Left Ventricle Longitudinal Axis Fitting and its Apex Estimation using a Robust Algorithm and its Performance: A Parametric Apex Model

For complete automatic left ventricle border detection in a cardiac frame, the apex needs to be located. .4s the apex zone has less contrast and is harder to identify [l], [4] in the gray scale left ventriculograms, we use the left ventricle’s longitudinal axis [2] to assist in apex location. To automatically find the longitudinal axis of the left ventricle in any frame, we find the longest segment from either the anterior aspect of aortic valve or the inferior aspect of the aortic valve to the left ventricle border. We assume that the ruled surface generated by the sequence of longitudinal axes through the cardiac cycle is of sufficiently simple form, so that the perturbation error, especially the large errors, between the automatically measured axis and the physzcian defined axis can, in part, be filtered out by a robust procedure. To discriminate those automatically determined axes that might differ significantly from the physician defined ground truth, we use Huber’s weight function in an iterative reweighted least square robust fitting. We show that when the variance of the inlier noise is 1 mm2 and variance of the outlier noise is 100 mm2 and outliers occur in 15% of the longitudinal axes, then the robustly estimated axis end points have a root mean square error of 2.2 mm. By contrast, with only inlier noise and using only 85% of the longitudinal axis data, the ordinary least squares estimate has a root mean square error of 1.34 mm. With both inlier and outlier noise, an ordinary least squares estimate would produce estimated apex vertices having a root mean square error of 10.5 mm. We demonstrate that for 90% of 1200 frames of clinical data, the automatically determined apex location is less than an arc length distance of 1% of the ventricle border length from the ground truth apex location as delineated by the cardiologist.