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標題: 使用自適應非等向性擴散方程式去除影像雜訊
Adaptive Anisotropic Diffusion Equation for Image Denoising
作者: 朱家敏
Chu, Chia-Min
關鍵字: nonlinear diffusion equation
出版社: 應用數學系所
引用: [1] A.C. Bovik, J.D. Gibson, A. Bovik, Handbook of Image and Video Processing, Academic Press, 2000. [2] F. Catte, P.L. Lions, J.M. Morel, and T. Coll, Image selective smoothing and edge detection by nonlinear diffusion, IEEE Trans. Pattern Anal. Machine Intell., 29 (1992), pp. 182-193. [3] G.-H. Cottet and L. Germain, Image Processing through Reaction Combined with Nonlinear Diffusion, Mathematics of Computation, 61 (1993), pp. 659-673. [4] R. C. Gonzalez and R. E. Woods, Digital Image Processing, Prentice Hall, 2002. [5] J. Jacur and K. Mikula, Solution of nonlinear diffusion appearing in image smoothing and edge detection, Applied Numerical Mathematics, 17 (1996), pp. 47-59. [6] D. Marr and E. Hildreth, Theory of edge detection, Proc. Roy. Soc. London Ser. B,(1980), pp. 187-217. [7] P. Perona and J. Malik, Scale-space and edge detection using anisotropic diffusion, IEEE Trans. Pattern Anal. Machine Intell, 12 (1990), pp. 629-639. [8] N. Sae-bae and S. Udomhunsakul, Adaptive Block-Based Singular Value Decomposition Filtering,4th International Conference on Computer Graphics, Imaging and Visualization [CGIV 2007](2007), 298-30. [9] Y. Shih , C. Rei and H. Wang, A novel PDE based image restoration: convection-diffusion equation for image denoising, Tech. report 07-1, Department of Applied Mathematics, National Chung Hsing University, 2007. [10] Y. Shih and H.C. Elman, Modified streamline diffusion schemes for convection-diffusion problems, Computers Math. Applic., 29 (1998), pp. 45-63. [11] J. L. Troutman, Variational Calculus with Elementary Convexity, Springer- Verlag, New York, 1983. [12] A. P. Witkin, Scale-space filtering, in Proceedings of IJCAI, Karlsruhe, (1983), pp. 1019-1021. [13] A. Rosenfeld and M. Thurston, Edge and curve detection for vtsual scene analysts, IEEE Trans. Compur., C-20 (1971), pp. 562-569. [14] M. Nitzberg and T. Shiota, Nonlinear image smoothing with edge and corner enhancement, Tech. report 90-2, Division of Applied Sciences, Hanard University, Cambridge, MA, 1990. [15] J. Weickert, Anisotropic Diffusion in Image Processing, Teubner Verlag, Stuttgart, 1996. [16] Yu-Li You, M. Kaveh, Wen-Yuan Xu, and A. Tannenbaum, Analysis and design of anisotropic diffusion for image processing, Department of Electrical Engineering, University of Minnesota, Minneapolis, MN 55455, 1994.
摘要: 在這篇論文中,我們提出自適應關聯性非線性方法來處理影像去雜訊和邊界 的保持。雖然許多的非線性擴散方程式去雜訊的方式已被廣泛的應用,然而有效 的去除雜訊的同時也保持住影像的邊界並使影像清晰仍是個相當難的問題。我們 提出一個新的非等向性非線性方程式,並使用自適應方法,使非線性擴散方程式 和某些低通濾波器相互相關聯的方式來修正影像的品質。在論文的數值實驗結果 中,我們所提出的方法和許多有名的去雜訊方程式做比較,實驗結果顯示我們提 出的方法在去除雜訊和保持邊界上有比較好的效果。
In this thesis, we present an adaptive correlation method for the image denoising and edge preservation. Several nonlinear diffusion filters have been widely implemented; however, it is still very difficult to preserve the image edge and clean the noise simultaneously. We propose a new anisotropic diffusion filter and consider an adaptive method that correlate a nonlinear diffusion filter with a linear low-pass filter for the smoothing. In numerical experiments, we compare our proposed methods with some popular nonlinear diffusion models and the result show the promise of the adaptive procedure removes the noisy and preserves the edge effectively.
其他識別: U0005-2307200814380800
Appears in Collections:應用數學系所



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