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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 two-dimensional 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 cross correlation 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 RMT-3S enables more visually similar results than HMT does.