结合L_(0)优化与拉普拉斯算子的图像平滑方法  

L_(0) Optimization Using Laplacian Operator for Image Smoothing

作　　者：李孟航 高珊珊[1,2,3] 韩慧健 张彩明[2,4,5] Li Menghang;Gao Shanshan;Han Huijian;Zhang Caiming(School of Computer Science and Technology,Shandong University of Finance and Economics,Jinan 250014;Shandong Provincial Key Laboratory of Digital Media Technology,Jinan 250014;Shandong China-U.S.Digital Media International Cooperation Research Center,Jinan 250014;Software College,Shandong University,Jinan 250101;Shandong Co-Innovation Center of Future Intelligent Computing,Yantai 264025)

机构地区：[1]山东财经大学计算机科学与技术学院,济南250014 [2]山东省数字媒体技术重点实验室,济南250014 [3]山东省中美数字媒体国际合作研究中心,济南250014 [4]山东大学软件学院,济南250101 [5]山东省未来智能计算协同创新中心,烟台264025

出　　处：《计算机辅助设计与图形学学报》2021年第7期1000-1014,共15页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金重点项目(U1909210,61772309,61902217);山东省自然科学基金(ZR2020MF037,ZR2019MF016,ZR2019MF051,ZR2019BF043);山东省重点研发计划(2019GGX101007);教育部规划基金(20YJA870013);山东省高等学校青创人才引育计划团队项目。

摘　　要：针对平滑过度使图像的细节特征损失导致失真的现象,提出了一种L0测度优化与二阶拉普拉斯算子结合的图像平滑方法,采用拉普拉斯算子约束图像颜色变化,通过对L0模型的优化减缓颜色梯度的变化,达到图像颜色平滑过渡的目的.为了在平滑过程中更好地保持图像边缘特征,引入Sobel算子作为能量函数正则项,并采用交替求解策略求解能量函数.在图像平滑领域经典图像以及通过网络引擎搜索得到的图像上与6种平滑方法以及7种去噪方法进行了定性和定量比较实验,结果表明,所提方法在图像平滑的同时能够降低图像细节特征的损失,有效地处理图像平滑中存在的阶梯状边缘以及颜色块状分布的现象,并去除图像中的多种噪声,而且所提方法的峰值信噪比和运行时间也较其他方法有所提升.Image smoothing often leads to the loss of image details and distortion because of over smoothing.An image smoothing method is presented which combines L0 optimization and the second-order Laplacian operator.Laplacian operator is used to constrain the color change of the image,and L0 optimization is used to minimize the change of the color gradient,so as to achieve the purpose of smooth color transition of the image.In order to keep the edge features of the image better in the process of smoothing,Sobel operator is introduced as the regular term of energy function,and the alternating solution strategy is adopted to solve the energy function.In the experiment,using the classical image in the field of image smoothing and the image obtained through network engine,the proposed method is compared qualitatively and quantitatively with 6 smoothing methods and 7 denoising methods.The experimental results show that the proposed method can reduce the loss of image details while smoothing the image,effectively deal with the phenomenon of stepped edges and color block distribution in the image smoothing,and effectively remove various noises in the image.And the peak signal-to-noise ratio and running time of the proposed method are improved compared with other methods.

关 键 词：图像平滑 图像去噪 L_(0)范数 拉普拉斯算子 SOBEL算子 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]