Multiscale Classification Using Complex Wavelets and Hidden Markov Tree Models

Multiresolution signal and image models such as the hidden Markov tree (HMT) aim to capture the statistical structures of smooth and singular (textured and edgy) regions. Unfortunately, models based on the orthogonal wavelet transform suffer from shift-variance, making them less accurate and realistic. In this paper, we extend the HMT modeling framework to the complex wavelet transform, which features near shift-invariance and improved angular resolution compared to the standard wavelet transform. The model is computationally efficient (featuring linear-time computation and processing algorithms) and applicable to general Bayesian inference problems as a prior density for the data. We develop a simple multiscale maximum likelihood classification scheme based on the complex wavelet HMT that outperforms methods based on real-valued wavelet HMTs. The resulting classifier can be used as a front end in a more sophisticated multiscale segmentation algorithm.