Hidden Markov Models for Images

In this paper we investigate how speech recognition techniques can be extended to image processing. We describe a method for learning statistical models of images using a second order hidden Markov mesh model. First, an image can be segmented in a way that best matches its statistical model by an approach related to the dynamic programming used for segmenting Markov chains. Second, given an image segmentation a statistical model (3D state transition matrix and observation distributions within states) can be estimated. These two steps are repeated until convergence to provide both a segmentation and a statistical model of the image. We also describe a semi-Markov modeling technique in which the distributions of widths and heights of segmented regions are modeled explicitly by gamma distributions in a way related to explicit duration modeling in HMMs. Finally, we propose a statistical distance measure between images based on the similarity of their statistical models for classication and retrieval tasks.