A chromaticity-brightness model for color images denoising in a Meyer’s “u + v” framework

Handle URI:
http://hdl.handle.net/10754/625764
Title:
A chromaticity-brightness model for color images denoising in a Meyer’s “u + v” framework
Authors:
Ferreira, Rita ( 0000-0002-7169-9141 ) ; Fonseca, Irene; Mascarenhas, M. Luísa
Abstract:
A variational model for imaging segmentation and denoising color images is proposed. The model combines Meyer’s “u+v” decomposition with a chromaticity-brightness framework and is expressed by a minimization of energy integral functionals depending on a small parameter ε>0. The asymptotic behavior as ε→0+ is characterized, and convergence of infima, almost minimizers, and energies are established. In particular, an integral representation of the lower semicontinuous envelope, with respect to the L1-norm, of functionals with linear growth and defined for maps taking values on a certain compact manifold is provided. This study escapes the realm of previous results since the underlying manifold has boundary, and the integrand and its recession function fail to satisfy hypotheses commonly assumed in the literature. The main tools are Γ-convergence and relaxation techniques.
KAUST Department:
Center for Uncertainty Quantification in Computational Science and Engineering (SRI-UQ); Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Ferreira R, Fonseca I, Mascarenhas ML (2017) A chromaticity-brightness model for color images denoising in a Meyer’s “u + v” framework. Calculus of Variations and Partial Differential Equations 56. Available: http://dx.doi.org/10.1007/s00526-017-1223-8.
Publisher:
Springer Nature
Journal:
Calculus of Variations and Partial Differential Equations
Issue Date:
11-Sep-2017
DOI:
10.1007/s00526-017-1223-8
Type:
Article
ISSN:
0944-2669; 1432-0835
Sponsors:
The authors acknowledge the funding of Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) through the ICTI CMU-Portugal Program in Applied Mathematics and UTACMU/MAT/0005/2009. The authors also thank the Center for Nonlinear Analysis (NSF Grant DMS-0635983), where part of this research was carried out. R. Ferreira was partially supported by the KAUST SRI, Center for Uncertainty Quantification in Computational Science and Engineering and by the Fundação para a Ciência e a Tecnologia through the grant SFRH/BPD/81442/2011. The work of I. Fonseca was partially supported by the National Science Foundation under Grant No. DMS-1411646. The work of L.M. Mascarenhas was partially supported by UID/MAT/00297/ 2013.
Additional Links:
http://link.springer.com/article/10.1007/s00526-017-1223-8
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorFerreira, Ritaen
dc.contributor.authorFonseca, Ireneen
dc.contributor.authorMascarenhas, M. Luísaen
dc.date.accessioned2017-10-03T12:49:38Z-
dc.date.available2017-10-03T12:49:38Z-
dc.date.issued2017-09-11en
dc.identifier.citationFerreira R, Fonseca I, Mascarenhas ML (2017) A chromaticity-brightness model for color images denoising in a Meyer’s “u + v” framework. Calculus of Variations and Partial Differential Equations 56. Available: http://dx.doi.org/10.1007/s00526-017-1223-8.en
dc.identifier.issn0944-2669en
dc.identifier.issn1432-0835en
dc.identifier.doi10.1007/s00526-017-1223-8en
dc.identifier.urihttp://hdl.handle.net/10754/625764-
dc.description.abstractA variational model for imaging segmentation and denoising color images is proposed. The model combines Meyer’s “u+v” decomposition with a chromaticity-brightness framework and is expressed by a minimization of energy integral functionals depending on a small parameter ε>0. The asymptotic behavior as ε→0+ is characterized, and convergence of infima, almost minimizers, and energies are established. In particular, an integral representation of the lower semicontinuous envelope, with respect to the L1-norm, of functionals with linear growth and defined for maps taking values on a certain compact manifold is provided. This study escapes the realm of previous results since the underlying manifold has boundary, and the integrand and its recession function fail to satisfy hypotheses commonly assumed in the literature. The main tools are Γ-convergence and relaxation techniques.en
dc.description.sponsorshipThe authors acknowledge the funding of Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) through the ICTI CMU-Portugal Program in Applied Mathematics and UTACMU/MAT/0005/2009. The authors also thank the Center for Nonlinear Analysis (NSF Grant DMS-0635983), where part of this research was carried out. R. Ferreira was partially supported by the KAUST SRI, Center for Uncertainty Quantification in Computational Science and Engineering and by the Fundação para a Ciência e a Tecnologia through the grant SFRH/BPD/81442/2011. The work of I. Fonseca was partially supported by the National Science Foundation under Grant No. DMS-1411646. The work of L.M. Mascarenhas was partially supported by UID/MAT/00297/ 2013.en
dc.publisherSpringer Natureen
dc.relation.urlhttp://link.springer.com/article/10.1007/s00526-017-1223-8en
dc.subject26B30en
dc.subject49J45en
dc.subject94A08en
dc.titleA chromaticity-brightness model for color images denoising in a Meyer’s “u + v” frameworken
dc.typeArticleen
dc.contributor.departmentCenter for Uncertainty Quantification in Computational Science and Engineering (SRI-UQ)en
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalCalculus of Variations and Partial Differential Equationsen
dc.contributor.institutionDepartment of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, USAen
dc.contributor.institutionDepartamento de Matemática, C.M.A. - F.C.T./U.N.L., Caparica, Portugalen
kaust.authorFerreira, Ritaen
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.