基于图像分解和相对全变分的图像平滑  

Image smoothing based on image decomposition and relative total variation

作　　者：刘业朋 杨得志 李思远 张帆 张彩明 LIU Ye-peng;YANG De-zhi;LI Si-yuan;ZHANG Fan;ZHANG Cai-ming(School of Computer Science and Technology,Shandong Technology and Business University,Yantai Shandong 264005,China;School of Software,Shandong University,Jinan Shandong 250101,China;Shandong Provincial Key Laboratory of Digital Media Technology,Shandong University of Finance and Economics,Jinan Shandong 250014,China)

机构地区：[1]山东工商学院计算机科学与技术学院,山东烟台264005 [2]山东大学软件学院,山东济南250101 [3]山东财经大学数字媒体重点实验室,山东济南250014

出　　处：《图学学报》2022年第6期1143-1149,共7页Journal of Graphics

基　　金：国家自然科学基金项目(62002200,62202268);山东省自然科学基金项目(ZR2020QF012,ZR2021QF134,ZR2021MF107);山东省高等学校青创科技支持计划创新团队(2021KJ069)。

摘　　要：图像平滑旨在去除图像中纹理细节信息的同时保留重要的结构边缘,因此如何正确区分二者成了图像平滑的关键。梯度作为计算图像变化速度的重要指标是区分结构边缘和纹理细节的有效度量,但不同图像以及同一图像不同区域中的纹理和边缘的梯度差异并非固定不变的。为了能够有效识别结构边缘和纹理细节,提出了基于图像分解和相对全变分的图像平滑方法。为了扩大结构边缘和纹理细节之间的差异,实现在尽可能不改变结构边缘的前提下降低纹理细节的梯度,以多方向的梯度为约束对图像进行分解,提取图像的平滑成分。在特定尺度下,基于图像的区域结构差异,采用相对全变分方法,在保留结构边缘的同时去除该尺度下的纹理细节。通过迭代优化,不断调整图像区域尺度,实现对不同尺度纹理细节的逐步去除。与现有算法相比,新方法在有效地去除纹理细节和完整地保留结构边缘方面都具有较好的视觉效果。The purpose of image smoothing is to process the image through certain technical methods, so as to remove the texture details in the image while preserving the important structural edges. Therefore, how to distinguish the two correctly has become the key to image smoothing. Gradients, as an important index for calculating the speed of image change, are an effective measure to distinguish the structural edges and texture details. However, the gradient difference between texture details and structural edges in different images or different regions of the same image is not fixed. In order to effectively distinguish structural edges and texture details based on gradients, an image smoothing method was proposed based on image decomposition and relative total variation. To expand the difference between the structural edges and texture details, the gradients of texture details were reduced without changing the gradients of structural edges as much as possible. The image was decomposed in frequency domain under the constraint of multi-directional gradient, and then the smooth components of the decomposed image were extracted. Next, for the smooth component of the input image, at the specific scale, based on the structural differences of a specific size region of the image, the relative total variation method was employed to remove the texture details at this scale while preserving the structure edges. Finally, through iterative optimization, the size of the image region was continuously adjusted to gradually remove texture details of different scales. Compared with the existing algorithms, the new method could attain better visual effects in effectively removing the texture details and completely preserving the structure edges.

关 键 词：图像分解 相对全变分 多尺度 梯度约束 图像平滑 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]