A Variational Histogram Equalization Method for Image Contrast Enhancement

Wei Wang; Michael K. Ng

doi:10.1137/130909196

A Variational Histogram Equalization Method for Image Contrast Enhancement

Wei Wang, Michael K. Ng^*

^*Corresponding author for this work

Research output: Contribution to journal › Journal article › peer-review

19 Citations (Scopus)

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Abstract

The main aim of this paper is to develop a histogram equalization algorithm for image contrast enhancement. Our idea is to propose a variational approach containing an energy functional to determine a local transformation such that the histogram can be redistributed locally, and the brightness of the transformed image can be preserved. In order to minimize the differences among the local transformation at the nearby pixel locations, the spatial regularization of the transformation is also incorporated into the functional for the equalization process. In the variational problem, we consider both H₁-norm regularization and total variation regularization of the transformation in the model. The existence and uniqueness of the minimizers of the two proposed models are studied and analyzed. Experimental results are reported to show that the performance of the proposed models are competitive with the other compared methods for several testing images.

Original language	English
Pages (from-to)	1823-1849
Number of pages	27
Journal	SIAM Journal on Imaging Sciences
Volume	6
Issue number	3
DOIs	https://doi.org/10.1137/130909196
Publication status	Published - 24 Sept 2013

Scopus Subject Areas

Mathematics(all)
Applied Mathematics

User-Defined Keywords

Alternating minimization
Contrast enhancement
Energy functional
Histogram equalization
Transformation function
Variational approach

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10.1137/130909196

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title = "A Variational Histogram Equalization Method for Image Contrast Enhancement",

abstract = "The main aim of this paper is to develop a histogram equalization algorithm for image contrast enhancement. Our idea is to propose a variational approach containing an energy functional to determine a local transformation such that the histogram can be redistributed locally, and the brightness of the transformed image can be preserved. In order to minimize the differences among the local transformation at the nearby pixel locations, the spatial regularization of the transformation is also incorporated into the functional for the equalization process. In the variational problem, we consider both H1-norm regularization and total variation regularization of the transformation in the model. The existence and uniqueness of the minimizers of the two proposed models are studied and analyzed. Experimental results are reported to show that the performance of the proposed models are competitive with the other compared methods for several testing images.",

keywords = "Alternating minimization, Contrast enhancement, Energy functional, Histogram equalization, Transformation function, Variational approach",

author = "Wei Wang and Ng, {Michael K.}",

note = "Funding information: Department of Mathematics, Tongji University, Shanghai, China ([email protected]). This author was supported by National Natural Science Foundation of China grant 11201341 and China Postdoctoral Science Foundation funded project (2012M511126 and 2013T60459). ^ Corresponding author. Centre for Mathematical Imaging and Vision and Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong ([email protected]). This author was supported by RGC GRF grant 202013 and HKBU FRG grant FRG/12-13/065. Publisher copyright: {\textcopyright} 2013, Society for Industrial and Applied Mathematics",

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AU - Wang, Wei

AU - Ng, Michael K.

N1 - Funding information: Department of Mathematics, Tongji University, Shanghai, China ([email protected]). This author was supported by National Natural Science Foundation of China grant 11201341 and China Postdoctoral Science Foundation funded project (2012M511126 and 2013T60459). ^ Corresponding author. Centre for Mathematical Imaging and Vision and Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong ([email protected]). This author was supported by RGC GRF grant 202013 and HKBU FRG grant FRG/12-13/065. Publisher copyright: © 2013, Society for Industrial and Applied Mathematics

PY - 2013/9/24

Y1 - 2013/9/24

N2 - The main aim of this paper is to develop a histogram equalization algorithm for image contrast enhancement. Our idea is to propose a variational approach containing an energy functional to determine a local transformation such that the histogram can be redistributed locally, and the brightness of the transformed image can be preserved. In order to minimize the differences among the local transformation at the nearby pixel locations, the spatial regularization of the transformation is also incorporated into the functional for the equalization process. In the variational problem, we consider both H1-norm regularization and total variation regularization of the transformation in the model. The existence and uniqueness of the minimizers of the two proposed models are studied and analyzed. Experimental results are reported to show that the performance of the proposed models are competitive with the other compared methods for several testing images.

AB - The main aim of this paper is to develop a histogram equalization algorithm for image contrast enhancement. Our idea is to propose a variational approach containing an energy functional to determine a local transformation such that the histogram can be redistributed locally, and the brightness of the transformed image can be preserved. In order to minimize the differences among the local transformation at the nearby pixel locations, the spatial regularization of the transformation is also incorporated into the functional for the equalization process. In the variational problem, we consider both H1-norm regularization and total variation regularization of the transformation in the model. The existence and uniqueness of the minimizers of the two proposed models are studied and analyzed. Experimental results are reported to show that the performance of the proposed models are competitive with the other compared methods for several testing images.

KW - Alternating minimization

KW - Contrast enhancement

KW - Energy functional

KW - Histogram equalization

KW - Transformation function

KW - Variational approach

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DO - 10.1137/130909196

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SN - 1936-4954

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JO - SIAM Journal on Imaging Sciences

JF - SIAM Journal on Imaging Sciences

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ER -

A Variational Histogram Equalization Method for Image Contrast Enhancement

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