电子学报 ›› 2022, Vol. 50 ›› Issue (1): 238-249.DOI: 10.12263/DZXB.20200821
王相海1,2, 宋若曦1, 曲思洁3, 穆振华1, 宋传鸣2
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:
基金资助:
WANG Xiang-hai1,2, SONG Ruo-xi1, QU Si-jie3, MU Zhen-hua1, SONG Chuan-ming2
Received:
2020-08-03
Revised:
2020-10-29
Online:
2022-01-25
Published:
2022-01-25
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.
中图分类号:
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.
Lena | Finger | Land | |
---|---|---|---|
Original image | ![]() | ![]() | ![]() |
Horizontal | ![]() | ![]() | ![]() |
Vertical | ![]() | ![]() | ![]() |
Diagonal | ![]() | ![]() | ![]() |
表1 图像Wavelet方向子带直方图统计
Lena | Finger | Land | |
---|---|---|---|
Original image | ![]() | ![]() | ![]() |
Horizontal | ![]() | ![]() | ![]() |
Vertical | ![]() | ![]() | ![]() |
Diagonal | ![]() | ![]() | ![]() |
变换域 | 树形结构 | 传递关系 |
---|---|---|
Wavelet[ | 四叉树 | 父子传递, 同方向, 同位置 |
Bandelet[ | 四叉树 | 父子传递, 同方向, 同位置 |
Directionlet[ | 八叉树 | 父子传递, 同方向, 同位置 |
Curvelet[ | 四叉树 | 父子传递, 同方向, 同位置 |
Contourlet[ | 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[ | 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[ | 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[ | 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 |
表2 经典MGA-HMT 系数传递关系
变换域 | 树形结构 | 传递关系 |
---|---|---|
Wavelet[ | 四叉树 | 父子传递, 同方向, 同位置 |
Bandelet[ | 四叉树 | 父子传递, 同方向, 同位置 |
Directionlet[ | 八叉树 | 父子传递, 同方向, 同位置 |
Curvelet[ | 四叉树 | 父子传递, 同方向, 同位置 |
Contourlet[ | 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[ | 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[ | 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[ | 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 |
1 | 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. |
2 | SINGH R, NIGAM S, SINGH A K, et al. Wavelet Transforms: From Classical to New Generation Wavelets[M]. Cham, GER: Springer, 2018. |
3 | VYAS A, YU S, PAIK J. Multiscale Transforms with Application to Image Processing[M]. Singapore, Singapore: Springer Singapore, 2018. |
4 | 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) | |
5 | CANDES E J. Ridgelets: theory and applications[EB/OL]. [2020]. https : // stat.uw.edu / seminars / ridgelets - theory - and - applications. |
6 | LE PENNEC E, MALLAT S. Bandelet image approximation and compression[J]. Multiscale Modeling & Simulation, 2005, 4(3): 992-1039. |
7 | CANDÈS E J, DONOHO D L. Curvelets and curvilinear integrals[J]. Journal of Approximation Theory, 2001, 113(1): 59-90. |
8 | 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. |
9 | 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. |
10 | 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. |
11 | 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. |
12 | 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. |
13 | 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. |
14 | 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) | |
15 | 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) | |
16 | 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) | |
17 | 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. |
18 | 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. |
19 | 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. |
20 | 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 . |
21 | 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. |
22 | 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. |
23 | 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. |
24 | 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. |
25 | 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. |
26 | 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. |
27 | 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. |
28 | 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) | |
29 | 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. |
30 | 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. |
