图像多尺度几何分析域隐马尔可夫树模型研究进展  

Advance in Multiscale Geometric Analysis Image Hidden Markov Tree Model

作　　者：王相海[1,2] 宋若曦 曲思洁 穆振华 宋传鸣[2] WANG Xiang-hai;SONG Ruo-xi;QU Si-jie;MU Zhen-hua;SONG Chuan-ming(School of Geography,Liaoning Normal University,Dalian,Liaoning 116029,China;School of Computer and Information Technology,Liaoning Normal University,Dalian,Liaoning 116081,China;School of Mathematics,Liaoning Normal University,Dalian,Liaoning 116029,China)

机构地区：[1]辽宁师范大学地理科学学院,辽宁大连116029 [2]辽宁师范大学计算机科学与信息技术学院,辽宁大连116081 [3]辽宁师范大学数学学院,辽宁大连116029

出　　处：《电子学报》2022年第1期238-249,共12页Acta Electronica Sinica

基　　金：国家自然科学基金(No.41971388,No.41671439);辽宁省高等学校创新团队支持计划(No.LT2017013)。

摘　　要：多尺度几何分析(Multiscale Geometric Analysis,MGA)为图像的高维奇异特性提供了一种更优、更稀疏的表示方法,从而为更好地捕捉图像中的多方向边缘和纹理特性提供了有效的支撑.图像MGA域隐马尔可夫树模型(Hidden Markov Tree,HMT)成功地对图像多尺度变换系数的统计特性及系数间的相关性进行刻画,为进一步挖掘图像更深层次特性提供了重要途径,在很大程度上提升了MGA在图像处理领域的有效性.本文对图像MGA域HMT模型的研究进展进行综述.先对传统MGA域HMT模型的发展进行分析和讨论,对其构建的一般过程进行了形式化描述;在此基础上,归纳了传统MGA域HMT模型存在的一些关键问题,并以此为导向对MGA变换域HMT模型的研究进展进行了分析和讨论;最后对MGA域HMT模型未来的发展情况进行了展望.Multiscale geometric analysis(MGA)provides a better representation for the high dimensional singular fea⁃ture of images,which provides a better support for capturing the multidirectional edges and textures of the image.The im⁃age hidden Markov tree(HMT)model can efficiently depict the statistical properties of the image multiscale transform coef⁃ficients and the correlation among them,which helps to further utilizing the deep features of the image.The success of MGA-HMT greatly improved the effectiveness of MGA in the field of image processing.This paper reviews the research progress of MGA-HMT model.Firstly,the development of the traditional MGA-HMT model is analyzed and discussed,the general process of its construction is defined.Based on this,some key issues of the traditional MGA-HMT model are sum⁃marized.Guided by these issues,the research progress of the MGA-HMT has been further studied.Finally,the future devel⁃opment of the MGA-HMT is prospected.

关 键 词：多尺度几何分析 隐马尔可夫模型 图像统计建模 概率图模型 研究进展 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]