Abstract
In this paper, a region-based shock-diffusion equation is presented for image denoising and edge sharpening. An image is divided into three-type different regions according to image features: edges, textures and details, and flat areas. For edges, a shock-type backward diffusion is performed in the gradient direction to the isophote line (edge), incorporating a forward diffusion in the isophote line direction; while for textures and details, a soft backward diffusion is done to enhance image features preserving a natural transition. Moreover, an isotropic diffusion is used to smooth flat areas simultaneously. Finally, a shock capturing scheme with a special limiter function is developed to speed the process with numerical stability. Experiments on real images show that this method produces better visual results of the enhanced images than some related equations.
This work is supported by the national natural science fund, China (No. 60472033), the Key Laboratory Project of Information Science & Engineering of Railway of National Ministry of Railways, China (No. TDXX0510), and the Technological Innovation Fund of Excellent Doctorial Candidate of Beijing Jiaotong University, China (No. 48007).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Castleman, K.R.: Digital Image Processing. Prentice-Hall, Englewood Cliffs (1995)
Aubert, G., Kornprobst, P.: Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations. Applied Mathematical Sciences, vol. 147. Springer, Heidelberg (2001)
Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Machine Intell. 12(7), 629–639 (1990)
Nitzberg, M., Shiota, T.: Nonlinear image filtering with edge and corner enhancement. IEEE Transactions on PAMI 14(8), 826–833 (1992)
You, Y.L., Xu, W., Tannenbaum, A., Kaveh, M.: Behavioral analysis of anisotropic diffusion in image processing. IEEE Trans. on Image Processing 5(11), 1539–1553 (1996)
Alvarez, L., Mazorra, L.: Signal and image restoration using shock filters and anisotropic diffusion. SIAM J. Numer. Anal. 31(2), 590–605 (1994)
Osher, S.J., Rudin, L.I.: Feature-oriented image enhancement using shock filters. SIAM J. Numer. Anal. 27, 919–940 (1990)
Kornprobst, P., Deriche, R., Aubert, G.: Image coupling, restoration and enhancement via PDE’s. IEEE ICIP 2, 458–461 (1997)
Gilboa, G., Sochen, N., Zeevi, Y.Y.: Image Enhancement and denoising by complex diffusion processes. IEEE Transactions on PAMI 26(8), 1020–1036 (2004)
Liu, R.X., Shu, Q.W.: Some new methods in Computing Fluid Dynamics. Science Press of China, Beijing (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Fu, S., Ruan, Q., Wang, W., Chen, J. (2006). Region-Based Shock-Diffusion Equation for Adaptive Image Enhancement. In: Zheng, N., Jiang, X., Lan, X. (eds) Advances in Machine Vision, Image Processing, and Pattern Analysis. IWICPAS 2006. Lecture Notes in Computer Science, vol 4153. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11821045_41
Download citation
DOI: https://doi.org/10.1007/11821045_41
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-37597-5
Online ISBN: 978-3-540-37598-2
eBook Packages: Computer ScienceComputer Science (R0)