基于梯度曲面面积与稀疏约束的图像平滑方法

doi:10.11772/j.issn.1001-9081.2020081325

计算机应用 ›› 2021, Vol. 41 ›› Issue (7): 2039-2047.DOI: 10.11772/j.issn.1001-9081.2020081325

所属专题：多媒体计算与计算机仿真

• 多媒体计算与计算机仿真 • 上一篇下一篇

基于梯度曲面面积与稀疏约束的图像平滑方法

李辉¹, 吴传生¹, 刘俊², 刘文³

1. 武汉理工大学理学院, 武汉 430070;
2. 东北师范大学数学与统计学院, 长春 130024;
3. 武汉理工大学航运学院, 武汉 430063

收稿日期:2020-08-31 修回日期:2020-10-26 出版日期:2021-07-10 发布日期:2020-12-29
通讯作者: 吴传生
作者简介:李辉(1995-),女,河南南阳人,硕士研究生,主要研究方向:计算机视觉、微分方程;吴传生(1957-),男,湖北天门人,教授,博士,主要研究方向:微分方程、小波分析、智能计算;刘俊(1987-),男,江西九江人,副教授,博士,主要研究方向:图像恢复、数值优化;刘文(1987-),男,湖北孝感人,副教授,博士,CCF会员,主要研究方向:计算机视觉、图像处理、计算航海科学。
基金资助:
国家自然科学基金资助项目（51609195，11701079）。

Image smoothing method based on gradient surface area and sparsity constraints

LI Hui¹, WU Chuansheng¹, LIU Jun², LIU Wen³

1. School of Natural Sciences, Wuhan University of Technology, Wuhan Hubei 430070, China;
2. School of Mathematics and Statistics, Northeast Normal University, Changchun Jilin 130024, China;
3. School of Navigation, Wuhan University of Technology, Wuhan Hubei 430063, China

Received:2020-08-31 Revised:2020-10-26 Online:2021-07-10 Published:2020-12-29
Supported by:
This work is partially supported by the National Natural Science Foundation of China (51609195, 11701079).

摘要/Abstract

摘要： 针对纹理图像在平滑过程中低对比度边缘易丢失和纹理细节抑制不彻底等问题，提出基于梯度曲面面积与稀疏约束的图像平滑方法。首先，将图像视作三维空间中的二维嵌入曲面，再在此基础上分析图像的几何特征并提出梯度曲面面积约束正则化项，以提高纹理抑制性能；其次，根据图像的统计特性，建立L₀梯度稀疏与自适应梯度曲面面积约束的混合正则化约束图像平滑模型；最后，采用交替方向乘子法对非凸非光滑的优化模型进行高效求解。通过纹理抑制、边缘检测、纹理增强和图像融合等方面的实验结果可知，所提出的图像平滑算法克服了L₀梯度最小化平滑方法易造成的阶梯效应和欠滤波等缺陷，能够在去除大量纹理信息的同时保持并锐化图像显著的边缘轮廓。

关键词: 图像平滑, 自适应梯度曲面面积约束, 纹理抑制, 边缘保持, 交替方向乘子法

Abstract: Concerning the problems of easy loss of low-contrast edges and incomplete suppression of texture details during texture image smoothing, an image smoothing method based on gradient surface area and sparsity constraints was proposed. Firstly, the image was regarded as a two-dimensional embedded surface in three-dimensional space. On this basis, geometric characteristics of the image were analyzed and the regularization term of the gradient surface area constraint was proposed, which improves the texture suppression performance. Secondly, based on the statistical characteristics of the image, a hybrid regularization constrained image smoothing model with L₀ gradient sparseness and adaptive gradient surface area constraints was established. At last, the alternating direction multiplier method was used to solve the non-convex non-smooth optimization model efficiently. The experimental results in texture suppression, edge detection, texture enhancement and image fusion show that the proposed algorithm overcomes the defects of L₀ gradient minimization smoothing method, such as staircase effect and insufficient filtering, and is able to maintain and sharpen the significant edge contours of the image while removing a large amount of texture information.

Key words: image smoothing, adaptive gradient surface area constraint, texture suppression, edge-preserving, alternating direction multiplier method

中图分类号:

TP391.41

李辉, 吴传生, 刘俊, 刘文. 基于梯度曲面面积与稀疏约束的图像平滑方法[J]. 计算机应用, 2021, 41(7): 2039-2047.

