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232 Chapter 6 ■ Thinning

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Figure 6.22: The force at a given pixel is the vector sum of the forces to all visible pixels.
Only boundary pixels exert a force, and only object pixels have the force computed.

The details of the growing process are relatively simple. First, a queue to
hold the points to be grown is defined. All the endpoints of the current stubs
are placed into the queue as potential starting points for the growth process.
Then points are removed from the queue one at a time and tested to see if
growth is possible; if so, it is added to the skeleton and the new skeletal point
is added to the queue if it, too, is a potential starting point.
To grow from a point P,the pointmustsatisfy twoconditions. P must have
exactly one or two 8-connected neighbors that are skeletal pixels, and if it has
two such neighbors, then these must be adjacent to each other. The preferred
direction of growth is through these neighbors towards P and beyond to the
next pixel. There will be three candidate pixels, and the one of these having the
smallest force magnitude is grown into: It is added to the skeleton and placed
on the queue for further growth steps. The growing process will stop when
the growth front hits an edge or other part of the skeleton.
At a subpixel level, the growth process first attempts to find new skeletal
pixels at double the previous resolution. Using the stub endpoints the regions
to be refined are identified, and forces are computed for each pixel at the
new resolution; the resolution doubles each time. Then the dot products are
computed as before, looking for zero crossings. When located, a zero crossing
becomes a skeletal pixel at the current resolution and also marks all containing
pixels at lower resolutions as skeletal. The refinement can be continued at