Multiscale analysis of similarities between images on Riemannian manifolds

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• dc.contributor.author Ballester, Coloma
• dc.contributor.author Calderero, Felipe
• dc.contributor.author Caselles, Vicente
• dc.contributor.author Facciolo Furlan, Gabriele
• dc.date.accessioned 2021-03-12T07:15:38Z
• dc.date.available 2021-03-12T07:15:38Z
• dc.date.issued 2014
• dc.description.abstract In this paper we study the problem of comparing two patches of an image defined on a Riemannian manifold, which can be defined by the image domain with a suitable metric depending on the image. The size of the patch will not be determined a priori, and we identify it with a variable scale. Our approach can be considered as a nonlocal extension (comparing two points) of the multiscale analyses defined using the axiomatic approach by Álvarez et al. [Arch. Ration. Mech. Anal., 123 (1993), pp. 199--257]. Following this axiomatic approach, we can define a set of similarity measures that appear as solutions of a degenerate partial differential equation. This equation can be further specified in the linear case, and we observe that it contains as a particular instance the case of using weighted Euclidean distances as comparison measures. Finally, we discuss the case of some morphological scale spaces that exhibit a higher complexity.en
• dc.description.sponsorship These authors acknowledge partial support by MICINN project, reference MTM2012-30772, by GRC reference 2009 SGR 773 funded by the Generalitat de Catalunya, and by the ERC Advanced Grant INPAINTING (grant 319899). The third author also acknowledges partial support by the ICREA Acad`emia prize for excellence in research also funded by the Generalitat de Catalunya.
• dc.format.mimetype application/pdf
• dc.identifier.citation Ballester C, Calderero F, Caselles V, Facciolo G. Multiscale analysis of similarities between images on Riemannian manifolds. Multiscale Model Simul. 2014 May 1;12(2):616-49. DOI: 10.1137/130926833
• dc.identifier.doi http://dx.doi.org/10.1137/130926833
• dc.identifier.issn 1540-3459
• dc.identifier.uri http://hdl.handle.net/10230/46738
• dc.language.iso eng
• dc.publisher SIAM (Society for Industrial and Applied Mathematics)
• dc.relation.ispartof Multiscale Modeling & Simulation. 2014 May 1;12(2):616-49
• dc.relation.projectID info:eu-repo/grantAgreement/ES/3PN/MTM2012-30772
• dc.relation.projectID info:eu-repo/grantAgreement/EC/FP7/319899
• dc.rights © Society for Industrial and Applied Mathematics
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.subject.keyword Multiscale analysisen
• dc.subject.keyword Similarity measuresen
• dc.subject.keyword Degenerate parabolic equationsen
• dc.title Multiscale analysis of similarities between images on Riemannian manifoldsen
• dc.type info:eu-repo/semantics/article
• dc.type.version info:eu-repo/semantics/acceptedVersion