Geodesic DT algorithms

In chapter 2, we saw that the most efficient algorithm to implement usual geodesic distance transformations was that of Verwer, Verbeek and Dekker [167]. It scans the pixels in order of increasing distance by bucket sorting the pixels in the propagation front.
Unfortunately, there are two major hindrances to the use of this algorithm to implement the B_d-geodesic DT. First of all, the neighborhoods to consider during the propagation would have the size of B_d, which is prohibitive for any non-trivial d. For instance, d=6 would require to consider 112 neighbors for each pixel. Secondly, the B_d-geodesic distances are real-valued. This makes them unsuitable as buckets' indexes.