Computational geometry: an introduction
Computational geometry: an introduction
Three-dimensional alpha shapes
ACM Transactions on Graphics (TOG)
An incremental algorithm for Betti numbers of simplicial complexes on the 3-spheres
Computer Aided Geometric Design - Special issue on grid generation, finite elements, and geometric design
Data models in geographic information systems
Communications of the ACM
The digital topology of sets of convex voxels
Graphical Models and Image Processing
Computer Vision
Topological persistence and simplification
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Computational topology at multiple resolutions: foundations and applications to fractals and dynamics
Pattern Classification (2nd Edition)
Pattern Classification (2nd Edition)
Databases and the geometry of knowledge
Data & Knowledge Engineering
Visualization of multivariate data with tail trees
Information Visualization
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A broad range of mathematical techniques, ranging from statistics to fuzzy logic, have been used to great advantage in intelligent data analysis. Topology - the fundamental mathematics of shape - has to date been conspicuously absent from this repertoire. This paper shows how topology, properly reformulated for a finite-precision world, can be useful in intelligent data analysis tasks.