Image Classi cation by a Two Dimensional Hidden Markov

Conventional block-based image classiication algorithms, such as CART and VQ based clas-siication, ignore the statistical dependency among image blocks. Consequently, these algorithms often suuer from over-localization. In order to beneet from the inter-block dependency, an image classiication algorithm based on a hidden Markov model (HMM) is developed. An HMM for image classiication, a two dimensional extension of the one dimensional HMM used for speech recognition, has transition probabilities conditioned on the states of neighboring blocks from both directions. Thus, the dependency in two dimensions can be reeected simultaneously. The HMM parameters are estimated by the EM algorithm. A two dimensional version of the Viterbi algorithm is also developed to classify optimally an image based on the trained HMM. An application of the HMM algorithm to document image and aerial image segmentation shows that the algorithm outperforms CART and Bayes VQ. For most block based image classiication algorithms, such as CART 1], images are divided into blocks and decisions are made independently for the class of each block. This approach leads to an issue of choosing block sizes. We do not want to choose a too large block size since this obviously causes crude classiication. On the other hand, if we choose a small block size, only very local properties belonging to the small block are examined in classiication. The penalty then comes from losing information about surrounding regions. A well known method in signal processing to attack this type of problem is to use context information. Trellis coding 2] in image compression is such an example. How to introduce \context" into classiiers is what is of interest to us. Previous work 3, 4] has looked into ways of taking advantage of context information to improve classiication performance for document image segmentation. Both block sizes and classiication rules can vary according to context. The improvement achieved demonstrates the potential of context information to help classiication. The purpose of this paper is to introduce a two dimensional hidden Markov model (2-D HMM) as a general framework for context dependent classiiers. The theory of hidden Markov models in one dimension (1-D HMMs) was developed in the 1960s Underlying an HMM is a basic Markov chain 14]. In fact, an HMM is simply a \Markov Source" as deened by Gallager 15]: a conditionally independent process on a Markov chain or, equivalently, a Markov chain viewed The authors are with the