A $p$-Laplacian model for uneven illumination enhancement of document images

[1] M. Athimethphat, V. Patanavijit, A non-linear illuminations balancing for reconstructed degraded
scanned text-photo image, 10th International Symposium on Communications and Information
Technologies, IEEE, 2010, 1158–1163.

[2] F.Z.A. Bella, M. El Rhabi, A. Hakim, A. Laghrib, Reduction of the non-uniform illumination using
nonlocal variational models for document image analysis, J. Franklin Inst. 355 (2018) 8225–8244.
[3] T. Chen, W. Yin, X.S. Zhou, D. Comaniciu, T.S. Huang, Illumination normalization for face recog-
nition and uneven background correction using total variation based image models, Proc. IEEE
Comput. Soc. Conf. Comput. Vis. 2 (2005) 532–539.

[4] M.G. Crandall, H. Ishii, P.L. Lions, User’s guide to viscosity solutions of second order partial
differential equations, Bull. Am. Math. Soc. 27 (1992) 1–67.
[5] M. Di Paola, G. Failla, M. Zingales, Physically-based approach to the mechanics of strong non-
local linear elasticity theory, J. Elastic. 97 (2009) 103–130.
[6] Y. Du, J. Cihlar, J. Beaubien, R. Latifovic, Radiometric normalization, compositing, and quality
control for satellite high resolution image mosaics over large areas, IEEE Trans. Geosci. Remote
Sens. 39 (2001) 623–634.
[7] P. Fife, Some nonclassical trends in parabolic and parabolic-like evolutions, Trends in nonlinear
analysis, Springer, 2003, 153–191.
[8] B. Gatos, I. Pratikakis, S.J. Perantonis, Adaptive degraded document image binarization, Pattern
Recognit. 39 (2006) 317–327.
[9] Y. Giga, Surface Evolution Equations, Springer, 2006.
[10] R.C. Gonzales, R.E. Woods, Digital Image Processing, 2002.
[11] E. Grisan, A. Giani, E. Ceseracciu, A. Ruggeri, Model-based illumination correction in retinal
images, 3rd IEEE Int. Symp. Biomed. Imaging, Nano to Macro, 2006, 984–987.
[12] E.H. Land, J.J. McCann, Lightness and retinex theory, Josa 61 (1971) 1–11.
[13] J.S. Lee, C.H. Chen, C.C. Chang, A novel illumination-balance technique for improving the quality
of degraded text-photo images, IEEE Trans. Circuits. Syst. Video Technol. 19 (2009) 900–905.
[14] F.W. Leong, M. Brady, J.O. McGee, Correction of uneven illumination (vignetting) in digital mi-
croscopy images, J. Clin. Pathol. 56 (2003) 619–621.

[15] G. Meng, S. Xiang, N. Zheng, C. Pan, Nonparametric illumination correction for scanned docu-
ment images via convex hulls, IEEE Trans. Pattern Anal. Mach. Intell. 35 (2012) 1730–1743.
[16] A. Nayak, S. Chaudhuri, Automatic illumination correction for scene enhancement and object
tracking, Image Vis. Comput. 24 (2006) 949–959.
[17] M. Ohnuma, K. Sato, Singular degenerate parabolic equations with applications to the p-laplace
diffusion equation, Hokkaido University Preprint Series in Mathematics 332 (1996) 1–20.
[18] L. Rosasco, M. Belkin, E.D. Vito, On learning with integral operators, J. Mach. Learn. Res. 11
(2010) 905–934.
[19] J. Sauvola, M. Pietik¨ainen, Adaptive document image binarization, Pattern Recognit. 33 (2000)
225–236.

[20] X. Shen, Q. Li, Y. Tian, L. Shen, An uneven illumination correction algorithm for optical remote
sensing images covered with thin clouds, Remote Sens. 7 (2015) 11848–11862.
[21] S.A. Silling, R. Lehoucq, Peridynamic theory of solid mechanics, Adv. Appl. Mech. 44, (2010),
73–168.
[22] B. Tan, J.G. Masek, R. Wolfe, F. Gao, C. Huang, E.F. Vermote, J.O. Sexton, G. Ederer, Improved
forest change detection with terrain illumination corrected landsat images, Remote Sens. Environ.
136 (2013) 469–483.