Advance in Multiscale Geometric Analysis Image Hidden Markov Tree Model

WANG Xiang-hai; SONG Ruo-xi; QU Si-jie; MU Zhen-hua; SONG Chuan-ming

doi:10.12263/DZXB.20200821

您当前的位置：

首页 >

文章列表页 >

Advance in Multiscale Geometric Analysis Image Hidden Markov Tree Model

SURVEYS AND REVIEWS | 更新时间：2025-12-08

- Advance in Multiscale Geometric Analysis Image Hidden Markov Tree Model
- ACTA ELECTRONICA SINICA Vol. 50, Issue 1, Pages: 238-249(2022)
- 作者机构：
  
  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
- 作者简介：
- 基金信息：
- DOI：10.12263/DZXB.20200821
  CLC： TP391;
- Received：03 August 2020，
  
  Revised：2020-10-29，
  
  Published：25 January 2022
- 稿件说明：
移动端阅览
王相海,宋若曦,曲思洁等.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(01):238-249.

WANG Xiang-hai,SONG Ruo-xi,QU Si-jie,et al.Advance in Multiscale Geometric Analysis Image Hidden Markov Tree Model[J].ACTA ELECTRONICA SINICA,2022,50(01):238-249.
王相海,宋若曦,曲思洁等.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(01):238-249. DOI： 10.12263/DZXB.20200821.

WANG Xiang-hai,SONG Ruo-xi,QU Si-jie,et al.Advance in Multiscale Geometric Analysis Image Hidden Markov Tree Model[J].ACTA ELECTRONICA SINICA,2022,50(01):238-249. DOI： 10.12263/DZXB.20200821.

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.

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.

关键词

Keywords

references

焦李成 . 图像多尺度几何分析理论与应用 [M]. 西安 : 西安电子科技大学出版社 , 2008 .

SINGH R , NIGAM S , SINGH A K , et al . Wavelet Transforms: From Classical to New Generation Wavelets [M]. Cham, GER : Springer , 2018 .

VYAS A , YU S , PAIK J . Multiscale Transforms with Application to Image Processing [M]. Singapore, Singapore : Springer Singapore , 2018 .

宋传鸣 , 赵长伟 , 刘丹 , 等 . 3D多尺度几何分析研究进展 [J]. 软件学报 , 2015 , 26 ( 5 ): 1213 - 1236 .

SONG C M , ZHAO C W , LIU D , et al . Advances in three-dimensional multiscale geometrical analysis [J]. Journal of Software , 2015 , 26 ( 5 ): 1213 - 1236 . (in Chinese)

CANDES E J . Ridgelets: theory and applications [EB/OL]. [2020] . https : // stat .uw.edu / seminars / ridgelets - theory - and - applications.

LE PENNEC E , MALLAT S . Bandelet image approximation and compression [J]. Multiscale Modeling & Simulation , 2005 , 4 ( 3 ): 992 - 1039 .

CANDÈS E J , DONOHO D L . Curvelets and curvilinear integrals [J]. Journal of Approximation Theory , 2001 , 113 ( 1 ): 59 - 90 .

EASLEY G , LABATE D , LIM W Q . Sparse directional image representations using the discrete shearlet transform [J]. Applied and Computational Harmonic Analysis , 2008 , 25 ( 1 ): 25 - 46 .

DO M N , VETTERLI M . Contourlets: A new directional multiresolution image representation [C]// Conference Record of the Thirty-Sixth Asilomar Conference on Signals, Systems and Computers . Rochester, NY, USA : IEEE , 2002 : 497 - 501 .

VELISAVLJEVIC V , BEFERULL-LOZANO B , VETTERLI M , et al . Directionlets: Anisotropic multidirectional representation with separable filtering [J]. IEEE Transactions on Image Processing , 2006 , 15 ( 7 ): 1916 - 1933 .

CROUSE M S , NOWAK R D , BARANIUK R G . Wavelet-based statistical signal processing using hidden Markov models [J]. IEEE Transactions on Signal Processing , 1998 , 46 ( 4 ): 886 - 902 .

