An image pixel based variational model for histogram equalization

We develop an image pixel based histogram equalization model for image contrast enhancement.A mean brightness term and a geometry constraint are incorporated in the proposed model.We propose to employ the alternating direction method of multipliers (ADMM) to solve the proposed model.The existence of the minimizer of the proposed model, and the convergence of the proposed algorithm are discussed. In this paper, we develop an image pixel based histogram equalization model for image contrast enhancement. The approach is to propose a variational model containing an energy functional to adjust the pixel values of an input image directly so that the resulting histogram can be redistributed to be uniform. This idea is different from existing histogram equalization algorithms where a histogram based on the input image is constructed, a mapping is determined to output a uniform histogram and then the pixel values of the input image are adjusted based on the mapping. In the variational model, a mean brightness term is incorporated to preserve the brightness of the input image, and a geometry constraint can also be added to keep the geometry structure of the input image. Theoretically, the existence of the minimizer of the proposed model, and the convergence of the proposed algorithm are given. Experimental results are reported to demonstrate that the performance of the proposed model are competitive with the other testing histogram equalization methods for several testing images.

[1]  Li Li,et al.  Contrast enhancement using non-overlapped sub-blocks and local histogram projection , 2011, IEEE Transactions on Consumer Electronics.

[2]  G. Sapiro,et al.  Histogram Modification via Differential Equations , 1997 .

[3]  Nicolas Papadakis,et al.  A Variational Model for Histogram Transfer of Color Images , 2011, IEEE Transactions on Image Processing.

[4]  Yücel Altunbasak,et al.  A Histogram Modification Framework and Its Application for Image Contrast Enhancement , 2009, IEEE Transactions on Image Processing.

[5]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[6]  Neil A. Dodgson,et al.  Color histogram specification by histogram warping , 2005, IS&T/SPIE Electronic Imaging.

[7]  Guillermo Sapiro,et al.  Histogram modification via partial differential equations , 1995, Proceedings., International Conference on Image Processing.

[8]  Irfan Altas,et al.  A variational approach to the radiometric enhancement of digital imagery , 1995, IEEE Trans. Image Process..

[9]  Dimitri P. Bertsekas,et al.  On the Douglas—Rachford splitting method and the proximal point algorithm for maximal monotone operators , 1992, Math. Program..

[10]  Turgay Çelik,et al.  Two-dimensional histogram equalization and contrast enhancement , 2012, Pattern Recognit..

[11]  Rui J. P. de Figueiredo,et al.  A nonlinear image contrast sharpening approach based on Munsell's scale , 2006, IEEE Transactions on Image Processing.

[12]  Rafael C. González,et al.  Local Determination of a Moving Contrast Edge , 1985, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[13]  Hao Ying,et al.  New algorithms for contrast enhancement in grayscale images based on the variational definition of histogram equalization , 2008, Integr. Comput. Aided Eng..

[14]  Qian Chen,et al.  Image enhancement based on equal area dualistic sub-image histogram equalization method , 1999, IEEE Trans. Consumer Electron..

[15]  Azeddine Beghdadi,et al.  Contrast enhancement technique based on local detection of edges , 1989, Comput. Vis. Graph. Image Process..

[16]  Abd. Rahman Ramli,et al.  Minimum mean brightness error bi-histogram equalization in contrast enhancement , 2003, IEEE Trans. Consumer Electron..

[17]  Abd. Rahman Ramli,et al.  Contrast enhancement using recursive mean-separate histogram equalization for scalable brightness preservation , 2003, IEEE Trans. Consumer Electron..

[18]  Anil Kokaram,et al.  The linear Monge-Kantorovitch linear colour mapping for example-based colour transfer , 2007 .

[19]  Zhongfu Ye,et al.  Flattest histogram specification with accurate brightness preservation , 2008 .

[20]  Chao Wang,et al.  Brightness preserving histogram equalization with maximum entropy: a variational perspective , 2005, IEEE Trans. Consumer Electron..

[21]  Mohsen Ebrahimi Moghaddam,et al.  An image contrast enhancement method based on genetic algorithm , 2010, Pattern Recognit. Lett..

[22]  Dalong Wang,et al.  Color image contrast enhancement using a local equalization and weighted sum approach , 2010, 2010 IEEE International Conference on Automation Science and Engineering.

[23]  Yeong-Taeg Kim,et al.  Contrast enhancement using brightness preserving bi-histogram equalization , 1997 .

[24]  John C. Russ,et al.  The Image Processing Handbook , 2016, Microscopy and Microanalysis.

[25]  Michael K. Ng,et al.  A Variational Histogram Equalization Method for Image Contrast Enhancement , 2013, SIAM J. Imaging Sci..

[26]  David Menotti,et al.  Multi-Histogram Equalization Methods for Contrast Enhancement and Brightness Preserving , 2007, IEEE Transactions on Consumer Electronics.

[27]  Guillermo Sapiro,et al.  Color histogram equalization through mesh deformation , 2003, Proceedings 2003 International Conference on Image Processing (Cat. No.03CH37429).