{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:11:18Z","timestamp":1760213478373,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2016,11,4]],"date-time":"2016-11-04T00:00:00Z","timestamp":1478217600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61371175"],"award-info":[{"award-number":["61371175"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"publisher","award":["HEUCFQ20150812"],"award-info":[{"award-number":["HEUCFQ20150812"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Multiresolution models such as the wavelet-domain hidden Markov tree (HMT) model provide a powerful approach for image modeling and processing because it captures the key features of the wavelet coefficients of real-world data. It is observed that the Laplace distribution is peakier in the center and has heavier tails compared with the Gaussian distribution. Thus we propose a new HMT model based on the two-state, zero-mean Laplace mixture model (LMM), the LMM-HMT, which provides significantly potential for characterizing real-world textures. By using the HMT segmentation framework, we develop LMM-HMT based segmentation methods for image textures and dynamic textures. The experimental results demonstrate the effectiveness of the introduced model and segmentation methods.<\/jats:p>","DOI":"10.3390\/e18110384","type":"journal-article","created":{"date-parts":[[2016,11,4]],"date-time":"2016-11-04T11:18:38Z","timestamp":1478258318000},"page":"384","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Texture Segmentation Using Laplace Distribution-Based Wavelet-Domain Hidden Markov Tree Models"],"prefix":"10.3390","volume":"18","author":[{"given":"Yulong","family":"Qiao","sequence":"first","affiliation":[{"name":"College of Information and Communication Engineering, Harbin Engineering University, No. 145 Nantong Street, Nangang District, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ganchao","family":"Zhao","sequence":"additional","affiliation":[{"name":"College of Information and Communication Engineering, Harbin Engineering University, No. 145 Nantong Street, Nangang District, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,11,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"326","DOI":"10.1109\/TIP.2012.2210234","article-title":"Automatic dynamic texture segmentation using local descriptors and optical flow","volume":"22","author":"Chen","year":"2013","journal-title":"IEEE Trans. Image Proc."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1109\/LSP.2014.2362613","article-title":"Hidden Markov model based dynamic texture classification","volume":"22","author":"Qiao","year":"2015","journal-title":"IEEE Signal Proc. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1016\/S0167-8655(98)00129-9","article-title":"Texture classification using multiresolution Markov random field models","volume":"20","author":"Wang","year":"1999","journal-title":"Pattern Recognit. Lett."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"762472","DOI":"10.1155\/2013\/762472","article-title":"Wavelet-based dynamic texture classification using Gumbel distribution","volume":"2013","author":"Qiao","year":"2013","journal-title":"Math. Probl. Eng."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"3167","DOI":"10.1109\/TIP.2016.2551365","article-title":"Semi-local scaling exponent estimation with box-penalty constraints and total-variation regularization","volume":"25","author":"Nelson","year":"2016","journal-title":"IEEE Trans. Image Proc."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Pustelnik, N., Wendt, H., Abry, P., and Dobigeon, N. (2015). Combining Local Regularity Estimation and Total Variation Optimization for Scale-Free Texture Segmentation.","DOI":"10.1109\/TCI.2016.2594139"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"898","DOI":"10.1109\/TPAMI.2010.161","article-title":"Contour detection and hierarchical image segmentation","volume":"33","author":"Arbelaez","year":"2011","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3488","DOI":"10.1109\/TIP.2015.2446948","article-title":"Factorization-based texture segmentation","volume":"24","author":"Yuan","year":"2015","journal-title":"IEEE Trans. Image Proc."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Sasidharan, R., and Menaka, D. (2013, January 3\u20135). Dynamic texture segmentation of video using texture descriptors and optical flow of pixels for automating monitoring in different environments. Proceedings of the International Conference on Communication and Signal Processing, Melmaruvathur, India.","DOI":"10.1109\/iccsp.2013.6577175"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"886","DOI":"10.1109\/78.668544","article-title":"Wavelet-based statistical signal processing using hidden Markov models","volume":"46","author":"Crouse","year":"1998","journal-title":"IEEE Trans. Signal Proc."