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ALPHA SIGNED

Alpha Shape Theory Extended

Total Cost €

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EC-Contrib. €

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Partnership

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Project "ALPHA" data sheet

The following table provides information about the project.

Coordinator
INSTITUTE OF SCIENCE AND TECHNOLOGY AUSTRIA 

Organization address
address: Am Campus 1
city: KLOSTERNEUBURG
postcode: 3400
website: www.ist.ac.at

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Austria [AT]
 Project website http://alpha.pages.ist.ac.at/
 Total cost 1˙678˙432 €
 EC max contribution 1˙678˙432 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2017-ADG
 Funding Scheme ERC-ADG
 Starting year 2018
 Duration (year-month-day) from 2018-07-01   to  2023-06-30

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    INSTITUTE OF SCIENCE AND TECHNOLOGY AUSTRIA AT (KLOSTERNEUBURG) coordinator 1˙678˙432.00

Map

 Project objective

Alpha shapes were invented in the early 80s of last century, and their implementation in three dimensions in the early 90s was at the forefront of the exact arithmetic paradigm that enabled fast and correct geometric software. In the late 90s, alpha shapes motivated the development of the wrap algorithm for surface reconstruction, and of persistent homology, which was the starting point of rapidly expanding interest in topological algorithms aimed at data analysis questions.

We now see alpha shapes, wrap complexes, and persistent homology as three aspects of a larger theory, which we propose to fully develop. This viewpoint was a long time coming and finds its clear expression within a generalized version of discrete Morse theory. This unified framework offers new opportunities, including (I) the adaptive reconstruction of shapes driven by the cavity structure;

(II) the stochastic analysis of all aspects of the theory; (III) the computation of persistence of dense data, both in scale and in depth;

(IV) the study of long-range order in periodic and near-periodic point configurations. These capabilities will significantly deepen as well as widen the theory and enable new applications in the sciences. To gain focus, we concentrate on low-dimensional applications in structural molecular biology and particle systems.

 Publications

year authors and title journal last update
List of publications.
2019 Herbert Edelsbrunner, Katharina Ölsböck
Holes and dependences in an ordered complex
published pages: 1-15, ISSN: 0167-8396, DOI: 10.1016/j.cagd.2019.06.003
Computer Aided Geometric Design 73 2020-03-19
2019 Herbert Edelsbrunner, Anton Nikitenko
Poisson–Delaunay Mosaics of Order k
published pages: 865-878, ISSN: 0179-5376, DOI: 10.1007/s00454-018-0049-2
Discrete & Computational Geometry 62/4 2020-03-19

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