Watershed of a continuous function
Signal Processing - Special issue on mathematical morphology and its applications to signal processing
Building and traversing a surface at variable resolution
VIS '97 Proceedings of the 8th conference on Visualization '97
Smooth view-dependent level-of-detail control and its application to terrain rendering
Proceedings of the conference on Visualization '98
Variable resolution triangulations
WADS '97 Selected papers presented at the international workshop on Algorithms and data structure
The watershed transform: definitions, algorithms and parallelization strategies
Fundamenta Informaticae - Special issue on mathematical morphology
Simplification of Tetrahedral meshes with accurate error evaluation
Proceedings of the conference on Visualization '00
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
Adaptive Real-Time Level-of-Detail-Based Rendering for Polygonal Models
IEEE Transactions on Visualization and Computer Graphics
A Multi-resolution Data Structure for Two-dimensional Morse-Smale Functions
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
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
Terrain modeling: a constrained fractal model
AFRIGRAPH '07 Proceedings of the 5th international conference on Computer graphics, virtual reality, visualisation and interaction in Africa
Describing shapes by geometrical-topological properties of real functions
ACM Computing Surveys (CSUR)
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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We propose a technique for simplification and multiresolution modeling of a terrain represented as a TIN. Our goal is to maintain the morphological structure of the terrain in the resulting multiresolution model. To this aim, we extend Morse theory, developed for continuous and differentiable functions, to the case of piecewise linear functions. We decompose a TIN into areas with uniform morphological properties (such as valleys, basins, etc.) separated by a network of critical lines and points. We describe an algorithm to compute the above decomposition and the critical net, and a TIN simplification algorithm that preserves them. On this basis, we build a multiresolution terrain model, which provides a representation of critical features at any level of detail.