Best linear unbiased estimator for Kalman filter based left ventricle tracking in 3D+T echocardiography

In this paper, we introduce the best linear unbiased estimator (BLUE) for the detection of endocardial edges in 3D+T echocardiography recordings. The maximum gradient (MG), step criterion (STEP) and max flow/min cut (MFMC) edge detectors have been previously applied for the detection of the endocardial edges. BLUE combines the responses of these 3 base estimators using statistical inferences. First, the base estimator bias and covariance properties are learned for each endocardial surface point at each cardiac cycle position. Then, these statistical properties are utilized to compute an optimal linear combination of the base detectors by BLUE. For the validation, MG, STEP, MFMC and BLUE were each employed in connection to a Kalman tracking frame- work. Comparative analyses showed that BLUE outper- forms the other estimators in surface and volumetric measurement accuracy.

1. Introduction

3D echocardiography is a widely used clinical diagnosis tool as it provides real-time, non-invasive and low cost acquisition of volumetric images of the heart. Automated segmentation and tracking of heart chambers in echocardiography images have received considerable attention in the recent years [15], [10], [21]. However, accurate detection of endocardial borders remains a challenging task due to reasons including (1) speckle noise, (2) shadowing that can result in missing boundaries, and (3) the existence of intra-cavity structures such as chordae tendineae, papillary muscles and valves [19].