skeletonization and ridge detection; Find ends of the skeleton;

Hi, I am trying to skeletonize images of filamentous structures; ideally I would like to obtain single picture width ridges with two ends. Of course, because of noise I get gaps and multiple branches. I want to fill the gaps and prune the branches. For this I need to find the ends of the skleton, branch points and isolated pixels. All those function are well supported by matlab, e.g. morphological operations or applylut. Yet, I spend many hours and didn't succided. Here is piece of the code for visualization:

E = bwmorph(im2skel, 'endpoints'); % im2skel is a skeletonized image
[re,ce] = find(E);
figure;
imshowpair(im2skel,E,'Scaling','independent'); 
hold on;
plot(ce,re,'.r','MarkerSize',15)
And this is a small subregion of the image:

My point is, that not all of the 'filaments' have two ends! Also, I would expect that each red dot will coincide with white pixel, is it a problem withy matlab visualization? I get exactly the same output using pice of code suggested by Steve on his blogg:

endpoint_fcn = @(nhood) (nhood(2,2) ~= 0) && (sum(nhood(:)) == 2);
endpoint_lut = makelut(endpoint_fcn, 3);
E = applylut(im2skel, endpoint_lut);

Here is other region of the same image:

It must be very simple, why I see isoletd red dot, which does not coincide with any pixel in the E image; Anyway, this other example shows long fiber, which is fragmented and I aim on reconecting it. I tried range of morphological operation, but I didn't succided on the large scale. Other way would be to use endpoints, but as I am showing, I do not get endpoints of all the fragments. First question: Do you have any suggestion why bwmorph(BW, 'endpoints') does not work in my situation? Second question: Can you suggest morphological operations to reconect fragments of the fiber, with certain threshold distance between ends ( e.g. up to 5 pixels)? Many thanks for any suggestions!