数学与计算机科学 |
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基于分数阶偏微分方程的图像放大模型 |
高冉1, 顾聪1, 李胜宏2 |
1. 中原工学院 理学院, 河南 郑州 450007; 2. 浙江大学 数学系, 浙江 杭州 310027 |
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Image zooming model based on fractional-order partial differential equation |
GAO Ran1, GU Cong1, LI Shenghong2 |
1. College of Science, Zhongyuan University of Technology, Zhengzhou 450007, China; 2. Department of Mathematics, Zhejiang University, Hangzhou 310027, China |
[1] 付树军,阮秋琦,王文洽.偏微分方程(PDEs)模型在图像处理中的若干应用[J].计算机工程与应用,2005(2):33-35. FU Shujun, YUAN Qiuqi, WANG Wenqia. Applications of PDEs model in image analysis and processing: A survey[J]. Computer Engineering and Applications,2005(2):33-35. [2] 张亶,陈刚.基于偏微分方程的图像处理[M].北京:高等教育出版社,2004. ZHANG Dan, CHEN Gang. Image Processing Based on PDEs[M]. Beijing:Higher Education Press,2004. [3] CHEN Y M, VEMURI B C, WANG L. Image denoising and segmentation via nonlinear diffusion[J]. Computers and Mathematics with Applications, 2000,39(5/6):131-149. [4] WEICKERT J. Coherence-enhancing diffusion filtering [J]. International Journal of Computer Vision,1999,31(2/3):111-127. [5] 阮秋琦,忤冀颖.数字图像处理中的偏微分方程方法[J].信号处理,2012,28(3):301-314. YUAN Qiuqi, WU Jiying. Partial differential equation method on digital image processing[J]. Signal Processing, 2012,28(3):301-314. [6] KIM H, CHA Y, KIM S. Curvature interpolation method for image zooming[J]. IEEE Transactions on Image Processing,2011,20(7):1895-1903. [7] 朱宁,吴静,王忠谦.图像放大的偏微分方程方法[J].计算机辅助设计与图形学学报,2005,17(19):1941-1945. ZHU Ning, WU Jing, WANG Zhongqian. Image zooming based on partial differential equations[J]. Journal of Computer-Aided Design & Computer Graphics,2005,17(19):1941-1945. [8] CRANDALL M G, ISHII H, LIONS P L. User's guide to viscosity solutions of second order partial linear differential equations[J]. Bull Amer Math Soc,1992,27:1-67. [9] RUDIN L, OSHER S. Feature-oriented image enhancement using shock filters[J]. SIAM J Numerical Analysis,1990,27:919-940. [10] GAO Ran, SONG Jinping, TAI Xuecheng. Image zooming algorithm based on partial differential equations technique[J]. International Journal of Numerical Analysis and Modeling,2009(6):5-18. [11] 蒲亦非,王卫星.数字图像的分数阶微分掩模及其数值运算规则[J].自动化学报,2007,33(11):1128-1135. PU Yifei, WANG Weixing. Fractional differential masks of digital image and their numerical implementation algorithms[J]. Acta Automatica Sinica,2007,33(11):1128-1135. [12] 杨柱中,周激流,黄梅,等.基于分数阶微分的边缘检测[J].四川大学学报:工程科学版,2008,40(1):152-156. YANG Zhuzhong, ZHOU Jiliu, HUANG Mei, et al. Edge detection based on fractional differential[J]. Journal of Sichuan University:Engineering Science Edition,2008,40(1):152-156. [13] 艾必刚,罗以宁,蒋涛,等.分数阶微分梯度算子在图像增强中的应用[J].四川大学学报:自然科学版,2009,46(2):343-347. AI Bigang, LUO Yining, JIANG Tao, et al. Applications of fractional-order differential gradient Operator in Image Enhancement[J]. Journal of Sichuan University: Natural Science Edition,2009,46(2):343-347. [14] PODLUBNY I. Fractional Differential Equations[M]. New York: Academic Press,1998. |
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