Exact histogram specification for digital images using a variational Approach

Journal of Mathematical Imaging and Vision

Volumn 46, Issue 3, 2013, Pages 309-325

  Nikolova, Mila ^a   Wen, You Wei ^b   Chan, Raymond ^c  

^a UNIVERSITÉ PARIS SACLAY   (France)

^b KUNMING UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^c CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Convex minimization; Exact histogram specification; Image processing; Minimizer analysis; Perturbation analysis; Restoration from quantization noise; Smooth nonlinear optimization; Strict ordering; Variational methods

Indexed keywords

CONVEX MINIMIZATION; EXACT HISTOGRAM SPECIFICATIONS; MINIMIZER ANALYSIS; PERTURBATION ANALYSIS; RESTORATION FROM QUANTIZATION NOISE; SMOOTH NONLINEAR OPTIMIZATIONS; STRICT ORDERINGS; VARIATIONAL METHODS;

GRAPHIC METHODS; NUMERICAL METHODS; PIXELS;

IMAGE PROCESSING;

EID: 84879462896     PISSN: 09249907     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10851-012-0401-8     Document Type: Article

References (57)

1. Arici, T., Dikbas, S., Altunbasak, Y.: A histogram modification framework and its application for image contrast enhancement. IEEE Trans. Image Process. 18(9), 1921-1935 (2009)
2. Aubert, G., Kornprobst, P.: Mathematical Problems in Image Processing, 2nd edn. Springer, Berlin (2006)
3. Avanaki, A.N.: Exact global histogram specification optimized for structural similarity. Opt. Rev. 16(6), 613-621 (2009)
4. Avez, A.: Calcul Différentiel. Masson, Paris (1991)
5. 1-TV models: bounds for the minimizers and parameter choice. Tech. report, hal-00722743, v2. See http://hal.archives-ouvertes.fr/hal-00722743
6. Bonnans, J.-F., Gilbert, J.-C., Lemaréchal, C., Sagastizábal, C.: Numerical Optimization (Theoretical and Practical Aspects). Springer, Berlin (2003)
7. Bioucas-Dias, J., Figueiredo, M., Nowak, R.: Total variation-based image deconvolution: a majorization-minimization approach. In: Proc. IEEE International Conference on Acoustics, Speech and Signal Processing ICASSP 2006, vol. 2, pp. 861-864, 14-19 May (2006)
8. Black, M., Rangarajan, A.: On the unification of line processes, outlier rejection, and robust statistics with applications to early vision. Int. J. Comput. Vis. 19, 57-91 (1996) (Pubitemid 126713881)
9. De Bruijn, N.G.: Some classes of integer-valued functions. Indag. Math. 17(3) (1955)
10. Cahen, P.-J., Chabert, J.-L.: Integer-valued Polynomials. Mathematical Surveys and Monographs, vol. 48. Amer. Math. Soc., Providence (1997)
11. Chan, R., Nikolova, M., Wen, Y.: A variational approach for exact histogram specification. In: Scale Space and Variational Methods in Computer Vision. Lecture Notes in Computer Science, vol. 6667, pp. 86-97 (2012)
12. Chen, S., Ramli, A.R.: Contrast enhancement using recursive mean-separate histogram equalization for scalable brightness preservation. IEEE Trans. Consum. Electron. 49(4), 1301-1309 (2003)
13. Cheng, H.D., Jiang, X.H., Sun, Y., Wang, J.: Color image segmentation: advances and prospects. Pattern Recognit. 34(12), 2259-2281 (2001) (Pubitemid 32961807)
14. Ciarlet, P.G.: Introduction to Numerical Linear Algebra and Optimization. Cambridge University Press, Cambridge (1989)
15. Coltuc, D., Bolon, P.: Robust watermarking by histogram specification. In: Image Processing. International Conference on ICIP 99, vol. 2, pp. 236-239. IEEE, New York (1999). 1999 (Pubitemid 30550236)
16. Coltuc, D., Bolon, P., Chassery, J.-M.: Exact histogram specification. IEEE Trans. Image Process. 15(5), 1143-1152 (2006)
17. Cox, I.J., Roy, S., Hingorani, S.L.: Dynamic histogram warping of image pairs for constant image brightness. In: International Conference on Image Processing, vol. 2, pp. 366-369 (1995)
18. Delon, J.: Midway image equalization. J. Math. Imaging Vis. 21(2), 119-134 (2004)
19. Dontchev, A.L., Zollezi, T.: Well-Posed Optimization Problems. Springer, New York (1993)
20. Evans, L.C., Gariepy, R.F.: Measure Theory and Fine Properties of Functions. Studies in Advanced Mathematics. CRC Press, Roca Baton (1992)
21. Ferradans, S., Xia, G.-S., Peyré, G., Aujol, J.-F.: Optimal transport mixing of Gaussian texture models. Tech. report, Preprint Hal-00662720 (2012)
22. Fiacco, A., McCormic, G.: Nonlinear Programming. Classics in Applied Mathematics. SIAM, Philadelphia (1990)
23. Figueiredo, M.A.T., Bioucas-Dias, J.M., Nowak, R.D.: Majorization- minimization algorithms for wavelet-based image restoration. IEEE Trans. Image Process. 16(12), 2980-2991 (2007) (Pubitemid 350201231)
