The watershed transform: definitions, algorithms and parallelization strategies
Fundamenta Informaticae - Special issue on mathematical morphology
Partitioning 3D Surface Meshes Using Watershed Segmentation
IEEE Transactions on Visualization and Computer Graphics
Morse-smale complexes for piecewise linear 3-manifolds
Proceedings of the nineteenth annual symposium on Computational geometry
A Smale-Like Decomposition for Discrete Scalar Fields
ICPR '02 Proceedings of the 16 th International Conference on Pattern Recognition (ICPR'02) Volume 1 - Volume 1
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)
Morphological analysis of terrains based on discrete curvature and distortion
Proceedings of the 16th ACM SIGSPATIAL international conference on Advances in geographic information systems
Laplace-Beltrami spectra as 'Shape-DNA' of surfaces and solids
Computer-Aided Design
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
SMI 2013: Generalized extrinsic distortion and applications
Computers and Graphics
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We investigate a morphological approach to the analysis and understanding of 3D scalar fields defined by volume data sets. We consider a discrete model of the 3D field obtained by discretizing its domain into a tetrahedral mesh. We use Morse theory as the basic mathematical tool which provides a segmentation of the graph of the scalar field based on relevant morphological features (such as critical points). Since the graph of a discrete 3D field is a tetrahedral hypersurface in 4D space, we measure the distortion of the transformation which maps the tetrahedral decomposition of the domain of the scalar field into the tetrahedral mesh representing its graph in R4, and we call it discrete distortion. We develop a segmentation algorithm to produce a Morse decompositions associated with the scalar field and its discrete distortion. We use a merging procedure to control the number of 3D regions in the segmentation output. Experimental results show the validity of our approach.