How to partition collagen into separate fibers?
Your data seems to be quite noisy in a sense that there are a lot of holes in the fibers. When you know a typical minimal size of a fiber (probably its widths), you could use a binary closing filter: 


Dilate the image with a structural element of the typical width of a fiber. Most likely a circle with a diameter equal to the minimal fiber widths could be appropriate.
Erode the image with the same structural element.
Use a skeletization algorithm on this data set.