| Hidden Markov Models (HMMs), a type of finite state machines for statistical modeling, have been successfully applied to speech recognition due to the fact that finite states in speech signals are amenable to the mechanism of HMMs. However, it is hard to directly apply HMMs to image modeling in the spatial domain, since there are too many states (gray-levels of pixels) in real-world images. Crouse et al have recently proposed a kind of wavelet-domain HMMs, in particular hidden Markov tree (HMT), for statistical modeling, since the wavelet transform can decorrelate image data by reducing the number of states of wavelet coefficients, thus making wavelet-domain HMMs manipulable and useful for statistical image modeling. In this dissertation, two important topics of wavelet-domain HMMs are studied in terms of their applications to statistical image modeling and processing. One is how to adapt wavelet-domain HMMs to a variety of statistical image processing problems with the efficient model training. The other is how to develop effective image processing algorithms using wavelet-domain HMMs for different applications. We firstly introduce wavelet-domain HMMs proposed Crouse et al, then several specific techniques are developed, including an efficient initialization method to improve the training efficiency, and the graphical grouping and classification schemes to improve the modeling accuracy. These improvements further inspire us to study wavelet-domain HMMs regarding their applications to image denoising, image segmentation, texture analysis, and texture synthesis. We are able to obtain state-of-the-art performance in these applications by developing powerful wavelet-domain HMMs as well as effective image processing algorithms. |
