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Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/DagRep.8.10.87
URN: urn:nbn:de:0030-drops-103499
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10349/
Breuß, Michael ;
Bruckstein, Alfred M. ;
Kiselman, Christer Oscar ;
Maragos, Petros
Weitere Beteiligte (Hrsg. etc.): Michael Breuß and Alfred M. Bruckstein and Christer Oscar Kiselman and Petros Maragos
Shape Analysis: Euclidean, Discrete and Algebraic Geometric Methods (Dagstuhl Seminar 18422)
Abstract
In computer vision, geometric processing and image analysis, the notation of a shape of a 3-D object has been studied either by an embedded manifold for the continuous stetting or as a collection of a discrete set of marker positions on the manifold. Within the last years, there have been many rapid developments in the field of shape representation, shape correspondence and shape manipulation with technical applications ranging from laser-range scanners to 3-D printing. Classic shape analysis tools from differential geometry have a fresh influence in the field, often powered by modern methods
from optimization and numerical computing. At the same time, discrete geometric methods and related techniques such as from mathematical
morphology have evolved significantly. Moreover, techniques like deep learning gained a significant influence in the development of corresponding
methods and tools. New developments from tropical geometry have a high potential for use in shape analysis.
The topics in our seminar addressed the sketched challenges and developments that will be useful for shape analysis. Especially we aimed to discuss the possibilities of combining fields like tropical geometry with more classical techniques as for instance from mathematical morphology. We discussed possibilities of applying machine learning methods in this context and considered recent advances from more classical fields like differential geometry and partial differential equations that can be useful for setting up and understanding shape analysis methods in all of these approaches.
This seminar brought together 26 researchers from North America and Europe engaged in recent and upcoming developments in shape analysis who view these challenges from different perspectives and who together discussed the pressing open problems and novel solutions to them.
BibTeX - Entry
@Article{breu_et_al:DR:2019:10349,
author = {Michael Breu{\ss} and Alfred M. Bruckstein and Christer Oscar Kiselman and Petros Maragos},
title = {{Shape Analysis: Euclidean, Discrete and Algebraic Geometric Methods (Dagstuhl Seminar 18422)}},
pages = {87--103},
journal = {Dagstuhl Reports},
ISSN = {2192-5283},
year = {2019},
volume = {8},
number = {10},
editor = {Michael Breu{\ss} and Alfred M. Bruckstein and Christer Oscar Kiselman and Petros Maragos},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2019/10349},
URN = {urn:nbn:de:0030-drops-103499},
doi = {10.4230/DagRep.8.10.87},
annote = {Keywords: algebraic geometry, mathematical morphology, optimization, shape analysis, shape reconstruction}
}
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Keywords: |
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algebraic geometry, mathematical morphology, optimization, shape analysis, shape reconstruction |
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Collection: |
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Dagstuhl Reports, Volume 8, Issue 10 |
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Issue Date: |
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2019 |
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Date of publication: |
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04.04.2019 |
