The FRAME Prior in Hidden Markov Random Field and Coupled Hidden Markov Modelling for TCA Image Analysis

Tooth Cementum Annulation (TCA) is an age estimation method carried out on thin cross sections of the root of the human tooth. Age is computed by adding the tooth eruption age to the count of annual incremental lines which are called tooth rings and appear in the cementum band. Algorithms to denoise and segment the digital image of the tooth section are considered a crucial step towards computer-assisted TCA. The approach in this paper relies on modelling the images as hidden Markov random fields and as coupled hidden Markov chains, where gray values are assumed to be pixelwise conditionally independent and normally distributed, given a hidden random field of labels. These unknown labels have to be estimated to segment the image. To account for long-range dependence among the observed values and for periodicity in the placement of tooth rings, the Gibbsian label distribution is specified by two different potential functions that incorporate macro-features of the TCA image, that is a FRAME model and a FRAME chain. An estimation of the model parameters is made by an EM algorithm exploiting the mean field approximation of the label distribution. Preprint submitted to Elsevier Science 31 March 2006 Segmentation is based on the predictive distribution of the labels given the observed gray values.