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. As the apex zone has less contrast and is harder to identify in the gray scale left ventriculograms, we use the left ventricle´s longitudinal axis 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 the 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 physician 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. The effects of inlier and outlier noise are discussed. 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