Watershed of a continuous function
Signal Processing - Special issue on mathematical morphology and its applications to signal processing
Evaluation of Methods for Ridge and Valley Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Properties of Ridges and Cores for Two-Dimensional Images
Journal of Mathematical Imaging and Vision
The “parallel vectors” operator: a vector field visualization primitive
VIS '99 Proceedings of the conference on Visualization '99: celebrating ten years
On discrete Morse functions and combinatorial decompositions
Discrete Mathematics
Optimal discrete Morse functions for 2-manifolds
Computational Geometry: Theory and Applications
Computing Optimal Morse Matchings
SIAM Journal on Discrete Mathematics
Stability of Persistence Diagrams
Discrete & Computational Geometry
Efficient Computation of Morse-Smale Complexes for Three-dimensional Scalar Functions
IEEE Transactions on Visualization and Computer Graphics
Theory and Algorithms for Constructing Discrete Morse Complexes from Grayscale Digital Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Memory-Efficient Computation of Persistent Homology for 3D Images Using Discrete Morse Theory
SIBGRAPI '11 Proceedings of the 2011 24th SIBGRAPI Conference on Graphics, Patterns and Images
Optimal Topological Simplification of Discrete Functions on Surfaces
Discrete & Computational Geometry
Vortex and Strain Skeletons in Eulerian and Lagrangian Frames
IEEE Transactions on Visualization and Computer 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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Extremal lines and surfaces are features of a 3D scalar field where the scalar function becomes minimal or maximal with respect to a local neighborhood . These features are important in many applications, e.g. computer tomography, fluid dynamics, cell biology . We present a novel topological method to extract these features using discrete Morse theory. In particular, we extend the notion of ‘separatrix persistence’ from 2D to 3D, which gives us a robust estimation of the feature strength for extremal lines and surfaces. Not only does it allow us to determine the most important (parts of) extremal lines and surfaces, it also serves as a robust filtering measure of noise-induced structures. Our purely combinatorial method does not require derivatives or any other numerical computations . © 2012 Wiley Periodicals, Inc.