for t = 1 to Number of erosion recursion

Erosion(GMST)

Push eroded vertices and edges {ei, vi} into a stack

end

Begin dilation operation

Mark all end vertices if their degrees are one

if the stack is not empty

Pop a vertex and edge {ei, vi} from the stack

if the vertex and edge extends from an end vertex of current graph

Add the vertex and edge back to the graph

Mark new end vertex

else

Discard the vertex and edge

end

end

Obtain the backbone graph, Gbb