SHAHDOOSTI H R , HAZAVEI S M . Image denoising in dual contourlet domain using hidden Markov tree models [J]. Digital Signal Processing , 2017 , 67 : 17 - 29 .

WANG X H , CHEN M Y , SONG C M , et al . Contourlet HMT model with directional feature [J]. Science China Information Sciences , 2012 , 55 ( 7 ): 1563 - 1578 .

金海燕 , 焦李成 , 刘芳 . 基于Curvelet域隐马尔可夫树模型的SAR图像去噪 [J]. 计算机学报 , 2007 , 30 ( 3 ): 491 - 497 .

JIN H Y , JIAO L C , LIU F . SAR image de-noising based on curvelet domain hidden Markov tree models [J]. Chinese Journal of Computers , 2007 , 30 ( 3 ): 491 - 497 . (in Chinese)

侯彪 , 徐婧 , 刘凤 , 等 . 基于第二代Bandelet域隐马尔可夫树模型的图像分割 [J]. 自动化学报 , 2009 , 35 ( 5 ): 498 - 504 .

HOU B , XU J , LIU F , et al . Image segmentation using second generation bandelet-domain hidden Markov tree models [J]. Acta Automatica Sinica , 2009 , 35 ( 5 ): 498 - 504 . (in Chinese)

王相海 , 倪培根 , 苏欣 , 等 . 非下采样Contourlet HMT模型 [J]. 中国科学: 信息科学 , 2013 , 43 ( 11 ): 1431 - 1444 .

WANG X H , NI P G , SU X , et al . The nonsubsampled Contourlet HMT model [J]. Scientia Sinica (Informationis) , 2013 , 43 ( 11 ): 1431 - 1444 . (in Chinese)

WANG X Y , LIU Y C , YANG H Y . Image denoising in extended Shearlet domain using hidden Markov tree models [J]. Digital Signal Processing , 2014 , 30 : 101 - 113 .

CHEN P Y , ZHANG Y C , JIA Z H , et al . Remote sensing image change detection based on NSCT-HMT model and its application [J]. Sensors , 2017 , 17 ( 6 ): 1295 .

HANZOULI-BEN SALAH H , LAPUYADE-LAHORGUE J , BERT J , et al . A framework based on hidden Markov trees for multimodal PET/CT image co-segmentation [J]. Medical Physics , 2017 , 44 ( 11 ): 5835 - 5848 .

QIAO Y L , ZHAO G C . Modified wavelet domain hidden tree model for texture segmentation [C]// Advanced Multimedia and Ubiquitous Engineering . Singapore, Singapore : Springer, Singapore , 2016 : DOI: 10.1007/978-981-10-1536-6_81 http://dx.doi.org/10.1007/978-981-10-1536-6_81 .

MURINTO , ARIBOWO E . Image segmentation using hidden markov tree methods in recognizing motif of batik [J]. Journal of Theoretical & Applied Information Technology , 2016 , 85 ( 1 ) : 27 - 33 .

EL-TAWEL G S , HELMY A K . An edge detection scheme based on least squares support vector machine in a contourlet HMT domain [J]. Applied Soft Computing , 2015 , 26 : 418 - 427 .

HUANG Z H , XIA L . Images denoising and enhancement based on dyadic wavelet domain hidden Markov models and interpolation [J]. International Journal of Signal Processing, Image Processing and Pattern Recognition , 2015 , 8 ( 9 ): 181 - 188 .

CUI D , LIU M , HU L , et al . The application of wavelet-domain hidden Markov tree model in diabetic retinal image denoising [J]. The Open Biomedical Engineering Journal , 2015 , 9 : 194 - 198 .

HANZOULI H , LAPUYADE-LAHORGUE J , MONFRINI E , et al . PET/CT image denoising and segmentation based on a multi observation and a multi scale Markov tree model [C]// 2013 IEEE Nuclear Science Symposium and Medical Imaging Conference (2013 NSS/MIC) . Seoul, Korea (South) : IEEE , 2013 : 1 - 4 .

HU K , YANG W , GAO X P . Microcalcification diagnosis in digital mammography using extreme learning machine based on hidden Markov tree model of dual-tree complex wavelet transform [J]. Expert Systems With Applications , 2017 , 86 : 135 - 144 .

