Extraction of maximal inscribed disks from discrete Euclidean distance maps

Detection of the set of centers of maximal disks is a key step toward generation of accurate skeletons on the basis of distance maps. Algorithms using approximate distance metrics are abundant and their theory has been well established. However, the resulting skeletons may be inaccurate and sensitive to rotation. In this paper, we study methods for detecting maximal disks from distance maps based on the exact Euclidean metric. We first show that no previous algorithm identifies the exact set of discrete maximal disks under Euclidean distance metric. We then propose new algorithms and show that they produce the exact set of maximal disks. The effectiveness of our algorithms is demonstrated with numerous examples