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Coherence-enhancing diffusion with the source term. (English) Zbl 1437.94016

Summary: Many texture images require the enhancement of coherent structures in various applications. Traditional coherence-enhancing diffusion filtering (CED) completes the interrupted lines and gaps but at the cost of reducing the contrast between coherent structures and the background. In this study, we introduce a source term into CED filtering to restore the initial image and the contrast lost by pure diffusion filters. Moreover, this new model combines contrast enhancement and diffusion processes, so it may be more suitable for dealing with white noise than the original CED. We assessed our method in terms of the theoretical and numerical properties changed by the source term. In our numerical assessment, we implemented our approach using an explicit scheme, which was accelerated by fast explicit diffusion. We compared the performance of our proposed approach with CED filtering based on fingerprint images.

MSC:

94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
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[2] Petrou, Maria; Sevilla, Pedro Garcia, Image Processing, Dealing with Texture, vol. 10 (2006), Wiley: Wiley Chichester
[4] Perona, Pietro; Malik, Jitendra, Scale-space and edge detection using anisotropic diffusion, IEEE Trans. Pattern Anal. Mach. Intell., 12, 7, 629-639 (1990)
[5] Weickert, Joachim, A review of nonlinear diffusion filtering. A review of nonlinear diffusion filtering, Scale-space Theory Comput. Vision (1997), Springer
[6] Nitzberg, Mark; Shiota, Takahiro, Nonlinear image filtering with edge and corner enhancement, IEEE Trans. Pattern Anal. Mach Intell., 14, 8, 826-833 (1992)
[7] Cottet, G.-H.; Germain, L., Image processing through reaction combined with nonlinear diffusion, Math. Comput., 61, 659-667 (1993) · Zbl 0799.35117
[8] Kass, Michael; Witkin, Andrew, Analyzing oriented patterns, Comput. Vision Graphics Image Process., 37, 3, 362-385 (1987), Elsevier
[9] Bigun, Josef, Optimal Orientation Detection of Linear Symmetry (1987), IEEE Computer Society Press, pp. 433-438
[11] Ravishankar Rao, A., Computing oriented texture fields, CVGIP: Graphical Models Image Process., 157-185 (1991)
[12] Jahne, Bernd, Spatio-temporal Image Processing: Theory and Scientific Applications, vol. 751 (1993), Springer- Verlag: Springer- Verlag New York · Zbl 0788.68161
[13] Joachim, Weickert, Scale-space Properties of Nonlinear Diffusion Filtering with a Diffusion Tensor, ((1994), Citeseer)
[14] Weickert, Joachim, Coherence-enhancing diffusion filtering, Int. J. Comput. Vision, 31, 111-127 (1999), Springer · Zbl 1505.94010
[15] Weickert, Joachim; Scharr, Hanno, A scheme for coherence-enhancing diffusion filtering with optimized rotation invariance, J. Visual Commun. Image Representation, 13, 1, 103-118 (2002), Elsevier
[16] Wang, Wenyuan, Generalized explicit schemes for coherence enhancing diffusion filtering, Opt. Eng., 47, 1 (2007)
[17] Grewenig, Sven; Weickert, Joachim; Bruhn, Andrés, From box filtering to fast explicit diffusion. From box filtering to fast explicit diffusion, Pattern Recognition (2010), Springer, pp. 533-542
[18] Weickert, Joachim, Coherence-enhancing shock filters. Coherence-enhancing shock filters, Pattern Recognition (2003), Springer, pp. 1-8
[19] Franken, Erik; Duits, Remco, Crossing-preserving coherence-enhancing diffusion on invertible orientation scores, Int. J. Comput. Vision, 85, 3, 253-278 (2009)
[21] Aubert, Gilles; Kornprobst, Pierre, Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations, vol. 147 (2006), Springer · Zbl 1110.35001
[22] Weickert, Joachim, Anisotropic Diffusion in Image Processing (1998), Teubner: Teubner Stuttgart · Zbl 0886.68131
[23] Kalaivani Narayanan, S.; Wahidabanu, R. S.D., Boosted nonlinear coherent diffusion for despeckling of diagnostic ultrasound images, Int. J. Comput. Technol. Appl., 2, 2, 284-294 (2011)
[24] Quittner, Pavol; Souplet, Philippe, Superlinear Parabolic Problems: Blow-up, Global Existence and Steady States (2007), Springer · Zbl 1128.35003
[25] Catté, Francine; Lions, Pierre-Louis; Morel, Jean-Michel; Coll, Tomeu, Image selective smoothing and edge detection by nonlinear diffusion, SIAM J. Numer. Anal., 29, 1, 182-193 (1992) · Zbl 0746.65091
[26] Nirenberg, Louis, Topics in Nonlinear Functional Analysis, vol. 6 (2001), American Mathematical Society · Zbl 0992.47023
[27] Brezis, Haim, Operateurs Maximaux Monotones et Semi-groupes de Contractions dans les espaces de Hilbert, vol. 5 (1973), Elsevier · Zbl 0252.47055
[28] Evans, Lawrence C., Partial Differential Equations: Graduate Studies in Mathematics, vol. 2 (1998), American Mathematical Society · Zbl 0902.35002
[29] Adams, Robert A.; Fournier, John J. F., Sobolev Spaces, vol. 140 (2003), Academic Press · Zbl 1098.46001
[30] Wu, Zhuoqun; Yin, Jingxue; Wang, Chunpeng, Elliptic & Parabolic Equations (2006), World Scientific Publishing Company Incorporated · Zbl 1108.35001
[33] Richardson, Lewis Fry, The approximate arithmetical solution by finite differences of physical problems involving differential equation, with an application to the stresses in a masonry dam, Trans. R. Soc. London Ser. A, 210, 307-357 (1910) · JFM 42.0873.02
[34] Weickert, Joachim, Nonlinear diffusion filtering. Nonlinear diffusion filtering, Handbook on Computer Vision and Applications (1999), Academic Press, pp. 423-450
[35] Weickert, Joachim; Ter Haar Romeny, B. M.; Viergever, Max A., Efficient and reliable schemes for nonlinear diffusion filtering, IEEE Trans. Image Process., 7, 3, 398-410 (1998)
[36] Welk, Martin; Steidl, Gabriele; Weickert, Joachim, Locally analytic schemes: a link between diffusion filtering and wavelet shrinkage, Appl. Comput. Harmonic Anal., 24, 2, 195-224 (2008), Elsevier · Zbl 1161.68831
[37] Calvetti, D.; Reichel, L., Adaptive Richardson iteration based on Leja points, J. Comput. Appl. Math., 71, 267-286 (1996) · Zbl 0863.65012
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