Hostname: page-component-7b7567c8c-kwt9d Total loading time: 0 Render date: 2026-11-14T04:00:48.659Z Has data issue: false hasContentIssue false
  • English
  • Français

A Multi-Exposure Variational Method for Retinex

Part of:Game theory, economics, social and behavioral sciences

Published online by Cambridge University Press:  31 January 2017

Xue Yang and
Yu-Mei Huang
Xue Yang*
Affiliation:
School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, Gansu Province, P.R. China
Yu-Mei Huang*
Affiliation:
School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, Gansu Province, P.R. China
*
*Corresponding author. Email addresses:sclylsyx@126.com (X. Yang), huangym@lzu.edu.cn (Y.-M. Huang)
*Corresponding author. Email addresses:sclylsyx@126.com (X. Yang), huangym@lzu.edu.cn (Y.-M. Huang)

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

Retinex theory explains how the human visual system perceives colors. The goal of retinex is to decompose the reflectance and the illumination from the given images and thereby compensating for non-uniform lighting. The existing methods for retinex usually use a single image with a fixed exposure to restore the reflectance of the image. In this paper, we propose a variational model for retinex problem by utilizing multi-exposure images of a given scene. The existence and uniqueness of the solutions of the proposed model have been elaborated. An alternating minimization method is constructed to solve the proposed model and its convergence is also demonstrated. The experimental results show that the proposed method is effective for reflectance recovery in retinex problem.

Keywords

Retinexreflectanceilluminationmulti-exposure imagesalternating minimization algorithm

MSC classification

Secondary:65K10: Optimization and variational techniques68U10: Image processing91-08: Computational methods

Information

Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 7 , Issue 1 , February 2017, pp. 156 - 171
Copyright
Copyright © Global-Science Press 2017 

References

[1] Bertalmo, M., Caselles, V. and Provenzi, E., Issues about retinex theory and contrast enhancement, Int. J. Comput. Vision, 83 (1) (2009), pp. 101–119.Google Scholar
[2] Brainard, D. H. and Wandell, B. A., Analysis of the retinex theory of color vision, J. Opt. Soc. Am. A, 3 (10) (1986), pp. 1651–1661.Google Scholar
[3] Chang, H., Ng, M., Wang, W. and Zeng, T., Retinex image enhancement via a learned dictionary, Opt. Eng., 54 (1) (2015), DOI: 10.1117/1.OE.54.1.013107.Google Scholar
[4] Fattal, R., Lischinski, D. and Werman, M., Gradient domain high dynamic range compression, ACM Trans. Graphics (TOG), 21 (3) (2002), pp. 249–256.Google Scholar
[5] Finlayson, G. D., Hordley, S. D. and Drew, M. S., Removing shadows from images, Prco. ECCV, 2353 (2002), pp. 823–836.Google Scholar
[6] Frankle, J. A. and McCann, J. J., Method and apparatus for lightness imaging, U. S. Patent, 4384336, May 17, 1983.Google Scholar
[7] Funt, B., Ciurea, F. and McCann, J. J., Retinex in MATLABTM , J. Electron. Imaging, 13 (1) (2004), pp. 48–57.Google Scholar
[8] Jobson, D. J., Rahman, Z. and Woodell, G. A., Properties and performance of a center/surround retinex, IEEE Trans. Image Process., 6 (3) (1997), pp. 451–462.Google Scholar
[9] Jobson, D. J., Rahman, Z. and Woodell, G. A., A multiscale retinex for bridging the gap between color images and the human observation of scenes, IEEE Trans. Image Process., 6 (7) (1997), pp. 965–976.Google Scholar
[10] Kimmel, R., Elad, M., Shaked, D., Keshet, R. and Sobel, I., A variational framework for retinex, Int. J. Comput. Vis., 52 (1) (2003), pp. 7–23.Google Scholar
[11] Land, E. H. and J. McCann, J., Lightness and retinex theory, J. Opt. Soc. Amer., 61 (1) (1971), pp. 1–11.Google Scholar
[12] Land, E. H., The retinex theory of color vision, Sci. Amer, 237 (6) (1977), pp. 108–128.Google Scholar
[13] Land, E. H., Recent advances in retinex theory and some implications for cortical computations: Color vision and the natural image, Proc. Natl. Acad. Sci. U.S.A, 80 (16) (1983), pp. 5163–5169.Google Scholar
[14] Ma, W., Morel, J. M., Osher, S. and Chien, A., An L1-based variational model for retinex theory and its applications to medical images, Proc. CVPR 2011, pp. 153–160.Google Scholar
[15] Ma, W. and Osher, S., A TV Bregman iterative model of retinex theory, Inverse Probl. Imaging, 6 (4) (2012), pp. 697–708.Google Scholar
[16] Morel, J. M., Petro, A. B. and Sbert, C., Fast implementation of color constancy algorithms, Proc. SPIE, 7241 (2009).Google Scholar
[17] Morel, J. M., Petro, A. B. and Sbert, C., A PDE formalization of retinex theory, IEEE Trans. Image Process., 19 (11) (2010), pp. 2825–2837.Google Scholar
[18] Ng, M. K. and Wang, W., A total variation model for retinex, SIAM J. Imaging Sci., 4 (1) (2011), pp. 345–365.Google Scholar
[19] PÉRez, P., Gangnet, M. and Blake, A., Poisson image editing, ACM Trans. Graphics (TOG), 22 (3) (2003), pp. 313–318.Google Scholar
[20] Raskar, R., Ilie, A. and Yu, J., Image fussion for context enhancement and video surrealism, Proc. NPAR ’04, 2004, pp. 85–152.Google Scholar
[21] Shen, F., Zhao, Y.-M, Jiang, X.-Z and Suwa, M., Recovering high dynamic range bymulti-exposure retinex, J. Vis. Commun. Image R, 20 (2009), pp. 521–531.Google Scholar
[22] Socolinsky, D. A. and Wolff, L. B., A new visualization paradigm for multispectral imagery and data fusion, Proc. Comp. Vis. and Pattern Rec., 1 (1999), pp. 319–324.Google Scholar
[23] Wang, Z. and Guo, D., Special Functions, Singapore: World Scientific, 15 (1989), pp. 654–655.Google Scholar
[24] Wang, W. and Ng, M. K., A nonlocal total variation model for image decomposition: Illumination and reflectance, Numer. Math., Theory Methods Appl., 7 (3) (2014), pp. 334–355.Google Scholar
[25] Wang, W. and He, C., A variational model with barrier functionals for retinex, SIAM J. Imaging Sci., 8 (3) (2015), pp. 1955–1980.Google Scholar
[26] Zosso, D., Tran, G. and Osher, S., A unifying retinex model based on non-local differential operators, Proc. SPIE, 8657 (2014).Google Scholar