Evaluation of Cardiac Ultrasound Data by Bayesian Probability Maps

Abstract

Abstract. In this paper we present improvements to our Bayesian approach for describing the position distribution of the endocardium in cardiac ultrasound image sequences. The problem is represented as a latent variable model, which represents the inside and outside of the endocardium, for which the posterior density is estimated. We start our construction by assuming a three-component Rayleigh mixture model: for blood, echocardiographic artifacts, and tissue. The Rayleigh distribution has been previously shown to be a suitable model for blood and tissue in cardiac ultrasound images. From the mixture model parameters we build a latent variable model, with two realizations: tissue and endocardium. The model is refined by incorporating priors for spatial and temporal smoothness, in the form of total variation, connectivity, preferred shapes and position, by using the principal components and location distribution of manually segmented training shapes. The posterior density is sampled by a Gibbs method to estimate the expected latent variable image which we call the Bayesian Probability Map, since it describes the probability of pixels being classified as either heart tissue or within the endocardium. By sampling the translation distribution of the latent variables, we improve the convergence rate of the algorithm. Our experiments show promising results indicating the usefulness of the Bayesian Probability Maps for the clinician since, instead of producing a single segmenting curve, it highlights the uncertain areas and suggests possible segmentations.