We modify the zone labeling algorithm to handle isosets by modifying phase 1 so that it uses depth first search to identify all isosets. We identify the critical isosets of types 1 through 3, and the regular isosets. We select an arbitrary point in each isoset as the label and only place the points of the isosets with neighbors outside the isoset on the heap, and immediately place all other the other isoset points in the appropriate zone file.
Phase 2 and 3 of the algorithm now compute a refinement of the segmentation, as some zones will be divided by regular isosets that are not actually criticalities. But this will not change the properties of the zones that our applications require, merely make some zones smaller. However, in 3-D we can use an isosurface algorithm that produces a traingle mesh to extract the relevant contour of the object in question for isovalues and and determine using Euler's formula whether a genus change has occurred. If not we can merge the corresponding zones. One such algorithm, of independent interest because it extends naturally to higher dimension (unlike the aformentioned marching cubes), is described below. It is remarkably simple and completely parallelizable.