Estimating persistent Betti numbers for discrete shape analysis


Autoria(s): Cavazza, Niccolò
Contribuinte(s)

Ferri, Massimo

Data(s)

06/06/2011

Resumo

Persistent Topology is an innovative way of matching topology and geometry, and it proves to be an effective mathematical tool in shape analysis. In order to express its full potential for applications, it has to interface with the typical environment of Computer Science: It must be possible to deal with a finite sampling of the object of interest, and with combinatorial representations of it. Following that idea, the main result claims that it is possible to construct a relation between the persistent Betti numbers (PBNs; also called rank invariant) of a compact, Riemannian submanifold X of R^m and the ones of an approximation U of X itself, where U is generated by a ball covering centered in the points of the sampling. Moreover we can state a further result in which, this time, we relate X with a finite simplicial complex S generated, thanks to a particular construction, by the sampling points. To be more precise, strict inequalities hold only in "blind strips'', i.e narrow areas around the discontinuity sets of the PBNs of U (or S). Out of the blind strips, the values of the PBNs of the original object, of the ball covering of it, and of the simplicial complex coincide, respectively.

Formato

application/pdf

Identificador

http://amsdottorato.unibo.it/3468/1/cavazza_niccolo_tesi.pdf

urn:nbn:it:unibo-2476

Cavazza, Niccolò (2011) Estimating persistent Betti numbers for discrete shape analysis, [Dissertation thesis], Alma Mater Studiorum Università di Bologna. Dottorato di ricerca in Matematica <http://amsdottorato.unibo.it/view/dottorati/DOT269/>, 23 Ciclo. DOI 10.6092/unibo/amsdottorato/3468.

Idioma(s)

en

Publicador

Alma Mater Studiorum - Università di Bologna

Relação

http://amsdottorato.unibo.it/3468/

Direitos

info:eu-repo/semantics/openAccess

Palavras-Chave #MAT/03 Geometria
Tipo

Tesi di dottorato

NonPeerReviewed