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曲率差分驱动的极小曲面滤波器

王满利 田子建 张元刚

引用本文: 王满利, 田子建, 张元刚. 曲率差分驱动的极小曲面滤波器[J]. 电子与信息学报, 2020, 42(3): 764-771. doi: 10.11999/JEIT190216 shu
Citation:  Manli WANG, Zijian TIAN, Yuangang ZHANG. Minimal Surface Filter Driven by Curvature Difference[J]. Journal of Electronics and Information Technology, 2020, 42(3): 764-771. doi: 10.11999/JEIT190216 shu

曲率差分驱动的极小曲面滤波器

    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
  • 基金项目: 国家自然科学基金(51674269)

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。

English

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  • 图 1  图像域Ω分解方法

    图 2  ui‚j邻域内3点的组合关系

    图 3  dk的近似求解方法

    图 4  MSF滤波器能量变化曲线

    图 5  MCF和MSF的降噪比较

    图 6  相同迭代次数下两滤波器降噪结果对比

    图 7  6种算法的降噪图像评价指标和运行时间比较

    图 8  MSF去除混合噪声的降噪图像对比

    表 1  降噪图像的评价指标数据

    噪声类型图像滤波器噪声方差噪声密度迭代次数PSNR.NPSNR.DCDERFSIM
    高斯噪声LenaMSF101028.111132.529012.34990.6873
    202022.147228.881912.35750.5065
    MCF101028.111131.248612.31280.6063
    202022.147228.708712.30200.4644
    HouseMSF5734.156035.954911.05430.6838
    101028.107232.453211.05820.5043
    202022.112928.556511.06000.3117
    MCF5734.156033.190111.04360.5879
    101028.107231.181611.04910.4750
    202022.112928.375311.04870.3315
    椒盐噪声peppersMSF0.05418.265934.340112.32450.8842
    0.10915.317632.092112.32290.8271
    MCF0.05418.265930.122712.30890.7940
    0.10915.317630.508712.28770.7083
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文章相关
  • 通讯作者:  田子建, tianzj0726@126.com
  • 收稿日期:  2019-04-04
  • 录用日期:  2019-10-26
  • 网络出版日期:  2019-11-11
  • 刊出日期:  2020-03-01
通讯作者: 陈斌, bchen63@163.com
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