FIGURE 10 East border (a), south border (b), and northwest corner (c) in Zhang and Suen algorithm.

Suen algorithm does not reproduce all details that are obtained with the more rigorous MAT, in many applications it provides a very good approximation that requires considerably fewer computations. In an application where the location of the central axis of the bone is sought, for example, both algorithms would lead to almost the same result. When the length of an elongated structure has to be measured, thinning can be used to determine the medial axis; distances between consecutive pairs of pixels can be added to obtain an estimate of length. Although the distance between two pixels that share a side is the width of one pixel, the distance between two pixels connected at their corners is \fl times longer. Figure 12 illustrates the use of thinning to quantify the length of DNA fragments [31]. The atomic force microscope image of DNA fragments in Fig 12a is segmented in Fig. 12b. The image in Fig. 12c shows the outcome of thinning where objects that are too short and those that touch the image edge are removed.

Thinning is used in numerous applications, including coronary arterial tree analysis [32], gastrointestinal endoscopic imaging [33], atomic force microscopy images of DNA fragments [31], ocular fundus imaging [34], and quantification of chromosome shapes [35]. Thinning algorithms that have only one step per iteration [36] and others that operate directly on the gray-scale image [37-39] are also available. Since the use of medial lines is particularly important in volumetric information, thinning algorithms for 3D data also have been suggested, using various approaches such as a 3D generalization of the Vornoi skeleton concept [40], hybrid thinning techniques [41], and voxel-coding [42].

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