Measuring the average thickness of traces in an image

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Here's the problem: I have a number of binary images composed by traces of different thickness. Below there are two images to illustrate the problem:

First Image - size: 711 x 643 px

711 x 643 example image

Second Image - size: 930 x 951 px

alt text

What I need is to measure the average thickness (in pixels) of the traces in the images. In fact, the average thickness of traces in an image is a somewhat subjective measure. So, what I need is a measure that have some correlation with the radius of the trace, as indicated in the figure below:

alt text

Notes

  • Since the measure doesn't need to be very precise, I am willing to trade precision for speed. In other words, speed is an important factor to the solution of this problem.

  • There might be intersections in the traces.

  • The trace thickness might not be constant, but an average measure is OK (even the maximum trace thickness is acceptable).

  • The trace will always be much longer than it is wide.

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