differentiable field is also presented.