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dc.contributor.author
Sakaridis, Christos
dc.contributor.author
Drakopoulos, Kimon
dc.contributor.author
Maragos, Petros
dc.date.accessioned
2018-01-16T17:04:36Z
dc.date.available
2017-09-26T13:39:52Z
dc.date.available
2017-09-26T14:00:33Z
dc.date.available
2018-01-16T17:04:36Z
dc.date.available
2017-12-16T12:09:52Z
dc.date.available
2018-01-16T17:03:11Z
dc.date.issued
2017
dc.identifier.issn
1936-4954
dc.identifier.other
10.1137/16M1100101
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/239563
dc.identifier.doi
10.3929/ethz-b-000187339
dc.description.abstract
Active contour models based on partial differential equations have proved successful in image segmentation, yet the study of their formulation on arbitrary geometric graphs, which place no restrictions in the spatial configuration of samples, is still at an early stage. In this paper, we introduce geometric approximations of gradient and curvature on arbitrary graphs, which enable a straightforward extension of active contour models that are formulated through level sets to such general inputs. We prove convergence in probability of our gradient approximation to the true gradient value and derive an asymptotic upper bound for the error of this approximation for the class of random geometric graphs. Two different approaches for the approximation of curvature are presented, and both are also proved to converge in probability in the case of random geometric graphs. We propose neighborhood-based filtering on graphs to improve the accuracy of the aforementioned approximations and define two variants of Gaussian smoothing on graphs which include normalization in order to adapt to graph nonuniformities. The performance of our active contour framework on graphs is demonstrated in the segmentation of regular images and geographical data defined on arbitrary graphs, using geodesic active contours and active contours without edges as representative models in our experiments.
en_US
dc.format
application/pdf
dc.language.iso
en
en_US
dc.publisher
SIAM
dc.rights.uri
http://rightsstatements.org/page/InC-NC/1.0/
dc.subject
Active contours
en_US
dc.subject
Graph segmentation
en_US
dc.subject
Random geometric graphs
en_US
dc.subject
Image segmentation
en_US
dc.title
Theoretical Analysis of Active Contours on Graphs
en_US
dc.type
Journal Article
dc.rights.license
In Copyright - Non-Commercial Use Permitted
dc.date.published
2017-09-07
ethz.journal.title
SIAM Journal on Imaging Sciences
ethz.journal.volume
10
en_US
ethz.journal.issue
3
en_US
ethz.pages.start
1475
en_US
ethz.pages.end
1510
en_US
ethz.version.deposit
publishedVersion
en_US
ethz.code.ddc
DDC - DDC::5 - Science::550 - Earth sciences
en_US
ethz.identifier.wos
ethz.publication.place
Philadelphia, PA
ethz.publication.status
published
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02140 - Dep. Inf.technologie und Elektrotechnik / Dep. of Inform.Technol. Electrical Eng.::02652 - Institut für Bildverarbeitung / Computer Vision Laboratory::03514 - Van Gool, Luc / Van Gool, Luc
en_US
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02140 - Dep. Inf.technologie und Elektrotechnik / Dep. of Inform.Technol. Electrical Eng.::02652 - Institut für Bildverarbeitung / Computer Vision Laboratory::03514 - Van Gool, Luc / Van Gool, Luc
en_US
ethz.date.deposited
2017-09-26T13:39:54Z
ethz.source
FORM
ethz.source
WOS
ethz.eth
yes
en_US
ethz.availability
Open access
en_US
ethz.rosetta.installDate
2018-02-08T13:52:46Z
ethz.rosetta.lastUpdated
2024-02-02T03:54:19Z
ethz.rosetta.versionExported
true
dc.identifier.olduri
http://hdl.handle.net/20.500.11850/221816
dc.identifier.olduri
http://hdl.handle.net/20.500.11850/187339
ethz.COinS
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