31 | 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. |
32 | 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. |
33 | 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. |
34 | KUSHARY D. The EM algorithm and extensions[J]. Technometrics, 1998, 40(3): 260. |
35 | 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. |
36 | 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. |
37 | 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. |
38 | 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. |
39 | 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. |
40 | 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. |
41 | GONGSIN I E, SAPORU F W O. A bivariate conditional Weibull distribution with application[J]. Afrika Matematika, 2020, 31(3/4): 565-583. |
42 | 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) | |
43 | 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) | |
44 | 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) | |
45 | 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. |
46 | 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. |
47 | 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. |
48 | 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. |
49 | 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. |
50 | 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. |
51 | SADEGHIGOL Z, KAHAEI M H, HADDADI F. Generalized beta Bayesian compressive sensing model for signal reconstruction[J]. Digital Signal Processing, 2017, 60: 163-171. |
52 | QIAO Y L, ZHAO G C. Texture segmentation using Laplace distribution-based wavelet-domain hidden Markov tree models[J]. Entropy, 2016, 18(11): 384. |
53 | 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) | |
54 | 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. |
55 | 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) | |
56 | 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. |
57 | 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. |
58 | 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. |
59 | 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. |
60 | 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. |
61 | 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. |
62 | 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. |
63 | 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. |
64 | 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. |
65 | 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) | |
66 | 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) | |
67 | 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. |
68 | LI Z Y, BORS A G. Steganalysis of meshes based on 3D wavelet multiresolution analysis[J]. Information Sciences, 2020, 522: 164-179. |
[1] | 李淑慧, 邓志红, 冯肖雪, 潘峰. 强杂波背景下基于变分贝叶斯推理的机载雷达目标跟踪算法[J]. 电子学报, 2022, 50(5): 1089-1097. |
[2] | 张明宇, 王琦, 于洋. 基于LSTM-DHMM的MOSFET器件健康状态识别与故障时间预测[J]. 电子学报, 2022, 50(3): 643-651. |
[3] | 王辛, 王晓峰, 李卫民. 一种求解最小割的警示传播算法[J]. 电子学报, 2019, 47(11): 2386-2391. |
[4] | 刘建伟, 黎海恩, 周佳佳, 罗雄麟. 概率图模型的表示理论综述[J]. 电子学报, 2016, 44(5): 1219-1226. |
[5] | 何玉文, 鲍长春, 夏丙寅. 基于AR-HMM在线能量调整的语音增强方法[J]. 电子学报, 2014, 42(10): 1991-1997. |
[6] | 王 超;郭渊博;马建峰;裴庆祺;徐 栋. 基于隐马尔可夫模型的资源滥用行为检测方法研究[J]. 电子学报, 2010, 38(6): 1383-1388. |
[7] | 姜慧研;何 炜. 基于胸部CT图像的肺癌识别方法的研究[J]. 电子学报, 2009, 37(8): 1664-1668. |
[8] | 宋 千;金 添;周智敏. 基于HMM核超球面支持向量机的 超宽带SAR未爆物检测[J]. 电子学报, 2009, 37(7): 1509-1515. |
[9] | 丁 辉;付梦印;王美玲. 基于NSCT的SMP立体匹配算法研究[J]. 电子学报, 2008, 36(4): 772-776. |
[10] | 周顺先;林亚平;王耀南;易叶青. 基于二阶隐马尔可夫模型的文本信息抽取[J]. 电子学报, 2007, 35(11): 2226-2231. |
[11] | 杨晓慧;焦李成;李 伟. 基于第二代bandelets的图像去噪[J]. 电子学报, 2006, 34(11): 2063-2067. |
[12] | 林亚平;刘云中;周顺先;陈治平;蔡立军. 基于最大熵的隐马尔可夫模型文本信息抽取[J]. 电子学报, 2005, 33(2): 236-240. |
[13] | 戴海生;朱小燕;罗予频;杨士元. 一种新的关键词确认方法[J]. 电子学报, 2005, 33(1): 101-105. |
[14] | 李玉. 2维隐马尔可夫模型的基本问题求解[J]. 电子学报, 2004, 32(11): 1833-1838. |
[15] | 焦李成, 谭山. 图像的多尺度几何分析:回顾和展望[J]. 电子学报, 2003, 31(S1): 1975-1981. |
阅读次数 | ||||||
全文 |
|
|||||
摘要 |
|
|||||