Integrated surface model optimization for freehand three-dimensional echocardiography

The major obstacle of three-dimensional (3-D) echocardiography is that the ultrasound image quality is too low to reliably detect features locally. Almost all available surface-finding algorithms depend on decent quality boundaries to get satisfactory surface models. We formulate the surface model optimization problem in a Bayesian framework, such that the inference made about a surface model is based on the integration of both the low-level image evidence and the high-level prior shape knowledge through a pixel class prediction mechanism. We model the probability of pixel classes instead of making explicit decisions about them. Therefore, we avoid the unreliable edge detection or image segmentation problem and the pixel correspondence problem. An optimal surface model best explains the observed images such that the posterior probability of the surface model for the observed images is maximized. The pixel feature vector as the image evidence includes several parameters such as the smoothed grayscale value and the minimal second directional derivative. Statistically, we describe the feature vector by the pixel appearance probability model obtained by a nonparametric optimal quantization technique. Qualitatively, we display the imaging plane intersections of the optimized surface models together with those of the ground-truth surfaces reconstructed from manual delineations. Quantitatively, we measure the projection distance error between the optimized and the ground-truth surfaces. In our experiment, we use 20 studies to obtain the probability models offline. The prior shape knowledge is represented by a catalog of 86 left ventricle surface models. In another set of 25 test studies, the average epicardial and endocardial surface projection distance errors are 3.2 ± 0.85 mm and 2.6 ± 0.78 mm, respectively.