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In picture processing it is often convenient to deal with a stick-like version (skeleton) of binary digital images. Although skeleton connectedness is not necessary for storage and retrieval purposes, this property is desirable when a structural description of images is of interest. In this paper a parallel procedure is described which, applied to a connected image, originates a connected skeleton made by the union of simple digital arcs. The procedure involves a step by step propagation of the background over the image. At every step, contour elements either belonging to the significant convex regions of the current image or being local maxima of the original image are selected as skeleton elements. Since the final set so obtained is not ensured to be connected, the configurations in correspondence of which disconnections appear are investigated and the procedures to avoid this shortcoming are given. The presence of the whole set of local maxima among the skeleton elements ensures the possibility of recovering the original image by means of a reverse distance transform. The details of the program implementing the proposed algorithm on a parallel processor are finally included.