## Shortcomings of the Geometric Snake

Geometric active contour models have the significant advantage over classical snakes that changes in topology due to the splitting and merging of multiple contours are handled in a natural way. However, they suffer in two specific ways:

1. They use only local information and hence are sensitive to local minima. This means they are attracted to noisy pixels and can fail to converge on the desired object when they rest at such strong "features." They fail to recognize, possibly weaker but true features further away in the image landscape, for lack of a better global understanding of the image. An example is shown in Fig. 10.7 (left).

Figure 10.7: Noise sensitivity and weak-edge leakage problems. In each case the evolving snake is shown in a light color and the final snake in a dark one.

2. The constant flow term makes the snake expand or shrink. It can speed up the convergence and push the snake into concavities easily when the objects have good contrast, i.e. when the gradient magnitudes at object boundaries are large. However, when the object boundary is indistinct or has gaps, the snake tends to leak through the boundary mainly because of this constant force. The second term in (10.8) is designed to attract the contour further close to the object boundary and also to pull back the contour if it leaks through the boundary, but the force may just not be strong enough since it still depends on the gradient values. It cannot resolve the existence of a weak edge. Figure 10.7 (right) demonstrates this shortcoming of the standard geometric snake. The evolving of the snake is based on the gradient information, and as there is a gradual change of the intensity, the contour leaks through.

The result of such failures is that the geometric snake will converge to a nonsensical form. Both these effects are demonstrated in Fig. 10.8 where the cells contain fuzzy borders and strong but tiny dark "granules" that have led the standard geometric snake astray (top-right image). The images in the bottom

Figure 10.8: Multiple objects—top row: initial snake and standard geometric snakes, bottom row: region segmentation used by RAGS and converged RAGS snakes (original image courtesy of Dr. Douglas Kline, Department of Biological Sciences, Kent State University, US) (color slide).

row of Fig. 10.8 show the region map used for the RAGS formulation outlined later in this chapter and the converged RAGS snakes. This figure also illustrates the power of the geometric snake in splitting to find multiple objects.