| Sobolev 广义度量下的各向异性扩散模型 |
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| 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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| 作者姓名： | 刘孝艳 冯象初 赵晨萍 |
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| 作者单位： | 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 |
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| 基金项目： | 国家自然科学基金(61271294,61362029,61379030,61472303)资助 |
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| 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.
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| 关 键 词： | 图像增强 图像扩散 偏微分方程 各向异性扩散 Sobolev空间 |
| 收稿时间： | 2014-08-08 |
| 修稿时间： | 2014-11-15 |
Anisotropic Diffusion Model Based on Generalized Metric in Sobolev Space |
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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 |
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| Authors: | LIU Xiao-Yan FENG Xiang-Chu ZHAO Chen-Ping |
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| Affiliation: | 1. School of Mathematics and Statistics, Xidian University, Xi'an 710126;;;2. Faculty of Science, Xi'an Shiyou University, Xi'an 710065 |
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| 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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| Keywords: | Image sharpening image diffusion partial differential equation anisotropic diffusion Sobolev space |
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