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A Convex Model for Edge-Histogram Specification with Applications to Edge-Preserving Smoothing

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Titel: A Convex Model for Edge-Histogram Specification with Applications to Edge-Preserving Smoothing
Autoren: Kelvin C. K. Chan, Raymond H. Chan, Mila Nikolova
Quelle: Axioms, Vol 7, Iss 3, p 53 (2018)
Verlagsinformationen: MDPI AG
Publikationsjahr: 2018
Bestand: Directory of Open Access Journals: DOAJ Articles
Schlagwörter: edge-histogram, edge-preserving smoothing, histogram specification, Mathematics, QA1-939
Beschreibung: The goal of edge-histogram specification is to find an image whose edge image has a histogram that matches a given edge-histogram as much as possible. Mignotte has proposed a non-convex model for the problem in 2012. In his work, edge magnitudes of an input image are first modified by histogram specification to match the given edge-histogram. Then, a non-convex model is minimized to find an output image whose edge-histogram matches the modified edge-histogram. The non-convexity of the model hinders the computations and the inclusion of useful constraints such as the dynamic range constraint. In this paper, instead of considering edge magnitudes, we directly consider the image gradients and propose a convex model based on them. Furthermore, we include additional constraints in our model based on different applications. The convexity of our model allows us to compute the output image efficiently using either Alternating Direction Method of Multipliers or Fast Iterative Shrinkage-Thresholding Algorithm. We consider several applications in edge-preserving smoothing including image abstraction, edge extraction, details exaggeration, and documents scan-through removal. Numerical results are given to illustrate that our method successfully produces decent results efficiently.
Publikationsart: article in journal/newspaper
Sprache: English
Relation: http://www.mdpi.com/2075-1680/7/3/53; https://doaj.org/toc/2075-1680; https://doaj.org/article/737674cad91d4adda4d8ae7945022c6a
DOI: 10.3390/axioms7030053
Verfügbarkeit: https://doi.org/10.3390/axioms7030053
https://doaj.org/article/737674cad91d4adda4d8ae7945022c6a
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  Data: A Convex Model for Edge-Histogram Specification with Applications to Edge-Preserving Smoothing
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Kelvin+C%2E+K%2E+Chan%22">Kelvin C. K. Chan</searchLink><br /><searchLink fieldCode="AR" term="%22Raymond+H%2E+Chan%22">Raymond H. Chan</searchLink><br /><searchLink fieldCode="AR" term="%22Mila+Nikolova%22">Mila Nikolova</searchLink>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: Axioms, Vol 7, Iss 3, p 53 (2018)
– Name: Publisher
  Label: Publisher Information
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  Data: MDPI AG
– Name: DatePubCY
  Label: Publication Year
  Group: Date
  Data: 2018
– Name: Subset
  Label: Collection
  Group: HoldingsInfo
  Data: Directory of Open Access Journals: DOAJ Articles
– Name: Subject
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  Data: <searchLink fieldCode="DE" term="%22edge-histogram%22">edge-histogram</searchLink><br /><searchLink fieldCode="DE" term="%22edge-preserving+smoothing%22">edge-preserving smoothing</searchLink><br /><searchLink fieldCode="DE" term="%22histogram+specification%22">histogram specification</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics%22">Mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22QA1-939%22">QA1-939</searchLink>
– Name: Abstract
  Label: Description
  Group: Ab
  Data: The goal of edge-histogram specification is to find an image whose edge image has a histogram that matches a given edge-histogram as much as possible. Mignotte has proposed a non-convex model for the problem in 2012. In his work, edge magnitudes of an input image are first modified by histogram specification to match the given edge-histogram. Then, a non-convex model is minimized to find an output image whose edge-histogram matches the modified edge-histogram. The non-convexity of the model hinders the computations and the inclusion of useful constraints such as the dynamic range constraint. In this paper, instead of considering edge magnitudes, we directly consider the image gradients and propose a convex model based on them. Furthermore, we include additional constraints in our model based on different applications. The convexity of our model allows us to compute the output image efficiently using either Alternating Direction Method of Multipliers or Fast Iterative Shrinkage-Thresholding Algorithm. We consider several applications in edge-preserving smoothing including image abstraction, edge extraction, details exaggeration, and documents scan-through removal. Numerical results are given to illustrate that our method successfully produces decent results efficiently.
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  Data: 10.3390/axioms7030053
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      – Text: English
    Subjects:
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        Type: general
      – SubjectFull: edge-preserving smoothing
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      – SubjectFull: histogram specification
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