The boundaries illustrated in Section 10.5, obtained using the watershed segmentation algo...

The boundaries illustrated in Section 10.5, obtained using the watershed segmentation algorithm, form closed loops (for example, see Figs. 10.56 and 10.58). Advance an argument that establishes whether or not closed boundaries always result from application of this algorithm.

FIGURE 10.56 (a) Image of blobs. (b) Image gradient. (c) Watershed lines. (d) Watershed lines superimposed on original image. (Courtesy of Dr. S. Beucher, CMM/Ecole des Mines de Paris.)

FIGURE 10.58 (a) Image showing internal markers (light gray regions) and external markers (watershed lines). (b) Result of segmentation. Note the improvement over Fig. 10.47(b). (Courtesy of Dr. S. Beucher, CMM/Ecole des Mines de Paris.)