由扩散张量导出的各向异性扩散模型的隐式数值模拟

计算物理 ›› 2005, Vol. 22 ›› Issue (4): 365-370.

由扩散张量导出的各向异性扩散模型的隐式数值模拟

刘朝霞¹, 常谦顺²

1. 北京应用物理与计算数学研究所, 北京 100088;
2. 中科院教学与系统科学研究院应用数学所, 北京 100080

收稿日期:2004-03-17 修回日期:2004-08-30 出版日期:2005-07-25 发布日期:2005-07-25
作者简介:刘朝霞(1974-),女,山东,讲师,从事数值分析与计算物理研究,北京8009信箱28分箱100088.

Implicit Numerical Simulations of an Anisotropic Diffusion Model Driven by Diffusion Tensors

LIU Zhao-xia¹, CHANG Qian-shun²

1. Institute of Applied Physics and Computational Mathematics, Beijing 100088, China;
2. Academy of Mathematics and System Sciences, Chinese Academy of Science, Beijing 100080, China

Received:2004-03-17 Revised:2004-08-30 Online:2005-07-25 Published:2005-07-25

摘要/Abstract

摘要： 研究了由扩散张量导出的各向异性扩散的图像处理模型,并构造了隐式差分格式,形成了有13条对角线的大型稀疏矩阵.利用代数多重网格法求解了这个线性代数方程组.并进行了数值试验.

关键词: 图像处理, 扩散张量, 各向异性扩散, 代数多重网格法

Abstract: A model of image processing for anisotropic diffusion driven by diffusion tensors is investigated. An implicit difference scheme is constructed. A large sparse matrix with 13 diagonals is formed with which general iterative methods don't work well. With algebraic multi-grid method (AMG), linear system of equations are solved.Numerical experiments are shown.

Key words: image processing, diffusion tensor, anisotropic diffusion, algebraic multi-grid method (AMG)

中图分类号:

O175
O241

刘朝霞, 常谦顺. 由扩散张量导出的各向异性扩散模型的隐式数值模拟[J]. 计算物理, 2005, 22(4): 365-370.

LIU Zhao-xia, CHANG Qian-shun. Implicit Numerical Simulations of an Anisotropic Diffusion Model Driven by Diffusion Tensors[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2005, 22(4): 365-370.

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