A multiclass anisotropic Mumford-Shah functional for segmentation of d-dimensional vectorial images

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• dc.contributor.author Garamendi, Juan Francisco
• dc.contributor.author Schiavi, Emanuele
• dc.date.accessioned 2024-03-13T10:02:43Z
• dc.date.available 2024-03-13T10:02:43Z
• dc.date.issued 2017
• dc.description Comunicació presentada a la 12th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2017), celebrada del 27 de febrer l'1 de març de 2017 a Porto, Portugal.
• dc.description.abstract We present a general model for multi-class segmentation of multi-channel digital images. It is based on the minimization of an anisotropic version of the Mumford-Shah energy functional in the class of piecewise constant functions. In the framework of geometric measure theory we use the concept of common interphases between regions (classes) and the value of the jump discontinuities of the (weak) solution between adjacent regions in order to define a minimal partition energy functional. The resulting problem is non-smooth and non-convex. Non-smoothness is dealt with highlighting the relationship of the proposed model with the well known Rudin, Osher and Fatemi model for image denoising when piecewise constant solutions (i.e partitions) are considered. Non-convexity is tackled with an optimal threshold of the ROF solution which we which generalize to multi-channel images through a probabilistic clustering. The optimal solution is then computed with a fixed point iteration. The result ing algorithm is described and results are presented showing the successful application of the method to Light Field (LF) images.
• dc.description.sponsorship The authors acknowledge partial support by TIN2015-70410-C2-1-R (MINECO/FEDER, UE) and by GRC reference 2014 SGR 1301, Generalitat de Catalunya.
• dc.format.mimetype application/pdf
• dc.identifier.citation Garamendi JF, Schiavi E. A multiclass anisotropic Mumford-Shah functional for segmentation of d-dimensional vectorial images. In: Imai F, Tremeau A, Braz J, editors. Proceedings of the 12th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2017) (Volume 4: VISAPP); 2017 Feb 27 - Mar 1; Porto, Portugal. Setúbal: SciTePress; 2017. p. 468-75. DOI: 10.5220/0006127804680475
• dc.identifier.doi http://dx.doi.org/10.5220/0006127804680475
• dc.identifier.isbn 9789897582257
• dc.identifier.uri http://hdl.handle.net/10230/59400
• dc.language.iso eng
• dc.publisher SCITEPRESS – Science and Technology Publications
• dc.relation.ispartof Imai F, Tremeau A, Braz J, editors. Proceedings of the 12th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2017) (Volume 4: VISAPP); 2017 Feb 27 - Mar 1; Porto, Portugal. Setúbal: SciTePress; 2017. p. 468-75
• dc.relation.projectID info:eu-repo/grantAgreement/ES/1PE/TIN2015-70410-C2-1-R
• dc.rights Copyright 2015 by SCITEPRESS – Science and Technology Publications, Lda. Distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND).
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/4.0/
• dc.subject.keyword Multi-channel
• dc.subject.keyword Image segmentation
• dc.subject.keyword Variational methods
• dc.subject.keyword Mumford-Shah
• dc.title A multiclass anisotropic Mumford-Shah functional for segmentation of d-dimensional vectorial images
• dc.type info:eu-repo/semantics/conferenceObject
• dc.type.version info:eu-repo/semantics/publishedVersion