The M-components of level sets of continuous functions in WBV

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• dc.contributor.author Ballester, Coloma
• dc.contributor.author Caselles, Vicente
• dc.date.accessioned 2021-03-26T09:25:06Z
• dc.date.available 2021-03-26T09:25:06Z
• dc.date.issued 2001
• dc.description.abstract We prove that the topographic map structure ofupper semicontinuous functions, defined in terms of classical connected components ofits level sets, and offunctions ofbounded variation (or a generalization, the WBV functions), defined in terms of M-connected components ofits level sets, coincides when the function is a continuous function in WBV . Both function spaces are frequently used as models for images. Thus, if the domain Ω ofthe image is Jordan domain, a rectangle, for instance, and the image u ∈ C(Ω)∩WBV (Ω) (being constant near ∂Ω), we prove that for almost all levels λ of u, the classical connected components ofpositive measure of[u ≥ λ] coincide with the M-components of[u ≥ λ]. Thus the notion of M-component can be seen as a relaxation ofthe classical notion ofconnected component when going from C(Ω) to WBV (Ω).en
• dc.description.sponsorship We acknowledge partial support by the TMR European project “Viscosity solutions and their applications”, reference FMRX-CT98-0234 and the CNRS through a PICS project.
• dc.format.mimetype application/pdf
• dc.identifier.citation Ballester C, Caselles V. The M-components of level sets of continuous functions in WBV. Publ Mat. 2001;45(2):477-527. DOI: 10.5565/PUBLMAT_45201_10
• dc.identifier.doi http://dx.doi.org/10.5565/PUBLMAT_45201_10
• dc.identifier.issn 0214-1493
• dc.identifier.uri http://hdl.handle.net/10230/46948
• dc.language.iso eng
• dc.publisher Universitat Autònoma de Barcelona
• dc.relation.ispartof Publicacions matemàtiques. 2001;45(2):477-527
• dc.rights © 2001 Departament de Matemàtiques. Universitat Autònoma de Barcelona
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.subject.keyword Mathematical morphologyen
• dc.subject.keyword Level setsen
• dc.subject.keyword Connected componentsen
• dc.subject.keyword Morse theoryen
• dc.subject.keyword Functions of bounded variationen
• dc.subject.keyword Sets of finite perimeteren
• dc.title The M-components of level sets of continuous functions in WBVen
• dc.type info:eu-repo/semantics/article
• dc.type.version info:eu-repo/semantics/publishedVersion