图像多尺度几何分析域隐马尔可夫树模型研究进展

doi:10.12263/DZXB.20200821

电子学报 ›› 2022, Vol. 50 ›› Issue (1): 238-249.DOI: 10.12263/DZXB.20200821

图像多尺度几何分析域隐马尔可夫树模型研究进展

王相海¹^,², 宋若曦¹, 曲思洁³, 穆振华¹, 宋传鸣²

^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

收稿日期:2020-08-03 修回日期:2020-10-29 出版日期:2022-01-25 发布日期:2022-01-25
作者简介:王相海男，1965年1月出生于吉林省汪清县.现为辽宁师范大学计算机与信息技术学院、地理科学学院教授、博士生导师.主要研究方向为多媒体信息处及遥感影像处理. E-mail:xhwang@lnnu.edu.cn
宋若曦女，1994年12月出生于内蒙古自治区通辽市.现为辽宁师范大学地理科学学院地图学与地理信息系统专业博士研究生.主要研究方向为高光谱影像处理. E-mail:srxlnnu@outlook.com
基金资助:
国家自然科学基金(41971388);辽宁省高等学校创新团队支持计划(LT2017013)

Advance in Multiscale Geometric Analysis Image Hidden Markov Tree Model

WANG Xiang-hai¹^,², SONG Ruo-xi¹, QU Si-jie³, MU Zhen-hua¹, SONG Chuan-ming²

^1.School of Geography，Liaoning Normal University，Dalian，Liaoning 116029，China
^2.School of Computer and Information Technology，Liaoning Normal University，Dalian，Liaoning 116081，China
^3.School of Mathematics，Liaoning Normal University，Dalian，Liaoning 116029，China

Received:2020-08-03 Revised:2020-10-29 Online:2022-01-25 Published:2022-01-25

摘要/Abstract

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.

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

Abstract:

Multiscale geometric analysis(MGA) provides a better representation for the high dimensional singular feature of images, which provides a better support for capturing the multidirectional edges and textures of the image. The image hidden Markov tree(HMT) model can efficiently depict the statistical properties of the image multiscale transform coefficients 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 summarized. Guided by these issues, the research progress of the MGA-HMT has been further studied. Finally, the future development of the MGA-HMT is prospected.

Key words: multiscale geometric analysis, hidden Markov model, image statistical modeling, probability graph model, research advance

中图分类号:

TP391

王相海, 宋若曦, 曲思洁, 穆振华, 宋传鸣. 图像多尺度几何分析域隐马尔可夫树模型研究进展[J]. 电子学报, 2022, 50(1): 238-249.

WANG Xiang-hai, SONG Ruo-xi, QU Si-jie, MU Zhen-hua, SONG Chuan-ming. Advance in Multiscale Geometric Analysis Image Hidden Markov Tree Model[J]. Acta Electronica Sinica, 2022, 50(1): 238-249.

图/表 10

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	Lena	Finger	Land
Original image
Horizontal
Vertical
Diagonal

	Lena	Finger	Land
Original image
Horizontal
Vertical
Diagonal

变换域	树形结构	传递关系
Wavelet^［11］	四叉树	父子传递，同方向，同位置
Bandelet^［15］	四叉树	父子传递，同方向，同位置
Directionlet^［36］	八叉树	父子传递，同方向，同位置
Curvelet^［25］	四叉树	父子传递，同方向，同位置
Contourlet^［35］	多为四叉树，可自由选择	父子传递，也可刻画不同方向，不同位置
NSCT^［16］	多为二叉树，可自由选择	父子传递，也可刻画不同方向，不同位置
Shearlet^［37］	多为四叉树，可自由选择	父子传递，也可刻画不同方向，不同位置
NSST^［38］	多为二叉树，可自由选择	父子传递，也可刻画不同方向，不同位置

变换域	树形结构	传递关系
Wavelet^［11］	四叉树	父子传递，同方向，同位置
Bandelet^［15］	四叉树	父子传递，同方向，同位置
Directionlet^［36］	八叉树	父子传递，同方向，同位置
Curvelet^［25］	四叉树	父子传递，同方向，同位置
Contourlet^［35］	多为四叉树，可自由选择	父子传递，也可刻画不同方向，不同位置
NSCT^［16］	多为二叉树，可自由选择	父子传递，也可刻画不同方向，不同位置
Shearlet^［37］	多为四叉树，可自由选择	父子传递，也可刻画不同方向，不同位置
NSST^［38］	多为二叉树，可自由选择	父子传递，也可刻画不同方向，不同位置

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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

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