3.6 Skeletonization

3.6 Skeletonization

A skeleton of a planar contour is a set of centers of bitangent circles that lie entirely inside the contour. One can construct a skeleton in a chemical medium using one of two following approaches: The first is based on excitation wave dynamics in Belousov-Zhabotinsky reactions, the second employs precipitation. Both approaches are based on Blum's ideas of grass fire transformation (Blum 1967, 1973).

The Belousov-Zhabotinsky computing medium stays in a trigger mode, wherein every elementary microvolume switches from one stable state to another. This coherent switching results in the spreading of wave front of the switching states. A laboratory prototype of a Belousov-Zhabotinsky processor is a thin, 0.5–1.5 mm, nonstirred reagent layer, placed in a siliconized reaction vessel. Two states of a microvolume can be classified by their colors: red and blue. Initially, a contour of a planar shape is projected onto the reaction space. The circular waves are generated. The waves run away from every point of the contour. Two wave fronts are formed—one wave front spreads inward the contour, another runs outward. Sites of meeting of inward-running waves are registered optically. They represent segments of a skeleton of the planar shape (Rambidi, Maximychev, and Usatov 1994a). The only disadvantage of the technique is that no stationary structure is formed.

We can avoid the unpleasant experience of having to chase an ever-changing wave front if we use a set of reactions wherein a colored precipitate is produced. Essentially the same palladium processor discussed with regard to the Voronoi diagram can easily handle this skeleton problem. We do not apply drops of potassium iodide but prepare a contour cut of a filter paper saturated with this reagent; the filter-paper contour is applied onto the gel with the palladium chloride. Diffusive wave fronts of potassium iodide spread inward (actually, they spread outward also but we do not care about this) from the contour. When and where wave fronts meet, no precipitate is formed, and thus a skeleton is seen as uncolored sites of the chemical processor (figure 3.2).

Figure 3.2: Skeleton of a planar shape constructed in experimental reaction-diffusion processor. Data shape is shown in black color, segments of the skeleton are uncolored. Photo of the original chemical processor designed by D. Tolmachev in 1996.

Unfortunately, the palladium processor (and its analogues, see Adamatzky 2001) is not simply a specialized processor, it has to be considered a disposable processor (the palladium processor is analogous to a photographic paper or a recordable compact disc, while the Belousov-Zhabotinsky processor is like an hourglass or a rewritable compact disc).