How do I fill the gaps in the pixels in the skeleton of an image and calculate the lengths?

Hello,

I have been working on a couple of neuronal images having green and blue channels in the image. I need to isolate the neurons and measure characteristics like average length of the neurons and the branching points as well. The green channel is of interest to me and therefore have isolated it, performed a series of morphological operations on it after converting it to a logical image, and finally performed an active contour segmentation with a chessboard mask. I then performed skeletonizing using bwskel but I got these results. I performed bwferet function but I didn't get the expected results. I want to fill the gaps in the skeleton in order to form a continous line of branches. Even though I used bwmorph function with 'bridge' parameter, I could not get the desired result. Could anyone please help me on this?

The first Image is Img1 (Original Image). The second Image is the segmented Image (figbw). The third image is the skeleton with gaps in between if you observe closely (figskel).

I wish the desired measurements and branching to be something like this:

The red lines are the measurements that I desire to obtain and the blue dots in between are the branching points of the neurons.

Thanks in Advance!