Computer Vision and Image Understanding
Molecular shape analysis based upon the morse-smale complex and the connolly function
Proceedings of the nineteenth annual symposium on Computational geometry
Fair morse functions for extracting the topological structure of a surface mesh
ACM SIGGRAPH 2004 Papers
Topology for Computing (Cambridge Monographs on Applied and Computational Mathematics)
Topology for Computing (Cambridge Monographs on Applied and Computational Mathematics)
Finding the Homology of Submanifolds with High Confidence from Random Samples
Discrete & Computational Geometry
Nonlinear Dimensionality Reduction
Nonlinear Dimensionality Reduction
Topological Methods in Data Analysis and Visualization: Theory, Algorithms, and Applications
Topological Methods in Data Analysis and Visualization: Theory, Algorithms, and Applications
Visualizing clusters in artificial neural networks using Morse theory
Advances in Artificial Neural Systems
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A methodology is proposed for inferring the topology underlying point cloud data. The approach employs basic elements of Morse Theory, and is capable of producing not only a point estimate of various topological quantities (e.g., genus), but it can also assesses their sampling uncertainty in a probabilistic fashion. Several examples of point cloud data in three dimensions are utilized to demonstrate how the method yields interval estimates for the topology of the data as a 2-dimensional surface embedded in R3.