KARKI R , ALSADOON A , PRASAD P W C , et al . A novel algorithm based on contourlet transform for extracting paint features to determine drawing style and authorship [J]. Indian Journal of Science and Technology , 2017 , 10 ( 12 ): 1 - 11 .

王相海 , 赵晓阳 , 毕晓昀 , 等 . 小波域多角度轮廓模板变分模型的单幅图像超分辨率重建 [J]. 电子学报 , 2018 , 46 ( 9 ): 2256 - 2262 .

WANG X H , ZHAO X Y , BI X Y , et al . Single image super-resolution reconstruction approach based on multi-angle contour templates variational calculus model in wavelet domain [J]. Acta Electronica Sinica , 2018 , 46 ( 9 ): 2256 - 2262 . (in Chinese)

ARGENTI F , BIANCHI T , ALPARONE L . Multiresolution MAP despeckling of SAR images based on locally adaptive generalized Gaussian pdf modeling [J]. IEEE Transactions on Image Processing , 2006 , 15 ( 11 ): 3385 - 3399 .

GAO Q W , LU Y X , SUN D , et al . Directionlet-based denoising of SAR images using a Cauchy model [J]. Signal Processing , 2013 , 93 ( 5 ): 1056 - 1063 .

HILL P R , ACHIM A M , BULL D R , et al . Dual-tree complex wavelet coefficient magnitude modelling using the bivariate Cauchy-Rayleigh distribution for image denoising [J]. Signal Processing , 2014 , 105 : 464 - 472 .

邓磊 . SAR图像处理方法-Contourlet域隐马尔可夫模型的应用 [M]. 北京 : 测绘出版社 , 2009 .

LIU M , WU Y , ZHANG P , et al . SAR target configuration recognition using locality preserving property and Gaussian mixture distribution [J]. IEEE Geoscience and Remote Sensing Letters , 2013 , 10 ( 2 ): 268 - 272 .

KUSHARY D . The EM algorithm and extensions [J]. Technometrics , 1998 , 40 ( 3 ): 260 .

PO D D Y , DO M N . Directional multiscale modeling of images using the contourlet transform [J]. IEEE Transactions on Image Processing , 2006 , 15 ( 6 ): 1610 - 1620 .

JING B , ZHAO J Q , JIAO L . Image segmentation using Directionlet-domain hidden Markov tree models [C]// Proceedings of 2011 IEEE CIE International Conference on Radar . Chengdu, China : IEEE , 2011 : 1615 - 1618 .

SHARMA A , CHUGH S . An efficient shearlet Bayesian network based approach for image denoising [J]. International Journal of Computer Applications , 2015 , 128 ( 10 ): 15 - 20 .

ELTAWEEL G S , HELMY A K . Fusion of multispectral and full polarimetric SAR images in NSST domain [J]. Computer Science Journals , 2014 , 8 ( 6 ) : 497 - 506 .

GOOSSENS B , PIZURICA A , PHILIPS W . Removal of correlated noise by modeling the signal of interest in the wavelet domain [J]. IEEE Transactions on Image Processing , 2009 , 18 ( 6 ): 1153 - 1165 .

WANG X Y , ZHANG N , ZHENG H L , et al . Extended shearlet HMT model-based image denoising using BKF distribution [J]. Journal of Mathematical Imaging and Vision , 2016 , 54 ( 3 ): 301 - 319 .

GONGSIN I E , SAPORU F W O . A bivariate conditional Weibull distribution with application [J]. Afrika Matematika , 2020 , 31 ( 3/4 ): 565 - 583 .

李晓峰 , 徐军 , 罗积军 , 等 . 基于Contourlet域HMT-3S模型的激光主动成像图像分割 [J]. 红外与激光工程 , 2012 , 41 ( 2 ): 531 - 536 .

