Image smoothing method based on gradient surface area and sparsity constraints

doi:10.11772/j.issn.1001-9081.2020081325

Journal of Computer Applications ›› 2021, Vol. 41 ›› Issue (7): 2039-2047.DOI: 10.11772/j.issn.1001-9081.2020081325

Special Issue: 多媒体计算与计算机仿真

• Multimedia computing and computer simulation • Previous Articles Next Articles

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).

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

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）。

Abstract

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

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

CLC Number:

TP391.41

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.

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.

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Image smoothing method based on gradient surface area and sparsity constraints

基于梯度曲面面积与稀疏约束的图像平滑方法

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