Linear multiscale analysis of similarities between images on Riemannian manifolds: practical formula and affine covariant metrics

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• dc.contributor.author Fedorov, Vadimca
• dc.contributor.author Arias Martínez, Pabloca
• dc.contributor.author Sadek, Ridaca
• dc.contributor.author Facciolo Furlan, Gabrieleca
• dc.contributor.author Ballester, Colomaca
• dc.date.accessioned 2015-12-03T09:37:25Z
• dc.date.available 2015-12-03T09:37:25Z
• dc.date.issued 2015ca
• dc.description.abstract In this paper we study the problem of comparing two patches of images defined on Riemannian/nmanifolds which in turn can be defined by each image domain with a suitable metric depending on/nthe image. For that we single out one particular instance of a set of models defining image similarities/nthat was earlier studied in [C. Ballester et al., Multiscale Model. Simul., 12 (2014), pp. 616–649],/nusing an axiomatic approach that extended the classical Alvarez–Guichard–Lions–Morel work to the ´/nnonlocal case. Namely, we study a linear model to compare patches defined on two images in RN/nendowed with some metric. Besides its genericity, this linear model is selected by its computational/nfeasibility since it can be approximated leading to an algorithm that has the complexity of the/nusual patch comparison using a weighted Euclidean distance. Moreover, we propose and study some/nintrinsic metrics which we define in terms of affine covariant structure tensors and we discuss their/nproperties. These tensors are defined for any point in the image and are intrinsically endowed with/naffine covariant neighborhoods. We also discuss the effect of discretization over the affine covariance/nproperties of the tensors. We illustrate our theoretical results with numerical experiments.
• dc.description.sponsorship The research of these authors was partially supported by MICINN project MTM2012-30772, by the ERC Advanced Grant INPAINTING (grant agreement 319899), and by GRC reference 2014 SGR 1301, Generalitat de Catalunya.
• dc.format.mimetype application/pdfca
• dc.identifier.citation Fedorov V, Arias P, Sadek R, Facciolo G, Ballester C. Linear multiscale analysis of similarities between images on Riemannian manifolds: practical formula and affine covariant metrics. SIAM J Imaging Sci. 2015; 8(3): 2021-2069. DOI 10.1137/141000002ca
• dc.identifier.doi http://dx.doi.org/10.1137/141000002
• dc.identifier.issn 1936-4954ca
• dc.identifier.uri http://hdl.handle.net/10230/25319
• dc.language.iso engca
• dc.publisher SIAM (Society for Industrial and Applied Mathematics)ca
• dc.relation.ispartof SIAM Journal on Imaging Sciences. 2015; 8(3): 2021-2069.
• dc.relation.projectID info:eu-repo/grantAgreement/EC/FP7/319899ca
• dc.relation.projectID info:eu-repo/grantAgreement/ES/3PN/MTM2012-30772
• dc.rights © 2015 Society for Industrial and Applied Mathematicsca
• dc.rights.accessRights info:eu-repo/semantics/openAccessca
• dc.subject.keyword Multiscale analysis
• dc.subject.keyword Similarity measures
• dc.subject.keyword Degenerate parabolic equations
• dc.subject.keyword Structure tensors
• dc.subject.keyword Affine invariance
• dc.title Linear multiscale analysis of similarities between images on Riemannian manifolds: practical formula and affine covariant metricsca
• dc.type info:eu-repo/semantics/articleca
• dc.type.version info:eu-repo/semantics/publishedVersionca