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

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Meshooo
Meshooo 2014-3-4
编辑： Meshooo 2014-3-4
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

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