Persistence barcodes for shapes

By Gunnar E. Carlsson, Afra Zomorodian, A. Collins, Leonidas J. Guibas. Eurographics Symposium on Geometry Processing, 2004

456 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Mathematical Physics, Radiology, Nuclear Medicine and Imaging

View Paper: https://www.semanticscholar.org/paper/21e23759348cb855edce7fe20ed233260a004b99

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Citations in the corpus

Decomposition of pointwise finite-dimensional persistence modules (2012, methodology): “complex.) Assuming that this persistence module is a direct sum of interval modules, it is found that the collection of such intervals, the barcode, is a useful invariant of the data; see for example [1, 6]. Our aim is to give a short proof of the following result, which enables the use of barcodes ”
A statistical approach to persistent homology (2006, background): “Using the PCD and the metric, one can construct a ﬁltered simplicial complex which approximates the unknown space X [dSC04, CZCG04].”
Vines and vineyards by updating persistence in linear time (2006, background): “the comparison of shapes, see also [5], and the analysis of discrete curvature measures, see [8].”
Bounds on spectral norms and barcodes (2018, background): “ersistence modules and boundary depth. We recall brie y the category pmod of persistence modules that we work with, together with their relevant properties. For detailed treatment of these topics see [12, 22, 23, 34, 49, 121]. Let K be a eld. A persistence module over K is a pair (V;ˇ) where, fVtg t”
Barcodes: The persistent topology of data (2007, background): “, optical character recognition) [5] and spike train data from implanted electrode arrays in the primary visual cortex of Macaque monkeys [4].”
Autonomous Hamiltonian flows, Hofer’s geometry and persistence modules (2014, background): “In this section we collect preliminaries on persistence modules, see [5, 11, 12, 14, 16, 25].”
Homological illusions of persistence and stability (2008, background): “The stability of persistence diagrams has been established in [25], opening the concept up to additional applications, including the inference of homology from point clouds, see also [76], the comparison of shapes, see also [16], and the analysis of discrete curvature measures, see”
Topological Data Analysis (2012, background): “The persistence barcode is the multiset of these l+m intervals and forms the parameterization [11].”
Proximity of persistence modules and their diagrams (2009, background): “For instance, in scalar ﬁeld analysis, they can be used to guide the simpliﬁcation of a real-valued function by iterative cancellation of critical pairs, ridding the data of its inherent topological noise [1, 17, 18].”
Stability of Persistence Diagrams (2005, methodology): “Are there other interesting metrics, on functions and persistence diagrams, for which an inequality like the one in the Main Theorem holds? For example, if the distance between persistence diagrams is measured as in [3], what metrics between functions give such an inequality, if any? Other open ques”
Random Projections of Smooth Manifolds (2009, methodology): “Additional algorithms have also been proposed for characterizing manifolds from sampled data without constructing an explicit embedding in RM [13, 15, 34] and for constructing functions on the point samples in RN that reflect the intrinsic structure of the manifold [4, 14].”
Robust global registration (2005, unknown): “We (cid:2)rst describe an algorithm for a general descriptor, and then show how we use the scale-space representation of the volume descriptor together with a persistence [CZCG04] algorithm to robustly select feature points at multiple scales.”
Persistence modules with operators in Morse and Floer theory (2017, background): “For detailed treatment of these topics see [8, 9, 12,17,34,62].”