Spherical Distance Transforms

We present three algorithms for computing correct distance fields on a unit sphere. These algorithms enhance conventional distance transform techniques with several extensions. The first algorithm is a wavefront scheme using quaternions. As a unit quaternion represents a single rotation corresponding to the distance on a sphere, correct distances can be evaluated. Second, we propose a Euclidean vector-based algorithm whose computation is much simpler than that of the first. In addition, we also propose sequential versions of these algorithms that take in linear time. This paper demonstrates several examples computed by these algorithms, and shows that correct distance fields can be obtained by all the methods, with the sequential algorithm being the fastest.