LI Hui, WU Chuansheng, LIU Jun, LIU Wen. Image smoothing method based on gradient surface area and sparsity constraints[J]. Journal of Computer Applications, 2021, 41(7): 2039-2047.

参考文献

[1] HE K, SUN J, TANG X. Guided image filtering[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,2013, 35(6):1397-1409.
[2] FATTAL R, AGRAWALA M, RUSINKIEWICZ S. Multiscale shape and detail enhancement from multi-light image collections[J]. ACM Transactions on Graphics,2007,26(3):No. 51-es.
[3] SUN Y,SCHAEFER S,WANG W. Image structure retrieval via L0 minimization[J]. IEEE Transactions on Visualization and Computer Graphics,2018,24(7):2129-2139.
[4] KIM B K,PARK R H,CHANG S. Tone mapping with contrast preservation and lightness correction in high dynamic range imaging[J]. Signal Image and Video Processing,2016,10(8):1425-1432.
[5] XU L,LU C,XU Y,et al. Image smoothing via L₀ gradient minimization[J]. ACM Transactions on Graphics,2011,30(6):No. 174.
[6] PERONA P, MALIK J. Scale-space and edge detection using anisotropic diffusion[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,1990,12(7):629-639.
[7] TOMASI C,MANDUCHI R. Bilateral filtering for gray and color images[C]//Proceedings of the 6th International Conference on Computer Vision. Piscataway:IEEE,1998:839-846.
[8] CHO H,LEE H,KANG H,et al. Bilateral texture filtering[J]. ACM Transactions on Graphics,2014,33(4):No. 128.
[9] ZHANG Q,SHEN X,XU L,et al. Rolling guidance filter[C]//Proceedings of the 2014 European Conference on Computer Vision, LNCS 8691. Cham:Springer,2014:815-830.
[10] KOU F,CHEN W,WEN C,et al. Gradient domain guided image filtering[J]. IEEE Transactions on Image Processing,2015,24(11):4528-4539.
[11] GUO X J,LI Y,MA J Y,et al. Mutually guided image filtering[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,2020,42(3):694-707.
[12] YOSHIMURA K,XIN Y,XIE N,et al. Structure-tensor-based anisotropic rolling filter for image smoothing[C]//Proceedings of the 2019 International Workshop on Advanced Image Technology, SPIE 11049. Bellingham,WA:SPIE,2019:No. 1104904.
[13] OCHOTORENA C N, YAMASHITA Y. Anisotropic guided filtering[J]. IEEE Transactions on Image Processing,2020,29:1397-1412.
[14] RUDIN L I,OSHER S,FATEMI E. Nonlinear total variation based noise removal algorithms[J]. Physica D:Nonlinear Phenomena,1992,60(1/2/3/4):259-268.
[15] FARBMAN Z, FATTAL R, LISCHINSKI D, et al. Edgepreserving decompositions for multi-scale tone and detail manipulation[J]. ACM Transactions on Graphics,2008,27(3):No. 67.
[16] CHENG X,ZENG M,LIU X. Feature-preserving filtering with L₀ gradient minimization[J]. Computers and Graphics,2014,38:150-157.
[17] XU L,YAN Q,XIA Y,et al. Structure extraction from texture via relative total variation[J]. ACM Transactions on Graphics,2012, 31(6):No. 139.
[18] LIU Q,XIONG B,YANG D,et al. A generalized relative total variation method for image smoothing[J]. Multimedia Tools and Applications,2016,75(13):7909-7930.
[19] LIU J,YAN M,ZENG J,et al. Image smoothing via gradient sparsity and surface area minimization[C]//Proceedings of the 2019 IEEE International Conference on Image Processing. Piscataway:IEEE,2019:1114-1118.
[20] XU L,REN J,YAN Q,et al. Deep edge-aware filters[C]//Proceedings of the 32nd International Conference on Machine Learning. New York:JMLR. org,2015:1669-1678.
[21] LIU S,PAN J,YANG M H. Learning recursive filters for lowlevel vision via a hybrid neural network[C]//Proceedings of the 2016 European Conference on Computer Vision,LNCS 9908. Cham:Springer,2016:560-576.
[22] WU H,ZHENG S,ZHANG J,et al. Fast end-to-end trainable guided filter[C]//Proceedings of the 2018 IEEE/CVF Conference on Computer Vision and Pattern Recognition. Piscataway:IEEE, 2018:1838-1847.
[23] FANG X, WANG M, SHAMIR A, et al. Learning explicit smoothing kernels for joint image filtering[J]. Computer Graphics Forum,2019,38(7):181-190.
[24] LI Y,HUANG J B,AHUJA N,et al. Joint image filtering with deep convolutional networks[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence,2019,41(8):1909-1923.
[25] 许建楼, 冯象初, 郝岩. 自适应二阶总广义变分图像恢复方法[J]. 光电子·激光,2013,24(2):378-383.(XU J L,FENG X C,HAO Y. Image restoration method with adaptive second order total generalized variation[J]. Journal of Optoelectronics·Laser, 2013,24(2):378-383.)
[26] 钟秋祥, 吴传生, 刘文. 含脉冲噪声模糊图像复原的自适应二阶变分模型[J]. 计算机应用研究,2018,35(10):3158-3163. (ZHONG Q X, WU C S, LIU W. Adaptive second-order variational model for restoring blurred images with impulse noise[J]. Application Research of Computers,2018,35(10):3158-3163.)
[27] BOYD S,PARIKH N,CHU E,et al. Distributed optimization and statistical learning via the alternating direction method of multipliers[J]. Foundations and Trends in Machine Learning, 2011,3(1):1-122.
[28] DONG B,ZHANG Y. An efficient algorithm for ℓ0 minimization in wavelet frame based image restoration[J]. Journal of Scientific Computing,2013,54(2/3):350-368.
[29] CHAMBOLLE A,DOSSAL C. On the convergence of the iterates of the "Fast Iterative Shrinkage/Thresholding Algorithm"[J]. Journal of Optimization Theory and Applications,2015,166(3):968-982.
[30] XIONG N,LIU R W,LIANG M,et al. Effective alternating direction optimization methods for sparsity-constrained blind image deblurring[J]. Sensors,2017,17(1):No. 174.
[31] GUO X,LI S,LI L,et al. Structure-texture decomposition via joint structure discovery and texture smoothing[C]//Proceedings of the 2018 IEEE International Conference on Multimedia and Expo. Piscataway:IEEE,2018:1-6.

