Thinning Algorithms for Gray-Scale Pictures

Elongated black objects in black-and-white pictures can be ``thinned´´ to arcs and curves, without changing their connectedness, by (repeatedly) deleting black border points whose deletion does not locally disconnect the black points in their neighborhoods. This technique generalizes to gray-scale pictures if we use a weighted definition of connectedness: two points are ``connected´´ if there is a path joining them on which no point is lighter than either of them. We can then ``thin´´ dark objects by changing each point´s gray level to the minimum of its neighbors´ gray levels, provided this does not disconnect any pair of points in its neighborhood. Examples illustrating the performance of this technique are given.