24. Gonzalez, R.C., Woods, R.E.: Digital Image Processing. Publishing House of Electronics Industry, Beijing (2005)
25. Gousseau, Y., Morel, J.M.: Are natural images of bounded variation? SIAM J. Math. Anal. 33(3), 634-648 (2001) (Pubitemid 33787278)
26. Hall, E.L.: Almost uniform distributions for computer image enhancement. IEEE Trans. Comput. C-23, 207-208 (1974)
27. Hazewinkel, M. (ed.): Diophantine Equations. Encyclopaedia of Mathematics. Springer, Berlin (2001)
28. Hunter, D., Lange, K.: A tutorial on MM algorithms. Am. Stat. 58(1), 30-37 (2004) (Pubitemid 38260327)
29. Jongen, H.T., Jonker, P., Twilt, F.: Nonlinear Optimization in Finite Dimensions, 1st edn. Kluwer Academic, Amsterdam (1986)
30. Kim, Y.: Contrast enhancement using brightness preserving bi-histogram equalization. IEEE Trans. Consum. Electron. 43(1), 1-8 (1997) (Pubitemid 127827459)
31. Lafontaine, J.: Introduction aux Variétés Différentielles, 2nd edn. EDP Sciences, France (2010)
32. Krishnan, D., Lin, P., Tai, X.: An efficient operator splitting method for noise removal in images. Commun. Comput. Phys. 1, 847-858 (2006)
33. Meyer, C.D.: Matrix Analysis and Applied Linear Algebra. SIAM, Philadelphia (2000)
34. Mignotte, M.: An energy based model for the image edge histogram specification problem. IEEE Trans. Image Process. 21, 379-386 (2012)
35. Mumford, D., Desolneux, A.: Pattern Theory: The Stochastic Analysis of Real-World Signals. A.K. Peters, Natick (2010)
36. Nesterov, Y.: Smooth minimization of non-smooth functions. Math. Program., Ser. A 103(1), 127-152 (2005) (Pubitemid 40537674)
37. Portilla, J., Simoncelli, E.P.: A parametric texture model based on joint statistics of complex wavelet coefficients. Int. J. Comput. Vis. 40, 49-71 (2000) (Pubitemid 32083683)
38. Lysaker, M., Tai, X.: Noise removal using smoothed normals and surface fitting. IEEE Trans. Image Process. 13(10), 1345-1357 (2004)
39. Narasimhan, S., Nayar, S.: Contrast restoration of weather degraded images. IEEE Trans. Pattern Anal. Mach. Intell. 25, 713-724 (2003)
40. Ni, K., Bresson, X., Chan, T., Esedoglu, S.: Local histogram based segmentation using the Wasserstein distance. Int. J. Comput. Vis. 84(1), 97-111 (2009)
41. Nikolova, M.: Local strong homogeneity of a regularized estimator. SIAM J. Appl. Math. 61, 633-658 (2000)
42. Nikolova, M.: A variational approach to remove outliers and impulse noise. J. Math. Imaging Vis. 20(1-2), 99-120 (2004)
43. Nikolova, M.: Weakly constrained minimization. Application to the estimation of images and signals involving constant regions. J. Math. Imaging Vis. 21(2), 155-175 (2004)
44. Pólya, G.: Über ganzwertige ganze Funktionen. Rend. Circ. Mat. Palermo 40, 1-16 (1915)
45. Pratt, W.K.: Digital Image Processing, 2nd edn. Wiley, New York (1991)
46. Rosenfeld, A., Kak, K.: Digital Picture Processing. Academic Press, Upper Saddle River (1982)
47. Reza, A.M.: Realization of the contrast limited adaptive histogram equalization (CLAHE) for real-time image enhancement. J. VLSI Signal Process. 38(1), 35-44 (2004)
48. Rolland, J.-P., Vo, V., Bloss, B., Abbey, C.K.: Fast algorithms for histogram matching: Application to texture synthesis. J. Electron. Imaging 9(1), 39-45 (2000)
49. Rudin, L., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica D 60, 259-268 (1992)
50. Russ, J.C.: The Image Processing Handbook, 2nd edn. CRC Press, New York (1995)
51. Sapiro, G., Caselles, V.: Histogram modification via partial differential equations. In: International Conference on Image Processing 1995, vol. 3, pp. 632-635. IEEE, New York (2002)
52. Sen, D., Sankar, P.: Automatic exact histogram specification for contrast enhancement and visual system based quantitative evaluation. IEEE Trans. Image Process. 20, 1211-1220 (2011)
53. Sim, K., Tso, C., Tan, Y.: Recursive sub-image histogram equalization applied to gray scale images. Pattern Recognit. Lett. 28, 1209-1221 (2007) (Pubitemid 46722640)
54. Tan, T., Sim, K., Tso, C.: Image enhancement using background brightness preserving histogram equalisation. Electron. Lett. 48(3), 155-157 (2012)
55. Vogel, C., Oman, M.: Iterative method for total variation denoising. SIAM J. Sci. Comput. 17, 227-238 (1996) (Pubitemid 126621162)
56. Wan, Y., Shi, D.: Joint exact histogram specification and image enhancement through the wavelet transform. IEEE Trans. Image Process. 16(9), 2245-2250 (2007) (Pubitemid 47316671)
57. Wang, C., Ye, Z.: Brightness preserving histogram equalization with maximum entropy: a variational perspective. IEEE Trans. Consum. Electron. 51(4), 1326-1334 (2005) (Pubitemid 46489041)