<title>Statistical shape description using Gaussian Markov random fields and its application to medical image segmentation</title>

Abstract

This paper introduces global shape modeling by means of Markov random fields and describes its use in medical image segmentation. The key point positions representing the shape of an object are assumed to be multivariate Gaussian distributed with a certain covariance structure which relates to the Markov property with respect to some neighborhood system. Since the neighborhood of a key point potentially contains both nearby and long distant key points, global key point interaction is not only realized by propagated local key point interaction, but also directly by long distant key point interaction. We restrict ourselves to the subclass of decomposable models, since a closed form expression for the maximum likelihood estimate of the covariance matrix from a set of training shapes is available in this case. The neighborhood system is either a priori defined or estimated. Our model building procedure is demonstrated for the 2D shape of spinal vertebra. The suitability of the derived shape models is investigated by generating new shape samples according to the models. Finding the object's boundary in a grey value image is formulated as maximum a posteriori estimation incorporating the shape model as a priori model. Our model-based segmentation procedure includes an easy and effective interactive improvement of the segmentation outcome.