Convex Hulls and Metric Gabriel Graphs - Cellular Automata in Image Processing and Geometry - page 189

Fig. 10.10 Distance fields from two particles
Fig. 10.11 Detected middles and paths back to both particles
build one distance field for each pair of seeds in the space, as we need the number
of states of the cells to be finite. However, a single distance field might allow for
the detection of middles of more than one pairs of seeds. This can be checked on
Fig. 10.12 which shows the evolution of the rules dist and back (using our yet-to-
be-defined detection of the middles cent) in the presence of many seeds. In the case
of this figure, we can even see that the result is connected. If this is always true
that the result of this pairwise construction is connected, then adding conv or majo
Fig. 10.12 Construction of pairwise convex hull