Exact solution to median surface problem using 3D graph search and application to parameter space exploration

In this paper we propose the generalized median surface problem and present an exact solution by applying a 3D graph search algorithm. To our knowledge this is a novel class of median computation problem which has not been considered before in the literature. In addition to the theoretic interest in median surface computation we also demonstrate its practical value by means of the task of parameter space exploration without ground truth, which is an effective means of dealing with the difficult parameter selection problem for image segmentation. We present a concrete application for artery boundary detection in sonography (ultrasound imaging). It will be shown that the median computation can not only avoid the parameter training, but also potentially achieve results comparable with trained parameters. The median-based approach can thus be a good alternate, particularly in situations with no ground truth available.