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

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    Type
    Article
    Authors
    Ferreira, Rita cc
    Fonseca, Irene
    Mascarenhas, M. Luísa
    KAUST Department
    Center for Uncertainty Quantification in Computational Science and Engineering (SRI-UQ)
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2017-09-07
    Online Publication Date
    2017-09-07
    Print Publication Date
    2017-10
    Permanent link to this record
    http://hdl.handle.net/10754/625764
    
    Metadata
    Show full item record
    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.
    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.
    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.
    Publisher
    Springer Nature
    Journal
    Calculus of Variations and Partial Differential Equations
    DOI
    10.1007/s00526-017-1223-8
    arXiv
    1603.07647
    Additional Links
    http://link.springer.com/article/10.1007/s00526-017-1223-8
    ae974a485f413a2113503eed53cd6c53
    10.1007/s00526-017-1223-8
    Scopus Count
    Collections
    Articles; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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