Computing contour trees in all dimensions
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Constructing a Reeb graph automatically from cross sections
IEEE Computer Graphics and Applications
Automatic extraction of Irregular Network digital terrain models
SIGGRAPH '79 Proceedings of the 6th annual conference on Computer graphics and interactive techniques
Morse Homology Descriptor for Shape Characterization
ICPR '04 Proceedings of the Pattern Recognition, 17th International Conference on (ICPR'04) Volume 4 - Volume 04
Discrete & Computational Geometry
Morse connections graph for shape representation
ACIVS'05 Proceedings of the 7th international conference on Advanced Concepts for Intelligent Vision Systems
Computing homology: a global reduction approach
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Detecting critical regions in multidimensional data sets
Computers & Mathematics with Applications
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We define a new mathematical model for the topological study of lattice height data. A discrete multivalued dynamical system framework is used to establish discrete analogies of a Morse function, its gradient field, and its stable and unstable manifolds in order to interpret functions numerically given on finite sets of pixels. We present efficient algorithms detecting critical components of a height function f and displaying connections between them by means of a graph, called the Morse connections graph whose nodes represent the critical components of f and edges show the existence of connecting trajectories between nodes. This graph encodes efficiently the topological structure of the data and makes it easy to manipulate for subsequent processing.