Baby Morse Theory for Statistical Inference from Point Cloud Data
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چکیده
A methodology is proposed for inferring the topology underlying point cloud data directly from 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.
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تاریخ انتشار 2011