Morphological dilation using PMN

The above problem can of course be solved by using an exact EDT by propagation algorithm, such as PMN. A further improvement can be obtained by merging the two steps into one. This way, we can perform the threshold dynamically when each point is considered in the propagation. The algorithm is then written

Algorithm 5   Mathematical morphology dilation by a variant of PMN

This implementation supposes that we know the size d of the ball B_d that we use as structuring element. The algorithm can of course be easily modified to allow the decision on the size d to be made during the dilation. The algorithm is fully progressive in the sense that it generates all dilations $X \oplus B_{d'}$ for every size $0 < d' \leq d$, during the process of creating $X \oplus B_d$.