Discrete 3D Tools Applied to 2D Grey-level Images

2D grey-level images are interpreted as 3D binary images, where grey-level plays the role of the third coordinate. In this way, algorithms devised to analyse 3D binary images can be used to analyse 2D grey-level images. We introduce an algorithm to smooth a 2D grey-level image by flattening its geometrical and grey-level peaks while simultaneously filling in geometrical and grey-level valleys, regarded as non significant in the problem domain. Then, we present an algorithm to compute an approximation of the convex hull of a 2D grey-level object, by building a covering polyhedron closely fitting the corresponding object in a 3D binary image. The obtained result will be convex both from the geometrical point of view and as concerns grey-levels. Finally, we illustrate an algorithm to skeletonize a 2D grey-level object by actually skeletonizing the top surface of the object in the corresponding 3D binary image.