王满利^{1, 2},
田子建^1,,,
张元刚³
1.中国矿业大学（北京）机电与信息工程学院 北京 100083
2.河南理工大学物理与电子信息学院 焦作 454000
3.兖矿集团信息化管理中心 邹城 273500
基金项目:国家自然科学基金（51674269）

详细信息

作者简介:王满利：男，1981年生，博士生，研究方向为信息与通信工程
田子建：男，1964年生，教授，研究方向为信息与通信工程

通讯作者:田子建　tianzj0726@126.com

中图分类号:TN713; TP391.41

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被引次数:0

出版历程

收稿日期:2019-04-04
修回日期:2019-10-26
网络出版日期:2019-11-11
刊出日期:2020-03-19

Minimal Surface Filter Driven by Curvature Difference

Manli WANG^{1, 2},
Zijian TIAN^1,,,
Yuangang ZHANG³
1. School of Mechanical Electronic & Information Engineering, China University of Mining and Technology (Beijing), Beijing 100083, China
2. School of Physics &Electronic Information Engineering, HeNan Polytechnic University, Jiaozuo 454000, China
3. Information Center of YanKuang Group, Zoucheng 273500, China
Funds:The National Natural Science Foundation of China (51674269)


摘要
摘要:为提高全变分图像降噪模型的降噪性能和边缘保持性能，该文提出一种曲率差分驱动的极小曲面滤波器。首先，在平均曲率滤波器模型基础上，引入自适应曲率差分边缘探测函数，建立曲率差分驱动的极小曲面滤波器模型；接着，从微分几何理论角度，阐述该能量泛函模型的物理意义和平均曲率能量减小方法；最后，在离散的图像域，通过迭代的方式使图像每个像素邻域内的曲面向极小曲面迭代进化，实现能量泛函的平均曲率能量极小化，从而能量泛函的总能量也完成极小化。实验表明，该滤波器不仅能去除高斯噪声、椒盐噪声，还能去除这两类噪声构成的混合噪声，其降噪性能和边缘保持性能优于同类型的其他5种全变分算法。
关键词:图像降噪/
滤波器/
能量泛函/
平均曲率/
极小曲面
Abstract:To improve performance of denoising and edge preservation of the total variational image denoising model, a curvature difference driven minimal surface filter is proposed. Firstly, the presented filter model is constructed by adding an adaptive edge detection function of curvature difference to the mean curvature filter model. After that, from the perspective of differential geometry theory, the physical meaning of the energy functional model and the method of reducing the average curvature energy are elaborated. Finally, in the discrete image domain, the surface in the neighborhood of each pixel of the image is iteratively evolved to the minimal surface to minimize the average curvature energy of the energy functional, so that the total energy of the energy functional is also minimized. Experiments show that the filter can not only remove Gauss noise and salt and pepper noise, but also remove the mixed noise composed of these two kinds of noise. Its performance of noise reduction and edge preservation is better than the other five total variational algorithms of the same kind.
Key words:Image denoising/
Filter/
Energy functional/
Mean curvature/
Minimal surface



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