Level lines selection with variational models for segmentation and encoding

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• dc.contributor.author Ballester, Coloma
• dc.contributor.author Caselles, Vicente
• dc.contributor.author Igual, Laura
• dc.contributor.author Garrido, Luís
• dc.date.accessioned 2023-04-27T06:16:17Z
• dc.date.available 2023-04-27T06:16:17Z
• dc.date.issued 2007
• dc.description.abstract This paper discusses the interest of the Tree of Shapes of an image as a region oriented image representation. The Tree of Shapes offers a compact and structured representation of the family of level lines of an image. This representation has been used for many processing tasks such as filtering, registration, or shape analysis. In this paper we show how this representation can be used for segmentation, rate distortion optimization, and encoding. We address the problem of segmentation and rate distortion optimization using Guigues algorithm on a hierarchy of partitions constructed using the simplified Mumford-Shah multiscale energy. To segment an image, we minimize the simplified Mumford-Shah energy functional on the set of partitions represented in this hierarchy. The rate distortion problem is also solved in this hierarchy of partitions. In the case of encoding, we propose a variational model to select a family of level lines of a gray level image in order to obtain a minimal description of it. Our energy functional represents the cost in bits of encoding the selected level lines while controlling the maximum error of the reconstructed image. In this case, a greedy algorithm is used to minimize the corresponding functional. Some experiments are displayed.
• dc.description.sponsorship The first and second authors acknowledge partial support by the Departament d’Universitats, Recerca i Societat de la Informaci´o de la Generalitat de Catalunya and by PNPGC project, reference BFM2003-02125. L. Igual acknowledges support by the French Space Agency (CNES) and the company THALES (France).
• dc.format.mimetype application/pdf
• dc.identifier.citation Ballester C, Caselles V, Igual L, Garrido L. Level lines selection with variational models for segmentation and encoding. J Math Imaging Vis. 2007;27(1):5-27. DOI: 10.1007/s10851-006-7252-0
• dc.identifier.doi http://dx.doi.org/10.1007/s10851-006-7252-0
• dc.identifier.issn 0924-9907
• dc.identifier.uri http://hdl.handle.net/10230/56588
• dc.language.iso eng
• dc.publisher Springer
• dc.relation.ispartof Journal of Mathematical Imaging and Vision. 2007;27(1):5-27.
• dc.relation.projectID info:eu-repo/grantAgreement/ES/1PN/BFM2003-02125
• dc.rights © Springer The final publication is available at Springer via http://dx.doi.org/10.1007/s10851-006-7252-0
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.subject.keyword mathematical morphology
• dc.subject.keyword tree structure
• dc.subject.keyword segmentation
• dc.subject.keyword rate distortion
• dc.subject.keyword morphological encoding
• dc.subject.keyword minimal description length
• dc.title Level lines selection with variational models for segmentation and encoding
• dc.type info:eu-repo/semantics/article
• dc.type.version info:eu-repo/semantics/acceptedVersion