Empirical Bayes estimator for endocardial edge detection in 3D+T echocardiography

This paper presents an empirical Bayes (EB) estimator for detection of endocardial edges in 3D+T echocardiography recordings. A maximum likelihood (ML) edge detector, proposed in a previous study, combines the responses of multiple edge detectors to improve the detection accuracy. We aim to further extend this approach with the use of contextual priors, that gives the probabilistic distribution of correct (yet unknown) endocardial edge positions. For training, a ML model that gives an optimal linear combination of multiple endocardial edge detectors is learned from a pre-segmented dataset. For a given test data, (1) ML edges are estimated using the learned ML model, (2) a conceptual prior is derived using the ML edge estimations in an empirical fashion, and (3) ML estimates and the conceptual prior are fused to produce empirical Bayes endocardial edge estimates. Comparative analyses show that EB reduces the mean square endocardial surface error with respect to ML estimations. This is due to the Stein effect that briefly asserts that the expected mean square error of the ML estimations should be reduced with the use of empirically-derived prior information.