LI X F , XU J , LUO J J , et al . Laser active image segmentation based on Contourlet-domain hidden Markov trees-3S model [J]. Infrared and Laser Engineering , 2012 , 41 ( 2 ): 531 - 536 . (in Chinese)

王相海 , 赵晓阳 , 朱毅欢 , 等 . 系数多状态关联的图像NSST-HMT模型 [J]. 中国科学: 信息科学 , 2019 , 49 ( 6 ): 708 - 725 .

WANG X H , ZHAO X Y , ZHU Y H , et al . Image NSST-HMT model with associated multi-state coefficients [J]. Scientia Sinica (Informationis) , 2019 , 49 ( 6 ): 708 - 725 . (in Chinese)

肖志云 , 文伟 , 彭思龙 . 小波域HMT模型参数的快速估计及其在图像降噪中的应用 [J]. 计算机应用 , 2004 , 24 ( 12 ): 7 - 10 .

XIAO Z Y , WEN W , PENG S L . Fast estimation of parameter in wavelet-domain HMT model and its application in image denoising [J]. Computer Applications , 2004 , 24 ( 12 ): 7 - 10 . (in Chinese)

YAN F X , PENG S L , CHENG L Z . Dual-tree complex wavelet hidden Markov tree model for image denoising [J]. Electronics Letters , 2007 , 43 ( 18 ): 973 .

WANG X H , MU Z H , SONG R X , et al . A hyperspectral image NSST-HMF model and its application in HS-pansharpening [J]. IEEE Transactions on Geoscience and Remote Sensing , 2020 , 58 ( 7 ): 4803 - 4817 .

YE W , ZHAO J H , WANG S , et al . Dynamic texture based smoke detection using Surfacelet transform and HMT model [J]. Fire Safety Journal , 2015 , 73 : 91 - 101 .

SAHU S M , SINGH H V , KUMAR B , et al . De-noising of ultrasound image using Bayesian approached heavy-tailed Cauchy distribution [J]. Multimedia Tools and Applications , 2019 , 78 ( 4 ): 4089 - 4106 .

MENG H , WANG K , GAO Y , et al . Adaptive Gaussian weighted Laplace prior regularization enables accurate morphological reconstruction in fluorescence molecular tomography [J]. IEEE Transactions on Medical Imaging , 2019 , 38 ( 12 ): 2726 - 2734 .

WANG X H , SONG R X , SONG C M , et al . The NSCT-HMT model of remote sensing image based on Gaussian-cauchy mixture distribution [J]. IEEE Access , 2018 , 6 : 66007 - 66019 .

SADEGHIGOL Z , KAHAEI M H , HADDADI F . Generalized beta Bayesian compressive sensing model for signal reconstruction [J]. Digital Signal Processing , 2017 , 60 : 163 - 171 .

QIAO Y L , ZHAO G C . Texture segmentation using Laplace distribution-based wavelet-domain hidden Markov tree models [J]. Entropy , 2016 , 18 ( 11 ): 384 .

张骥祥 . 小波变换和马尔可夫随机场在图像处理中的应用研究 [D]. 天津 : 天津大学 , 2007 .

ZHANG J X . Research on the Application of Wavelet Transform and Markov Random Field to Image Processing [D]. Tianjin, China : Tianjin University , 2007 . (in Chinese)

FAN G L , XIA X G . Wavelet-based texture analysis and synthesis using hidden Markov models [J]. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications , 2003 , 50 ( 1 ): 106 - 120 .

侯彪 , 翟艳霞 , 焦李成 . 用于SAR图像分割的第二代Bandelet域HMT-3S模型 [J]. 红外与毫米波学报 , 2010 , 29 ( 2 ): 145 - 149 .

HOU B , ZHAI Y X , JIAO L C . Second generation bandelet-domain hidden Markov tree-3s model for sar image segmentation [J]. Journal of Infrared and Millimeter Waves , 2010 , 29 ( 2 ): 145 - 149 . (in Chinese)

WANG X H , SONG R X , MU Z H , et al . An image NSCT-HMT model based on copula entropy multivariate Gaussian scale mixtures [J]. Knowledge-Based Systems , 2020 , 193 : 105387 .

MEILIJSON I . A fast improvement to the em algorithm on its own terms [J]. Journal of the Royal Statistical Society: Series B (Methodological) , 1989 , 51 ( 1 ): 127 - 138 .

