Have you had a chance to take a look at this example?
It talks about various fundamental image processing techniques (edge detection, morphological operation etc.) to segment a cell. I would start here and try to understand how the code works for an example image. And then replace the example image with your image and play with the parameters to get it to appropriate values to see what you can make of it. For e.g. I blindly stuck your image into the code and changed the sobel fudge factor to 1.75 to get a decent edge detection. After this, you can play with other morphological operations to remove disturbances and sharpen the edges. The function bwmorph with the skeletonize operation (documentation here) might help in thinning out the lines.
