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Sobolev 广义度量下的各向异性扩散模型

刘孝艳,  冯象初,  赵晨萍

文章导航 > 自动化学报  > 2015 >  41(2): 320-329
刘孝艳, 冯象初, 赵晨萍. Sobolev 广义度量下的各向异性扩散模型. 自动化学报, 2015, 41(2): 320-329. doi: 10.16383/j.aas.2015.c140564
引用本文: 刘孝艳, 冯象初, 赵晨萍. Sobolev 广义度量下的各向异性扩散模型. 自动化学报, 2015, 41(2): 320-329. doi: 10.16383/j.aas.2015.c140564
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LIU Xiao-Yan, FENG Xiang-Chu, ZHAO Chen-Ping. Anisotropic Diffusion Model Based on Generalized Metric in Sobolev Space. ACTA AUTOMATICA SINICA, 2015, 41(2): 320-329. doi: 10.16383/j.aas.2015.c140564
Citation: LIU Xiao-Yan, FENG Xiang-Chu, ZHAO Chen-Ping. Anisotropic Diffusion Model Based on Generalized Metric in Sobolev Space. ACTA AUTOMATICA SINICA, 2015, 41(2): 320-329. doi: 10.16383/j.aas.2015.c140564
shu

Sobolev 广义度量下的各向异性扩散模型

doi: 10.16383/j.aas.2015.c140564
  • 1.

    西安电子科技大学数学与统计学院 西安 710126;

  • 2.

    西安石油大学理学院 西安 710065

基金项目: 

国家自然科学基金(61271294,61362029,61379030,61472303)资助

详细信息
    作者简介:

    冯象初 西安电子科技大学数学与统计学院教授. 1999 年获西安电子科技大学理学博士学位. 主要研究方向为数值分析, 小波, 图像处理的偏微分方程方法.E-mail: xcfeng@mail.xidian.edu.cn

    通讯作者:

    刘孝艳 西安电子科技大学数学与统计学院博士研究生, 西安石油大学理学院讲师. 主要研究方向为变分及偏微分方程在图像处理中的应用. 本文通信作者.E-mail: feng2001410@163.com

Anisotropic Diffusion Model Based on Generalized Metric in Sobolev Space

  • 1.

    School of Mathematics and Statistics, Xidian University, Xi'an 710126;

  • 2.

    Faculty of Science, Xi'an Shiyou University, Xi'an 710065

Funds: 

Supported by National Natural Science Foundation of China (61271294, 61362029, 61379030, 61472303)

摘要

    摘要
  • 摘要: 给出了Sobolev空间的一种广义度量, 在该度量下提出了一个新的各向异性增强、扩散方程. 广义度量中的变系数, 较好地控制了方程的扩散行为, 使得新模型不仅能有效增强图像的细节特征, 而且能在噪声去除和边缘保护之间取得较好的平衡, 同时给出了相应的隐式离散算法. 仿真实验结果表明, 新模型和算法是行之有效的.
    Abstract: A generalized metric is defined in Sobolev space, based on which an anisotropic sharpening/diffusion equation is presented. Since the space-varying coefficient of the generalized metric can control the diffusion behavior better, the proposed model can not only highlight the image detail effectively but also achieve a good balance between noise removal and edge preservation. The corresponding implicit algorithm is then developed. Simulation results show that the new model and algorithm are feasible.
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    • 参考文献(25)
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出版历程
  • 收稿日期:  2014-08-08
  • 修回日期:  2014-11-15
  • 刊出日期:  2015-02-20

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