Statistical Image Modeling and Processing Using Wavelet-Domain Hidden Markov Models - Nonlinear Signal and Image Processing: Theory, Methods and Applications - page 382

be useful for the applications where the nonredundant DWT is preferred, e.g.,
compression-domain image segmentation and feature extraction, etc. More-
over, the proposed maximum likelihood-based texture synthesis algorithm
can also be applied to other HMM in the redundant DWT that has a moderate
feature size, such as the HMT of complex wavelet transform 53 and the vector
HMM of steerable wavelet transform. 9

10.6 Conclusions

In this chapter, we have studied wavelet-domain statistical image modeling
and processing. In particular, we have investigated wavelet-domain hidden
Markov models (HMMs), which were originally proposed in Reference 1
for statistical signal/image processing. We first improved wavelet-domain
HMMs in terms of their training efficiency and modeling accuracy by devel-
oping several new techniques that further inspire our studies toward four
applications: image denoising, image segmentation, and texture analysis and
synthesis. With these techniques we can obtain state-of-the-art performance
or promising results by developing new wavelet-domain HMMs as well as
efficient image processing algorithms.

•

We show that training efficiency and modeling accuracy of wavelet-
domain HMMs are important in their applications to practical signal
and image processing problems. Specifically, an efficient EM initial-
ization scheme can improve the training performance of HMMs, es-
pecially for those newly developed HMMs, i.e., HMT-2, LCHMM,
and HMT-3S. Meanwhile, the graphical grouping and classification
schemes have been found efficient for obtaining more accurate sta-
tistical modeling.

•

We suggest that spatial adaptability and nonstructured local re-
gional modeling are essential to the application of wavelet-domain
HMMs to image denoising. Thus, a new local contextual hidden
Markov model (LCHMM) was proposed, one that provides state-
of-the-art denoising performance with improved visual quality at
low computational complexity.

•

We argue that the performance of multiscale Bayesian segmentation
can be improved by strengthening two factors: contextual modeling
and texture characterization. A new joint multicontext and multi-
scale (JMCMS) approach to Bayesian segmentation was developed
to consider the first factor. In JMCMS, contextual behavior can be ac-
cumulated both across scales and via multiple-context models. On
the other hand, a new wavelet-domain HMM, HMT-3S, was pro-
posed to emphasize the second factor by providing more accurate