I am new to image analysis. Do you know how to binarize this image in such a way to get the fibers only?

I have tried different threshold techniques etc, but I was not successful. I do not mind what tool I should use but I prefer .NET or Matlab.
PS: I did not know where to put my answer, so I put it at StackOverflow.
Based on the comments, it seems you are having difficulty translating the proposed Mathematica solutions into MATLAB. Here is my attempt:
@Nakilon solution
Note that there are differences at the edges. In the Mathematica documentation, it vaguely says:
But there is no direct match for this behavior, instead MATLAB gives you the option to customize the padding at the boundaries of the images.
@belisarius solution