ZHANG Q , WANG L , MA Z K , et al . A novel video fusion framework using surfacelet transform [J]. Optics Communications , 2012 , 285 ( 13/14 ): 3032 - 3041 .

LATIF G , BUTT M M , KHAN A H , et al . Multiclass brain Glioma tumor classification using block-based 3D Wavelet features of MR images [A]. 2017 4th International Conference on Electrical and Electronic Engineering (ICEEE) [C]. Ankara, Turkey : IEEE , 2017 : 333 - 337 .

GUO K H , LABATE D . Analysis and detection of surface discontinuities using the 3D continuous shearlet transform [J]. Applied and Computational Harmonic Analysis , 2011 , 30 ( 2 ): 231 - 242 .

ZHU X X , TUIA D , MOU L C , et al . Deep learning in remote sensing: A comprehensive review and list of resources [J]. IEEE Geoscience and Remote Sensing Magazine , 2017 , 5 ( 4 ): 8 - 36 .

LIU Y , CHEN X , WANG Z F , et al . Deep learning for pixel-level image fusion: Recent advances and future prospects [J]. Information Fusion , 2018 , 42 : 158 - 173 .

ALKAWAZ M H , SEONG C C , RAZALLI H . Handwriting detection and recognition improvements based on hidden Markov model and deep learning [C]// 2020 16th IEEE International Colloquium on Signal Processing & Its Applications (CSPA) . Langkawi, Malaysia : IEEE , 2020 : 106 - 110 .

KASUGAI T , TSUZUKI Y , SAWADA K , et al . Image recognition based on convolutional neural networks using features generated from separable lattice hidden Markov models [C]// 2018 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference (APSIPA ASC) . Honolulu, HI, USA : IEEE , 2018 : 324 - 328 .

宋瑞霞 , 李成华 , 王小春 , 等 . V-系统的小波函数的数学结构 [J]. 中国科学: 数学 , 2016 , 46 ( 6 ): 867 - 876 .

SONG R X , LI C H , WANG X C , et al . Mathematical structure of wavelet functions of the V-system [J]. Scientia Sinica (Mathematica) , 2016 , 46 ( 6 ): 867 - 876 . (in Chinese)

宋瑞霞 , 孙坦坦 , 孙相东 , 等 . 广义V-系统的构造及相应的快速变换 [J]. 计算机辅助设计与图形学学报 , 2018 , 30 ( 5 ): 808 - 815 .

SONG R X , SUN T T , SUN X D , et al . The construction of generalized V-system and the corresponding fast transformation [J]. Journal of Computer-Aided Design & Computer Graphics , 2018 , 30 ( 5 ): 808 - 815 . (in Chinese)

MALAFRONTE D , VITO E , ODONE F . Space-time signal analysis and the 3D shearlet transform [J]. Journal of Mathematical Imaging and Vision , 2018 , 60 ( 7 ): 1008 - 1024 .

LI Z Y , BORS A G . Steganalysis of meshes based on 3D wavelet multiresolution analysis [J]. Information Sciences , 2020 , 522 : 164 - 179 .

Views

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

Regionalized Decision Algorithm for Human-Machine Shared Control Based on Gaussian Hidden Markov Model

Research on Time-Serial Location Data Publication Based on Local Differential Privacy

EM-HMM Multiple Frequency Line Tracking Algorithm

Online Energy Adjustment Using AR-HMM for Speech Enhancement

Development and Prospect of Image Multiscale Geometric Analysis

Related Author

LIU Yang

SU Wei-xing

LIU Fang

ZHU Tian-he

KANG Hai-yan

JI Yuan-rui

LI Huan-run

WANG Jia-ding

Related Institution

Tianjin Key Laboratory of Autonomous Intelligence Technology and Systems, Tiangong University

BBT-E-6 Complete Vehicle, BMW Brilliance Automotive Ltd.

School of Information Management, Beijing Information Science and Technology University

Dept.of Computer ScienceShanghai UniversityShanghai 200072China

Dept.of AutomationShanghai UniversityShanghai 200072China

⁰