Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/17684
標題: 邊緣保持的影像去雜訊研究
The image denoising process with the edge preservation
作者: 黃宣瑜
Huang, Hsuan-Yu
關鍵字: The Gray Digital Images;灰階數位影像;The Diffusion Equation;The Fourier Series;Delta Functions;Smooth;擴散方程式;傅立葉級數;Delta函數;平滑化
出版社: 應用數學系所
引用: [1] 李佩璇, “應用傅立葉小波轉換於正子斷層掃描正弦圖去雜訊及 影像重建”. 中原大學, 電機工程學系研究所, 94 碩士論文. [2] 莊周敏, “利用ECG訊號之離散小波轉換於個人身份辨識研究”. 逢甲大學, 自動控制工程學系研究所, 94 碩士論文. [3] 劉家榮, “小波函數在影像壓縮和編輯之應用”. 逢甲大學,應用數學研究所,94 碩士論文. [4] Rafael C. Gonzalez, and Richard E. Woods, “Digital Image Processing”. 2nd ed. New Jersey:Prentice-Hall, 2002. [5] Ram P. Kanwal, “Generalized Functions Theory and Applications”. Third Edition. [6] Martin Welk, and Joachim Weickert, “SEMIDISCRETE AND DISCRETE WELL-POSEDNESS OF SHOCK FILTERING”. Mathematical Image Analysis Group Faculty of Mathematics and Computer Science, Bldg. 27 Saarland University, 66041 Saarbruecken, Germany. [7] Fr´edo Durand, and Julie Dorsey, “Fast Bilateral Filtering for the Display of High-Dynamic-Range Images”. Laboratory for Computer Science, Massachusetts Institute of Technology. [8] JUNG-HUA WANG, and HSIEN-CHU CHIU, “HAF: an Adaptive Fuzzy Filter for Restoring Highly Corrupted Images by Histogram Estimation”. Department of Electrical Engineering National Taiwan Ocean University Keelung, Taiwan, R.O.C. [9] G. Ramponi, G.L. Sicuranza, “Quadratic digital filters for image processing,” IEEE Transactions on ASSP, 1988, 36 (6): 1263-1285. [10] S. Guillon, P. Baylou, M. Najim, N. Keskes, “Adaptive nonlinear filters for 2D and 3D images enhancement,” Signal Processing, 1998, 67: 237-254. [11] Y. B. Yuan, T.V. Vorburger, J. F. Song(2),and T. B. Renegar, “A Simplified Realization for the Gaussian Filter in Surface Metrology”. In X. International Colloquium on Surfaces, Chemnitz (Germany), Jan. 31 - Feb. 02, 2000, M. Dietzsch, H. Trumpold, eds. (Shaker Verlag GmbH, Aachen, 2000), p. 133. [12] P. Perona, and J. Malik, “Scale-space and edge detection using anisotropic diffusion”. IEEE Trans. Pattern Analysis and Machine Interlligence, 1990. [13] Michael J. Black, Guillermo Sapiro, David H. Marimont, and David Heeger, “Robust Anisotropic Diffusion”. IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 7, NO. 3, MARCH 1998. [14] A. Ben Hamza, and Hamid Krim, “Image Denoising: A Nonlinear Robust Statistical Approach”. IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 49, NO. 12, DECEMBER 2001. [15] S. K. Weeratunga, and C. Kamath, “A comparison of PDEbased non-linear anisotropic diffusion techniques for image denoising”. This article was submitted to Image Processing: Algorithms and Systems II, SPIE Electronic Imaging, Santa Clara, January 2003. [16] Guy Gilboa, Nir Sochen, and Yehoshua Y. Zeevi, “Image Enhancement and Denoising by Complex Diffusion Processes”. IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, VOL. XX, NO. Y, MONTH 2003. [17] SHUJUN FU, QIUQI RUAN, WENQIA WANG, and JINGNIAN CHEN, “Combining Bidirectional Flow Equation and Fuzzy Sets for Adaptive Image Sharpening”. School of Mathematics and System Science, Shandong University, Jinan, 250100, China. [18] Guido Gerig, Olaf Kubler, Ron Kikinis, and Ferenc A. Jolesz, “Nonlinear Anisotropic Filtering of MRI Data”. IEEE TRANSACTIONS ON MEDICAL IMAGING. VOL. 1 I . NO. 2. JUNE 1’192. [19] Kurt Bryan, “The Dirac Delta Function”. [20] J. Canny, “A computational approach to edge detection”. IEEE Trans. Pattern Analysis and Machine Interlligence, 1986. [21] Mihir Sen, “ANALYTICAL HEAT TRANSFER”. Department of Aerospace and Mechanical Engineering University of Notre Dame Notre Dame, IN 46556. [22] R. Chris Camphouse, “Approximations and Object-Oriented Implementation for a Parabolic Partial Di_erential Equation”. Thesis submitted to the Faculty of the Virginia Polytechnic Institute and State University in partial ful_llment of the requiremnts for the degree of Master of Science in Mathematics.
摘要: 
本文將擴散方程式應用在影像處理去雜訊的功能上,並達成邊緣保留之目的。
灰階數位影像可以視為矩陣的整數資料型態,我們利用傅立葉級數(Fourier series),將矩陣中每一列的整數資料以傅立葉級數展開,當作擴散方程式的起始條件。亦將擴散方程式的全解以傅立葉級數展開,因此擴散方程式的全解即成為不同時間所代表灰階數位影像中的灰階值,隨著時間的增加,代表雜訊的高頻部份將會逐漸衰減,因此達成去除雜訊的目的,但同時,物件的邊緣輪廓也將同時逐漸衰減,為了克服此問題,我們加入由Delta函數所組成的熱源。Delta函數由影像中物件的邊緣位置決定,其效用只影響了全解中穩態解的部份,並不會隨著時間而與暫態解一起衰減,因此加入熱源後的擴散方程式就能將灰階數位影像平滑化(smoothing)的同時,也可以將物件的銳利邊緣保留而避免被模糊的缺點。

The paper presents the diffusion equation applied on the image denoising process with the edge preservation.
The gray digital images can be regarded as matrixes with the integer data type. In each row of matrix, the integer data sequence can be represented by the Fourier series expansion and it can be regarded as the initial condition of the diffusion equation. The complete solutions of diffusion equation can be expanded by Fourier series; therefore, the gray scale of the gray level digital image is equivalent to the complete solutions of the diffusion equation. The high frequency part of the transition solution is going to decrease in the complete solution as the time increasing which achieve the aim of image denoising purpose. But simultaneously, the edge of accessory also at the same time gradually will attenuation, in order to overcome this question, we accede to the heat source which is composed by the Delta function. The location of Delta functions are decided by the sharp edge positions of the image. It only influences the steady states solution which is the part of the complete solution and does not attenuate together with the transition condition solution as the time increased. The diffusion equation can be used to smooth the gray digital image and to preserve the sharp edge avoiding the shortness of edge blurred.
URI: http://hdl.handle.net/11455/17684
其他識別: U0005-2808200601552600
Appears in Collections:應用數學系所

Show full item record
 

Google ScholarTM

Check


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.