How to move and modify edges freely in a binary image similar to impoly?

Dear all,

I have an image similar to the one I show below. The image is binary and contains only edges. Now I want to have full control of these edges such that I can modify them, like the way we control the shape we get from impoly.

I was thinking to use bwmorph 'branchpoints' to determine the vertices. But how to connect the lines between the vertices correctly?

Any suggestion will be appreciated.

Meshoo