摘要
针对全变分(TV)正则项不利于保持图像拐角及已有分解变分模型中零散度向量函数被忽略的问题,提出一个水平集曲率引导的图像分解模型。首先,分析图像的曲率与梯度的关系,将水平集曲率与低通滤波器结合加入模型正则项。同时,对用于刻画纹理的H^(-1)泛函,保留其忽略的零散度向量函数,给出带零散度向量函数约束的图像分解模型。然后,给出假设模型的算法及求解步骤。最后,用不同的图像在三个变分模型上进行分解实验,并展示了结构、纹理和零散度向量函数的向量场信息。结果表明,该模型能明显提高图像分解效果。
Aiming at the problem that the total variation(TV)regularization term is not conducive to keeping the corner of the image,and the zero divergence vector function is neglected in the existing decomposition variational model,a level set curvature-guided image decomposition model is proposed.Firstly,the relationship between image curvature and gradient is analyzed,and the level set curvature and low-pass filter are combined to add the regularization term of the model.At the same time,for the H^(-1) functional which is used to describe texture,the image decomposition model with the constraint of the divergence-free vector function is designed by keeping the neglected divergence-free vector function.Then,the algorithm and solving steps of the hypothesis model are given.Finally,three variational models are used to decompose different images.Meanwhile,structure,texture and the vector field information of zero divergence-free vector function is presented.The results show that the proposed model can significantly improve the image decomposition effect.
作者
尚婉清
许建楼
郭雨莹
SHANG Wanqing;XU Jianlou;GUO Yuying(School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang Henan 471023, China)
出处
《佳木斯大学学报（自然科学版）》
CAS
2021年第6期155-159,共5页
Journal of Jiamusi University：Natural Science Edition
基金
国家自然科学基金(U1504603)
河南省重点高校基金(18A120002,20A110014)
河南科技大学青年科学基金(2015QN021)。
关键词
水平集曲率
零散度向量
交替方向法
图像分解
level-set curvature
divergence-free vector
alternate direction method
image decomposition
作者简介
尚婉清(1997-),女,硕士,研究方向:图像处理的变分方法、数值优化与深度学习。
