After gathering everything together, I came to the following optimal sequence of actions in GIMP:
1) Discoloration luminosity (i.e. the 2nd paragraph).
2) copy the layer.
3) Filters - > Enhance - → Remove spots (despeckle filter from England; he median blur on steroids), the radius is 15, the black level -1 (minus one), the white level 256.
4) Switch layer mode to "Difference".
5) Information of the image.
7) And just now.
Input levels: 0-left slider, right slider 235, the average slider all the way to the right (writes in this case 0.10) did not change (0 and 255 respectively).
9) the long-Awaited profit.
The result for the example above: