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

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Název: A Convex Model for Edge-Histogram Specification with Applications to Edge-Preserving Smoothing
Autoři: Kelvin C. K. Chan, Raymond H. Chan, Mila Nikolova
Zdroj: Axioms, Vol 7, Iss 3, p 53 (2018)
Informace o vydavateli: MDPI AG
Rok vydání: 2018
Sbírka: Directory of Open Access Journals: DOAJ Articles
Témata: edge-histogram, edge-preserving smoothing, histogram specification, Mathematics, QA1-939
Popis: 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.
Druh dokumentu: article in journal/newspaper
Jazyk: 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
Dostupnost: https://doi.org/10.3390/axioms7030053
https://doaj.org/article/737674cad91d4adda4d8ae7945022c6a
Přístupové číslo: edsbas.2C4C19AC
Databáze: BASE
Popis
Abstrakt: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.
DOI:10.3390/axioms7030053