Both the HK and SC methods have the problem that it is impossible to have an exact zero value, because of image noise and small shape variations. Therefore, zero-thresholds are used to decide if a value is zero or not. Everything below a certain threshold is recognised as zero. Figure 1 shows the classification regions for the HK segmentation (left) and the SC segmentation (right) for the same threshold value. The graphs are drawn to the same scale. Regions are labelled using the shapes from Tables 1 & 2.
The classification regions of the approaches are quit different
With the HK classification the cylinder area gets narrower for high
curvatures. On the other hand, with the SC classification the cylinder
area uses a constant range of the shape index.
As 
becomes smaller
(ie the radius in the x direction becomes bigger) the HK algorithm
becomes more strict about what is cylindrical by requiring more elongated
shapes to have thinner radii, whereas the SC algorithm allows the maximal
radius to scale up as the shape elongates.
Figure 1: Classification for HK (left) and SC (right) methods.
Dashed lines are determined by the threshold values and separate the
classification regions