Discussion

With a computational complexity proportional to the size of $( X \oplus B ) \setminus X$, this algorithm performs as well as, but not significantly better than Vincent's [169]. Both algorithms out-perform any other method, either in precision or in cost.
Both algorithms have additional capabilities that can make them more interesting for a particular application: On one hand, Vincent's algorithm can also be used to perform dilations with structural elements of arbitrary shape. On the other hand, this algorithm is limited to Euclidean balls, but can be stopped at any distance d and provide $X \oplus B_d$. For instance, it can easily perform dilations with elements B_d of increasing size, until some criterion is met, as we do in the next chapter.