Discrete 3D tools applied to 2D grey-level images

• 2D grey-level images are interpreted as 3D binary images, where the grey-level plays the role of the third coordinate. In this way, algorithms devised for 3D binary images can be used to analyse 2D grey-level images. Here, we present three such algorithms. The first algorithm smoothes 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. The second algorithm computes 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 result obtained is convex both from the geometrical point of view and as concerns grey-levels. The third algorithm skeletonizes a 2D grey-level object by skeletonizing the top surface of the object in the corresponding 3D binary image.

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