Detecting meandering rivers in images
A very simple measure would be to compare each row in the image with the row above it, allowing some horizontal shift.

I've hacked together this simple algorithm in Mathematica:

Mean[MapThread[
  Function[{line1, line2},
   Min[Table[Norm[line1 - RotateLeft[line2, shift]], {shift, -5, 5}]]
   ], {s[[2 ;;]], s[[;; -2]]}]]


It simply takes each pair of adjacent rows, rotates one of the rows by -5..5 pixels, and takes the smallest euclidean distance. This yields one euclidean distance for each row pair. I simply take the mean (but depending on your actual data, a truncated mean or median might be more robust).

These are the results I get for artificially generated samples (Formula: Normalize(random noise * (1-factor) + signal * factor))



If I plot the result against the signal strength, the algorithm seems to measure the "meandering river signal strength" quite well:



EDIT: I forgot to normalize the input samples. Fixed that an uploaded new result images