计算机应用 ›› 2012, Vol. 32 ›› Issue (12): 3385-3388.DOI: 10.3724/SP.J.1087.2012.03385

• 图形图像技术 • 上一篇    下一篇

基于Priwitt算子的偏微分方程图像去噪模型

刘西林,王泽文,邱淑芳   

  1. 东华理工大学 理学院,南昌 330013
  • 收稿日期:2012-06-21 修回日期:2012-08-06 发布日期:2012-12-29 出版日期:2012-12-01
  • 通讯作者: 王泽文
  • 作者简介:刘西林(1986-), 男, 山西忻州人,硕士研究生, 主要研究方向:基于偏微分方程的图像处理;〓王泽文(1974-),男,江西上饶人,教授,博士,主要研究方向:数学物理反问题及其数值解法、基于偏微分方程的图像处理;〓邱淑芳(1972-),江西进贤人,副教授,硕士,主要研究方向:数学建模、基于偏微分方程的图像处理。
  • 基金资助:
    江西省自然科学基金资助项目;江西省教育厅科技项目

PDE-based Image Noise Removal Models Based on Priwitt Operator

LIU Xi-lin,WANG Ze-wen,QIU Shu-fang   

  1. School of Science,East China Institute of Technology,Nanchang Jiangxi 330013,China
  • Received:2012-06-21 Revised:2012-08-06 Online:2012-12-29 Published:2012-12-01
  • Contact: WANG Ze-wen

摘要: 利用归一化的Priwitt微分算子作为权重,提出了两种融合Gauss曲率和平均曲率扩散的偏微分方程去噪模型,使得它们在去除噪声的同时能保持图像的重要特征。首先,对噪声图像进行Gauss滤波并计算滤波后图像的Priwitt微分算子;然后,新模型根据归一化的Priwitt微分算子自适应地平衡于高斯曲率扩散去噪与平均曲率扩散去噪之间,从而去除图像的噪声。利用偏微分方程有限差分法给出了新模型的离散迭代格式,并进行了数值实验。实验结果表明,新模型不仅迭代收敛的速度快,而且在均方误差和峰值信噪比两个评价指标上均优于单一曲率扩散去噪模型,并更好地保持了图像的细节特征。

关键词: 图像去噪, 高斯曲率, 平均曲率, Priwitt算子

Abstract: Using the normal Priwitt operator as weights, two denoising models based on Partial Differential Equation (PDE), which integrated the Gauss curvature and mean curvature diffusion, were proposed for keeping important features effectively while removing noises. First, the normal Priwitt operator of the filtered image obtained by the Gauss filter from noise image was calculated; second, the proposed models adaptively obtain the balance between the Gauss curvature diffusion noise removal and the mean curvature diffusion noise removal, thus removing noises of image. The iterative schemes of the proposed models were presented by the difference method of PDE. Then some numerical experiments were carried out. Results of experiments show that the proposed models not only converge quickly, but also are better than the denoising model based on single curvature diffusion, and better maintain the image features.

Key words: Image denoising, Gauss curvature, mean curvature, Priwitt operator

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