Deformable Registration of Biomedical Images Using 2D Hidden Markov Models

Robust registration of unimodal and multimodal images is a key task in biomedical image analysis, and is often utilized as an initial step on which subsequent analysis techniques critically depend. We propose a novel probabilistic framework, based on a variant of the 2D hidden Markov model, namely, the turbo hidden Markov model, to capture the deformation between pairs of images. The hidden Markov model is tailored to capture spatial transformations across images via state transitions, and modality-specific data costs via emission probabilities. The method is derived for the unimodal setting (where simpler matching metrics may be used) as well as the multimodal setting, where different modalities may provide very different representations for a given class of objects, necessitating the use of advanced similarity measures. We utilize a rich model with hundreds of model parameters to describe the deformation relationships across such modalities. We also introduce a local edge-adaptive constraint to allow for varying degrees of smoothness between object boundaries and homogeneous regions. The parameters of the described method are estimated in a principled manner from training data via maximum likelihood learning, and the deformation is subsequently estimated using an efficient dynamic programming algorithm. Experimental results demonstrate the improved performance of the proposed approach over the state-of-the-art deformable registration techniques, on both unimodal and multimodal biomedical data sets.