Fourth-order partial differential equations for image enhancement

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Second-order partial differential equations have been studied as a useful tool for noise removal. The Perona-Malik model [P. Perona, Malik, Scale space and edge detection using anisotropic diffusion, IEEE Trans. Pattern Anal. Mach. Intell. 12 (1990) 6296391 has an edge preserving property but have sometimes the undesirable blurred effect. In this paper, we propose improved models by combining Catte et al.'s model [F. Catte', P.L. Lions, J.M. Morel, T. Coll, Image selective smoothing and edge detection by nonlinear diffusion, SIAM J. Numer. Anal. 129 (1992) 182-193] with fourth-order terms. We prove the existence and uniqueness of the proposed models. Then, we show numerical evidence of the power of resolution of these models with respect to other known models as the Perona-Malik model, the Catte et al.'s model, the modified total variation model by Chan et al. [T. Chan, A. Marquina, P. Mulet, Second order differential functionals in total variation-based image restoration. Available from: < http://www.math.ucia.edu/ chan >], etc. (c) 2005 Elsevier Inc. All rights reserved.
Publisher
ELSEVIER SCIENCE INC
Issue Date
2006-04
Language
English
Article Type
Article
Keywords

ANISOTROPIC DIFFUSION; EDGE-DETECTION

Citation

APPLIED MATHEMATICS AND COMPUTATION, v.175, no.1, pp.430 - 440

ISSN
0096-3003
DOI
10.1016/j.amc.2005.07.043
URI
http://hdl.handle.net/10203/91005
Appears in Collection
MA-Journal Papers(저널논문)
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