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Fast Ordering Algorithm for Exact Histogram Specification

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Titel: Fast Ordering Algorithm for Exact Histogram Specification
Autoren: Nikolova, Mila, Steidl, Gabriele
Weitere Verfasser: Centre de Mathématiques et de Leurs Applications (CMLA), École normale supérieure - Cachan (ENS Cachan)-Centre National de la Recherche Scientifique (CNRS), University of Kaiserslautern Kaiserslautern, The work of Mila Nikolova was supported in part by the "FMJH Program Gaspard Monge in optimization and operation research", and by the support to this program from EDF.
Quelle: https://hal.archives-ouvertes.fr/hal-00870501 ; 2013.
Verlagsinformationen: HAL CCSD
Publikationsjahr: 2013
Bestand: Archive ouverte HAL (Hyper Article en Ligne, CCSD - Centre pour la Communication Scientifique Directe)
Schlagwörter: Exact histogram specification, Strict-ordering, Variational methods, Smooth nonlinear optimization, Fast large-scale algorithms, Convex minimization, Image processing, [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing
Beschreibung: This paper provides a fast algorithm to order in a strict way the integer gray values in digital images which can be applied for exact histogram specification. Our algorithm is based on the ordering procedure by the variational approach in [9]. This variational method was shown to be superior to other state-of-the art ordering algorithms in terms of faithful total strict ordering but not in speed. Indeed, the relevant functionals are in general difficult to minimize because their gradient is nearly flat over vast regions. In this paper we propose a simple and fast fixed point algorithm to minimize the functionals. The fast convergence of our algorithm results from known analytical properties of the model. In particular the original image is a good starting point for the iterations and the involved inverse functions admit a simple explicit form. Only a few iteration steps of this algorithm provide an image whose pixels can be ordered in a strict and faithful way. Numerical experiments confirm that our algorithm outperforms by far its main competitors in speed and quality. Moreover, in contrast to other ordering algorithms we can handle large images commonly taken by commercial cameras. Concerning applications the proposed ordering algorithm is the basis of the hue and range preserving color image enhancement method proposed in [11].
Publikationsart: report
Sprache: English
Relation: hal-00870501; https://hal.archives-ouvertes.fr/hal-00870501; https://hal.archives-ouvertes.fr/hal-00870501/document; https://hal.archives-ouvertes.fr/hal-00870501/file/hs_fast_v2_IEEE.pdf
Verfügbarkeit: https://hal.archives-ouvertes.fr/hal-00870501
https://hal.archives-ouvertes.fr/hal-00870501/document
https://hal.archives-ouvertes.fr/hal-00870501/file/hs_fast_v2_IEEE.pdf
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  Data: Fast Ordering Algorithm for Exact Histogram Specification
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  Data: <searchLink fieldCode="AR" term="%22Nikolova%2C+Mila%22">Nikolova, Mila</searchLink><br /><searchLink fieldCode="AR" term="%22Steidl%2C+Gabriele%22">Steidl, Gabriele</searchLink>
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  Data: Centre de Mathématiques et de Leurs Applications (CMLA)<br />École normale supérieure - Cachan (ENS Cachan)-Centre National de la Recherche Scientifique (CNRS)<br />University of Kaiserslautern Kaiserslautern<br />The work of Mila Nikolova was supported in part by the "FMJH Program Gaspard Monge in optimization and operation research", and by the support to this program from EDF.
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  Data: <i>https://hal.archives-ouvertes.fr/hal-00870501 ; 2013</i>.
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  Data: 2013
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  Data: <searchLink fieldCode="DE" term="%22Exact+histogram+specification%22">Exact histogram specification</searchLink><br /><searchLink fieldCode="DE" term="%22Strict-ordering%22">Strict-ordering</searchLink><br /><searchLink fieldCode="DE" term="%22Variational+methods%22">Variational methods</searchLink><br /><searchLink fieldCode="DE" term="%22Smooth+nonlinear+optimization%22">Smooth nonlinear optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Fast+large-scale+algorithms%22">Fast large-scale algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Convex+minimization%22">Convex minimization</searchLink><br /><searchLink fieldCode="DE" term="%22Image+processing%22">Image processing</searchLink><br /><searchLink fieldCode="DE" term="%22[INFO%2EINFO-TS]Computer+Science+[cs]%2FSignal+and+Image+Processing%22">[INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing</searchLink><br /><searchLink fieldCode="DE" term="%22[SPI%2ESIGNAL]Engineering+Sciences+[physics]%2FSignal+and+Image+processing%22">[SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing</searchLink>
– Name: Abstract
  Label: Description
  Group: Ab
  Data: This paper provides a fast algorithm to order in a strict way the integer gray values in digital images which can be applied for exact histogram specification. Our algorithm is based on the ordering procedure by the variational approach in [9]. This variational method was shown to be superior to other state-of-the art ordering algorithms in terms of faithful total strict ordering but not in speed. Indeed, the relevant functionals are in general difficult to minimize because their gradient is nearly flat over vast regions. In this paper we propose a simple and fast fixed point algorithm to minimize the functionals. The fast convergence of our algorithm results from known analytical properties of the model. In particular the original image is a good starting point for the iterations and the involved inverse functions admit a simple explicit form. Only a few iteration steps of this algorithm provide an image whose pixels can be ordered in a strict and faithful way. Numerical experiments confirm that our algorithm outperforms by far its main competitors in speed and quality. Moreover, in contrast to other ordering algorithms we can handle large images commonly taken by commercial cameras. Concerning applications the proposed ordering algorithm is the basis of the hue and range preserving color image enhancement method proposed in [11].
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  Data: https://hal.archives-ouvertes.fr/hal-00870501<br />https://hal.archives-ouvertes.fr/hal-00870501/document<br />https://hal.archives-ouvertes.fr/hal-00870501/file/hs_fast_v2_IEEE.pdf
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RecordInfo BibRecord:
  BibEntity:
    Languages:
      – Text: English
    Subjects:
      – SubjectFull: Exact histogram specification
        Type: general
      – SubjectFull: Strict-ordering
        Type: general
      – SubjectFull: Variational methods
        Type: general
      – SubjectFull: Smooth nonlinear optimization
        Type: general
      – SubjectFull: Fast large-scale algorithms
        Type: general
      – SubjectFull: Convex minimization
        Type: general
      – SubjectFull: Image processing
        Type: general
      – SubjectFull: [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing
        Type: general
      – SubjectFull: [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing
        Type: general
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      – TitleFull: Fast Ordering Algorithm for Exact Histogram Specification
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            NameFull: Nikolova, Mila
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            NameFull: Steidl, Gabriele
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            NameFull: Centre de Mathématiques et de Leurs Applications (CMLA)
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            NameFull: École normale supérieure - Cachan (ENS Cachan)-Centre National de la Recherche Scientifique (CNRS)
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            NameFull: University of Kaiserslautern Kaiserslautern
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            NameFull: The work of Mila Nikolova was supported in part by the "FMJH Program Gaspard Monge in optimization and operation research", and by the support to this program from EDF.
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              Type: published
              Y: 2013
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