Topological estimation using witness complexes

By Vin de Silva, Gunnar E. Carlsson. Symposium on Point Based Graphics, 2004

456 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/957aafd3a7c8736f286b7638eb89d6db5ed309b1

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In Computational Theory and Mathematics

In Computer Vision and Pattern Recognition

Citations in the corpus

Topology and data (2009, background): “Precisely, we have the following definition from [8].”
Probability measures on the space of persistence diagrams (2011, background): “The majority of the literature in TDA has focused on the mathematical properties captured by the summaries and the computational issues that arise in obtaining these summaries [1, 2, 3].”
Topological Data Analysis (2012, background): “The weak witness complex is the simplest of a family of witness complexes [21].”
Stability of Persistence Diagrams (2005, background): “We first address a problem also studied in [9], namely estimating the homology groups of a closed subset X of a metric space M from a set of possibly inaccurate point samples.”
On the Local Behavior of Spaces of Natural Images (2007, background): “It is a theorem that barcodes are in bijective correspondence with isomorphism classes of directed systems of vector spaces (Zomorodian and Carlsson 2004).”
Vines and vineyards by updating persistence in linear time (2006, background): “lished in [7], opening the concept up to additional applications, including the inference of homology from point clouds, see also [9],”
Zigzag Persistence (2008, background): “It follows that V and R( V ) have the same decomposition structure.”
Inferring spatial and signaling relationships between cells from single cell transcriptomic data (2020, methodology): “We follow a method proposed to approximate the topology induced by point clouds.[7].”
Barcodes: The persistent topology of data (2007, background): “The witness complex of Carlsson and de Silva [8, 9, 14] is one solution to this problem.”
Homological illusions of persistence and stability (2008, methodology): “One is the denoising of alpha-beta witness complexes as introduced in [5]; see also [76].”