Wavelet-Based Texture Analysis and Synthesis Using Hidden Markov Models

Wavelet-domain hidden Markov models (HMMs), in particular hidden Markov tree (HMT), were recently proposed and applied to image processing, where it was usually assumed that three subbands of the 2-D discrete wavelet transform (DWT), i.e. HL, LH, and HH, are independent. In this paper, we study wavelet-based texture analysis and synthesis using HMMs. Particularly, we develop a new HMM, called HMT-3S, for statistical texture characterization in the wavelet-domain. In addition to the joint statistics captured by HMT, the new HMT-3S can also exploit the crosscorrelation across DWT subbands. Meanwhile, HMT-3S can be characterized by using the graphical grouping technique, and has the same tree structure as HMT. The proposed HMT-3S is applied to texture analysis, including classification and segmentation, and texture synthesis with improved performance over HMT. Specifically, for texture classification, we study four wavelet-based methods, and experimental results show that HMT-3S provides the highest percentage of correct classification of over 95% upon a set of 55 Brodatz textures. For texture segmentation, we demonstrate that more accurate texture characterization from HMT-3S allows the significant improvements in terms of both classification accuracy and boundary localization. For texture synthesis, we develop an iterative maximum likelihood-based texture synthesis algorithm which adopts HMT or HMT-3S to impose the joint statistics of the texture DWT, and it is shown that the new HMT-3S enables more visually similar results than HMT does. Index Terms — Textures analysis, texture synthesis, texture classification, texture segmentation, statistical texture models, wavelet transform, hidden Markov models. Corresponding Author Dr. Xiang-Gen Xia Department of Electrical and Computer Engineering University of Delaware Newark, DE 19716 Tel:(302) 831 8038 Fax:(302) 831 4316 Email: [email protected] ∗G. Fan was with the Department of Electrical and Computer Engineering, University of Delaware, Newark, DE 19716, USA. He is now with the School of Electrical and Computer Engineering, Oklahoma State University, OK 74078, USA, E-mail: [email protected], Tel/Fax: (405) 744-1547/9198. X.-G. Xia is with the Department of Electrical and Computer Engineering, University of Delaware, Newark, DE 19716, USA, E-mail: [email protected], Tel/Fax: (302) 831-8038/4316. This work was partially supported by the Office of Naval Research (ONR) under Grant N00014-98-1-0644 and Grant N00014-0-110059, and the Air Force Office of Scientific (AFOSR) under Grant No. F49620-00-1-0086.