How many points are needed to determine a geometric surface?

Miha Polanc (2016) How many points are needed to determine a geometric surface?. EngD thesis.

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Abstract

A geometric surface can be approximately described using a finite point-sample. The main question of this thesis is the following: how many points, depending on the sampling model and surface genus, are needed to confidently reconstruct the original geometric surface. First we present different sampling models of surface points — the uniform and the random sample. We use topological methods, in particular persistent homology, to process our data. Using Javaplex software package we construct a filtration with Vietoris-Rips simplicial complexes and consider the bar-code diagram of its Betti numbers. Finally we present our computational results for both the sphere and the geometric torus with respect to the two sampling models , and several options for further improvements.

Item Type:

Thesis (EngD thesis)

Keywords:

Vietoris-Rips complex, Betti numbers, Javaplex, persistent homology, sphere, torus.

Number of Pages:

Language of Content:

Slovenian

Mentor / Comentors:

Name and Surname	ID	Function
Izr. prof. dr. Gašper Fijavž	246	Mentor

Link to COBISS:

http://www.cobiss.si/scripts/cobiss?command=search&base=51012&select=(ID=1537149123)

Institution:

University of Ljubljana

Department:

Faculty of Computer and Information Science

Item ID:

3565

Date Deposited:

12 Sep 2016 14:12

Last Modified:

28 Sep 2016 13:23

URI:

http://eprints.fri.uni-lj.si/id/eprint/3565

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