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1056","DOI":"10.1109\/83.931100","article-title":"Bayesian tree-structured image modeling using wavelet-domain hidden Markov models","volume":"10","author":"Romberg","year":"2001","journal-title":"IEEE Trans. Signal Proc."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2551","DOI":"10.1109\/TSP.2004.832006","article-title":"Computational methods for hidden Markov tree models\u2014An application to wavelet trees","volume":"52","author":"Durand","year":"2004","journal-title":"IEEE Trans. Signal Proc."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1309","DOI":"10.1109\/83.941855","article-title":"Multiscale image segmentation using wavelet-domain hidden Markov Models","volume":"10","author":"Choi","year":"2001","journal-title":"IEEE Trans. Signal Proc."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/j.firesaf.2015.03.001","article-title":"Dynamic texture based smoke detection using Surfacelet transform and HMT model","volume":"73","author":"Ye","year":"2015","journal-title":"Fire Saf. J."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1016\/j.asoc.2014.12.023","article-title":"Color image segmentation using PDTDFB domain hidden Markov tree model","volume":"29","author":"Wang","year":"2015","journal-title":"Appl. Soft Comput."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Teodoro, A., Bioucas-Dias, J., and Figueiredo, M. (2016). Image Restoration and Reconstruction Using Variable Splitting and Class-Adapted Image Priors.","DOI":"10.1109\/ICIP.2016.7533014"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Hajri, H., Ilea, I., Said, S., Bombrun, L., and Berthoumieu, Y. (2016). Riemannian Laplace distribution on the space of symmetric positive definite matrices. Entropy, 18.","DOI":"10.3390\/e18030098"},{"key":"ref_18","unstructured":"Nath, V.K., and Mahanta, A. (2011, January 18\u201321). Image denoising based on Laplace distribution with local parameters in Lapped transform domain. Proceedings of the International Conference on Signal Processing and Multimedia Applications, Seville, Spain."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2980","DOI":"10.1109\/TIP.2007.909318","article-title":"Majorization-minimization algorithms for wavelet-based image restoration","volume":"16","author":"Figueiredo","year":"2007","journal-title":"IEEE Trans. Image Proc."},{"key":"ref_20","first-page":"975","article-title":"Some Bayes\u2019 estimators for Laplace distribution under different loss functions","volume":"22","author":"Huda","year":"2014","journal-title":"J. Babylon Univ."},{"key":"ref_21","unstructured":"Bishop, C.M. (2006). Pattern Recognition and Machine Learning, Springer."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/j.2517-6161.1977.tb01600.x","article-title":"Maximum-likelihood from incomplete data via the EM algorithm","volume":"39","author":"Dempster","year":"1977","journal-title":"J. R. Stat. Soc. Ser. B"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Song, X.M., and Fan, G.L. (2003, January 14\u201317). Unsupervised Bayesian image segmentation using wavelet-domain hidden Markov models. Proceedings of the International Conference on Image Processing, Barcelona, Spain.","DOI":"10.1117\/12.507049"},{"key":"ref_24","unstructured":"Brauer, S. (2014). A Probabilistic Expectation Maximization Algorithm for Multivariate Laplacian Mixtures. [Master\u2019s Thesis, Paderborn University]."},{"key":"ref_25","unstructured":"Brodatz, P. (1966). Textures: A Photographic Album for Artists & Designers, Dover."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1627","DOI":"10.1016\/j.patrec.2010.05.009","article-title":"DynTex: A comprehensive database of dynamic textures","volume":"31","author":"Fazekas","year":"2010","journal-title":"Pattern Recognit. Lett."},{"key":"ref_27","unstructured":"The DynTex Database. Available online: http:\/\/dyntex.univ-lr.fr\/index.html."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/18\/11\/384\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:34:43Z","timestamp":1760211283000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/18\/11\/384"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,11,4]]},"references-count":27,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2016,11]]}},"alternative-id":["e18110384"],"URL":"https:\/\/doi.org\/10.3390\/e18110384","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2016,11,4]]}}}