http://www.dagstuhl.de/17021

08. – 13. Januar 2017, Dagstuhl Seminar 17021

Functoriality in Geometric Data

Organisatoren

Mirela Ben-Chen (Technion – Haifa, IL)
Frédéric Chazal (INRIA Saclay – Île-de-France, FR)
Leonidas J. Guibas (Stanford University, US)
Maks Ovsjanikov (Ecole Polytechnique – Palaiseau, FR)

Auskunft zu diesem Dagstuhl Seminar erteilt

Dagstuhl Service Team

Dokumente

Dagstuhl Report, Volume 7, Issue 1 Dagstuhl Report
Motivationstext
Teilnehmerliste
Gemeinsame Dokumente
Programm des Dagstuhl Seminars [pdf]

Summary

Across science, engineering, medicine and business we face a deluge of data coming from sensors, from simulations, or from the activities of myriads of individuals on the Internet. The data often has a geometric character, as is the case with 1D GPS traces, 2D images, 3D scans, and so on. Furthermore, the data sets we collect are frequently highly correlated, reflecting information about the same or similar entities in the world, or echoing semantically important repetitions/symmetries or hierarchical structures common to both man-made and natural objects.

A recent trend, emerging independently in multiple theoretical and applied communities is to understand geometric data sets through their relations and interconnections, a point of view that can be broadly described as exploiting the functoriality of data, which has a long tradition associated with it in mathematics. Functoriality, in its broadest form, is the notion that in dealing with any kind of mathematical object, it is at least as important to understand the transformations or symmetries possessed by the object or the family of objects to which it belongs, as it is to study the object itself. This general idea been successfully applied in a large variety of fields, both theoretical and practical, often leading to deep insights into the structure of various objects as well as to elegant and efficient methods in various application domains, including computational geometry, computer vision and computer graphics.

This seminar brought together researchers and practitioners interested in notions of similarity, correspondence and, more generally, relations across geometric data sets. Mathematical and computational tools for the construction, analysis, and exploitation of such relational networks were the central focus of this seminar.

License
  Creative Commons BY 3.0 Unported license
  Mirela Ben-Chen, Frédéric Chazal, Leonidas J. Guibas, and Maks Ovsjanikov

Classification

  • Computer Graphics / Computer Vision
  • Multimedia
  • Optimization / Scheduling

Keywords

  • Computational Geometry
  • Geometry Processing
  • Data Analysis

Buchausstellung

Bücher der Teilnehmer 

Buchausstellung im Erdgeschoss der Bibliothek

(nur in der Veranstaltungswoche).

Dokumentation

In der Reihe Dagstuhl Reports werden alle Dagstuhl-Seminare und Dagstuhl-Perspektiven-Workshops dokumentiert. Die Organisatoren stellen zusammen mit dem Collector des Seminars einen Bericht zusammen, der die Beiträge der Autoren zusammenfasst und um eine Zusammenfassung ergänzt.

 

Download Übersichtsflyer (PDF).

Publikationen

Es besteht weiterhin die Möglichkeit, eine umfassende Kollektion begutachteter Arbeiten in der Reihe Dagstuhl Follow-Ups zu publizieren.

Dagstuhl's Impact

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