Hidden Markov multiresolution texture segmentation using complex wavelets

In block-based statistical texture segmentation approaches, modeling the global dependency between blocks as well as local statistics within a block is important for segmentation performance. A hidden Markov model (HMM) can be combined with a hidden Markov tree (HMT) to form an HMM-HMT model, which captures both global and local properties. Unfortunately, the real wavelet transform, on which the model is based, is not shift-invariant, which degrades the accuracy of the model. Further, its usual implementation uses a single block size, which does not take full advantage of the multiresolution property of wavelets. The HMM-HMT model is modified to use the shift-invariant complex wavelet transform. We also propose a maximum likelihood multiresolution segmentation algorithm, which handles several blocks sizes at once. Global dependencies between blocks are captured through the HMM, while the local statistics are modeled by the complex wavelet HMTs. This method is compared with other models for several test images to demonstrate its competitive performance, especially at small block sizes.