I can't help but wonder how much you can automate the process? Geologists regularly let software automatically identify mineral grains, determine the locations of borders between different minerals , and the report the percentage of each mineral in a microscopic image. It needs checking to be certain that one correctly defined the visual parameters of each mineral, but checking is way faster than circling each mineral grain by hand and then calculating their area.
I guess to get the thickness of the fiber you'd need a program that chooses a random location, determines if it is fiber (dark) or background (light), then, if fiber, checks all of the adjecent pixels to see if they are still fiber, and then progress outwards from the starting point in all directions till it encounters pixels in the background colour. Once the boundaries of that fiber are thus determined then it can measure the shortest distance between one edge and another to determine the thickness of that point. Repeat 100 times. Or 1000. The computer doesn't mind doing repetitive tasks.