Thinning and crest restoration in graylevel images

Involved people : Gilles Bertrand, Francisco Nivando Bezerra, Michel Couprie.

Thinning and skeletonization are significant applications of topological concepts to image processing. Many thinning algorithms for the binary images were proposed. However, the use of such algorithms supposes a preliminary segmentation of the image, which implies a loss of information.

We propose an algorithm of skeletonisation acting directly on a graylevel image. This algorithm guarantees the safeguarding of the topology of the different image cross-sections. We also propose a method for "filtering" such skeletons, i.e. to selectively simplify the topology, according to a criterion of local contrast (see also the sections "Topology of graylevel images" and "Fingerprint recognition").

In addition, when one meets in images some elongated and thin objects, it is frequent that such objects are "cut" by the effect of the noise, and one would wish to be able to reconnect these objects. If one regards an image as a topographic relief, an elongated object can be seen like a crest, and the reconnection of this object is reduced to the detection and the elimination of narrow passes in the crest. Within the framework of the cross-section topology, we propose an effective and rigorously defined method to achieve this work. This method applies in particular to gradient images, which by nature consist of thin lines corresponding to contours of the objects of the original image (fig. 11) [ CBB99 ].


(a)	(b)

(c)	(d)

Figure 11: (a) : An gradient image, reversed and thinned. (b) : Image (a) thresholded at level 58. (c) : After the crest restoration applied to (a). (d) : Image (c) thresholded at level 58.