曲率差分驅動的極小曲面濾波器

王滿利; 田子建; 張元剛

doi:10.11999/JEIT190216

曲率差分驅動的極小曲面濾波器

doi: 10.11999/JEIT190216

王滿利^{1, 2},
田子建^1, ,,
張元剛³

1.
中國礦業(yè)大學（北京）機電與信息工程學院北京 100083
2.
河南理工大學物理與電子信息學院焦作 454000
3.
兗礦集團信息化管理中心鄒城 273500

基金項目: 國家自然科學基金（51674269）

詳細信息

作者簡介:
王滿利：男，1981年生，博士生，研究方向為信息與通信工程

田子建：男，1964年生，教授，研究方向為信息與通信工程

通訊作者:
田子建　tianzj0726@126.com

中圖分類號: TN713; TP391.41
計量
- 文章訪問數(shù): 2466
- HTML全文瀏覽量: 1010
- PDF下載量: 64
- 被引次數(shù): 0
出版歷程
- 收稿日期: 2019-04-04
- 修回日期: 2019-10-26
- 網(wǎng)絡出版日期: 2019-11-11
- 刊出日期: 2020-03-19

Minimal Surface Filter Driven by Curvature Difference

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:
為提高全變分圖像降噪模型的降噪性能和邊緣保持性能，該文提出一種曲率差分驅動的極小曲面濾波器。首先，在平均曲率濾波器模型基礎上，引入自適應曲率差分邊緣探測函數(shù)，建立曲率差分驅動的極小曲面濾波器模型；接著，從微分幾何理論角度，闡述該能量泛函模型的物理意義和平均曲率能量減小方法；最后，在離散的圖像域，通過迭代的方式使圖像每個像素鄰域內(nèi)的曲面向極小曲面迭代進化，實現(xiàn)能量泛函的平均曲率能量極小化，從而能量泛函的總能量也完成極小化。實驗表明，該濾波器不僅能去除高斯噪聲、椒鹽噪聲，還能去除這兩類噪聲構成的混合噪聲，其降噪性能和邊緣保持性能優(yōu)于同類型的其他5種全變分算法。
- 圖像降噪 /
- 濾波器 /
- 能量泛函 /
- 平均曲率 /
- 極小曲面
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.
- Image denoising /
- Filter /
- Energy functional /
- Mean curvature /
- Minimal surface

HTML全文

圖 1 圖像域Ω分解方法

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圖 2 u_i?j鄰域內(nèi)3點的組合關系

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圖 3 d_k的近似求解方法

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圖 4 MSF濾波器能量變化曲線

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圖 5 MCF和MSF的降噪比較

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圖 6 相同迭代次數(shù)下兩濾波器降噪結果對比

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圖 7 6種算法的降噪圖像評價指標和運行時間比較

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圖 8 MSF去除混合噪聲的降噪圖像對比

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表 1 降噪圖像的評價指標數(shù)據(jù)

噪聲類型	圖像	濾波器	噪聲方差噪聲密度	迭代次數(shù)	PSNR.N	PSNR.D	CDE	RFSIM
高斯噪聲	Lena	MSF	10	10	28.1111	32.5290	12.3499	0.6873
		MSF	20	20	22.1472	28.8819	12.3575	0.5065
		MCF	10	10	28.1111	31.2486	12.3128	0.6063
		MCF	20	20	22.1472	28.7087	12.3020	0.4644
	House	MSF	5	7	34.1560	35.9549	11.0543	0.6838
			10	10	28.1072	32.4532	11.0582	0.5043
			20	20	22.1129	28.5565	11.0600	0.3117
		MCF	5	7	34.1560	33.1901	11.0436	0.5879
			10	10	28.1072	31.1816	11.0491	0.4750
			20	20	22.1129	28.3753	11.0487	0.3315
椒鹽噪聲	peppers	MSF	0.05	4	18.2659	34.3401	12.3245	0.8842
		MSF	0.10	9	15.3176	32.0921	12.3229	0.8271
		MCF	0.05	4	18.2659	30.1227	12.3089	0.7940
		MCF	0.10	9	15.3176	30.5087	12.2877	0.7083

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