Three-dimensional Euclidean distance transformation and its application to shortest path planning

摘要

In this paper, we present a novel method to obtain the three-dimensional Euclidean distance transformation (EDT) in two scans of the image. The shortest path can be extracted based on the distance maps using the minimum value tracing. The EDT is obtained correctly and efficiently in a constant time for arbitrary types of images, including the existence of obstacles. By adopting the new dynamically rotational mathematical morphology, we not only guarantee the collision-free in the shortest path, but also reduce the time complexity dramatically.