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From binary to grey scale convex hulls

Soille P.

Fundamenta Informaticae

2000

Vol. 41, Nr 1,2

131-146

The convex hull of a set is the smallest convex set containing this set. In IR2, this definition is equivalent to the intersection of all half-planes containing the set. We show that this latter definition is nothing but an algebraic closing that can be applied to 2-D grey scale images. The resulting grey scale image is convex, in the sense that all its cross-sections are convex. An efficient translation-invariant implementation, leading to a decreasing family of convex sets that converges to an exact discrete convex hull, is proposed.