algorithm - Measuring the average thickness of traces in an image

Question

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

Second Image - size: 930 x 951 px

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:

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.

Answer 1

I'd suggest this algorithm:

1. Apply a distance transformation to the image, so that all background pixels are set to 0, all foreground pixels are set to the distance from the background
2. Find the local maxima in the distance transformed image. These are points in the middle of the lines. Put their pixel values (i.e. distances from the background) image into a list
3. Calculate the median or average of that list