A justification of a fast surface tracking algorithm

Abstract

In many three-dimensional (3D) imaging applications in science, medicine, and engineering, object information captured in a 3D digital image is visualized and analyzed based on object surfaces extracted from the image. Recently Gordon and Udupa ( Comput. Vision Graphics Image Process. 45, 1989, 196–214) reported a fast algorithm for tracking such surfaces, whose correct behavior has only been a conjecture but observed nonetheless in all uses of this algorithm in a variety of biomedical applications. In the present paper, we prove the correctness of their algorithm by showing that the surfaces generated by the algorithm correspond to connected components of boundary elements and that they possess Jordan boundary properties.