منابع مشابه
Multiresolution Topological Simplification
Persistent homology has been advocated as a new strategy for the topological simplification of complex data. However, it is computationally intractable for large data sets. In this work, we introduce multiresolution persistent homology for tackling large datasets. Our basic idea is to match the resolution with the scale of interest so as to create a topological microscopy for the underlying dat...
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We formalize a notion of topological simplification within the framework of a filtration, which is the history of a growing complex. We classify a topological change that happens during growth as either a feature or noise depending on its lifetime or persistence within the filtration. We give fast algorithms for computing persistence and experimental evidence for their speed and utility.
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These tutorial notes provide an introduction, review, and discussion of the state-of-the-art on simplification methods, Level Of Detail, and multiresolution models for surface meshes, and of their applications. The problem of approximating a surface with a triangular mesh is formally introduced, and major simplification techniques are classified, reviewed, and compared. A general framework is i...
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Multiresolution surfaces are especially useful for fast rendering, real-time display, and progressive transmission. This paper reviews major surface simplification techniques and multiresolution surface reconstruction approaches. Based on comparison among various approximation algorithms we propose an appropriate measure for surface approximation accuracy and essential concepts for multiresolut...
متن کاملOn-line topological simplification of weighted graphs
We describe two efficient on-line algorithms to simplify weighted graphs by eliminating degree-two vertices. Our algorithms are on-line in that they react to updates on the data, keeping the simplification up-to-date. The supported updates are insertions of vertices and edges; hence, our algorithms are partially dynamic. We provide both analytical and empirical evaluations of the efficiency of ...
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ژورنال
عنوان ژورنال: Journal of Computational Biology
سال: 2015
ISSN: 1066-5277,1557-8666
DOI: 10.1089/cmb.2015.0104