基于梯度曲面面积与稀疏约束的图像平滑方法

Image smoothing method based on gradient surface area and sparsity constraints

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 12

编辑推荐

Metrics

[1]	陈利霞, 班颖, 王学文. 基于张量核范数与3D全变分的背景减除[J]. 计算机应用, 2020, 40(9): 2737-2742.
[2]	沈马锐, 李金城, 张亚, 邹健. 基于非凸全变差正则的核磁共振图像重构算法[J]. 计算机应用, 2020, 40(8): 2358-2364.
[3]	耿源谦, 吴传生, 刘文. 混合非凸非光滑正则化约束的模糊图像盲复原[J]. 计算机应用, 2020, 40(4): 1171-1176.
[4]	龙鹏, 鲁华祥. LoG边缘算子改进的加权引导滤波算法[J]. 计算机应用, 2015, 35(9): 2661-2665.
[5]	许浩锋, 凌青. 分布式在线交替方向乘子法[J]. 计算机应用, 2015, 35(6): 1595-1599.
[6]	高乾坤王玉军王惊晓. 基于交替方向乘子法的非光滑损失坐标优化算法[J]. 计算机应用, 2013, 33(07): 1912-1916.
[7]	丁静. M-估计耦合双边滤波的正则化超分辨率重建[J]. 计算机应用, 2010, 30(11): 3005-3007.
[8]	丛维郭定辉. 用于图像去噪的改进型非线性扩散方程[J]. 计算机应用, 2008, 28(7): 1764-1765.
[9]	熊保平杜民. 基于PDE图像去噪方法[J]. 计算机应用, 2007, 27(8): 2025-2026.
[10]	caojiannong 孙承志 . 图像分割中区域灰度重叠问题研究[J]. 计算机应用, 2006, 26(9): 2077-2080.
[11]	王勋毕笃彦 . 一种变分自适应中值滤波算法[J]. 计算机应用, 2006, 26(9): 2059-2062.
[12]	党向盈吴锡生赵勇 . 基于边缘最大相关性的快速图像插值算法[J]. 计算机应用, 2006, 26(12): 2880-2883.