9.2.2 Discussion of criticality graph and zone labeling algorithm.

Observe that the algorithm labels all data readings and criticalities, by a highest valued first labeling, through the entire dataset. At any point in time when precisely all points greater than or equal to a particular $\tau$ have been labeled, these are precisely the lattice points that comprise components of $\bf {X}_{\delta}^{\geq \tau}$. Moreover, when the algorithm terminates, the lattice points labeled by p are precisely the lattice points contained in $\zeta (p)$.

The volume of the component of a zone that contains a criticality, can be used to determine the relative importance of the criticality. For example, some critical 4-hit face saddles will produce a hole that is smaller than one hypercube, containing only one Low reading. In this case, the Low will itself be a minimum and the zone of the saddle will be very small. We can regard both the saddle and minimum as producing only textural features (smaller than the sampling distance) and cull them, if desired. In this manner we can reduce the number of criticalities. For example, in the criticality graph of figure 24 the component of the zone of l containing l is extremely small. The minimum l (with value 50) could be culled with little change. Similarly, if criticalities c and f were removed, only one small object, which immediately merges with the object created by d, would be lost.