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Detecting thick edges

How can I detect thick edges in an image, without detecting double edges?

How can I get from this image description

as close as possible to this:

image description

I realise why Canny, Sobel or Laplace will not work in this case. They will all find two edges, from black to white, and from white to black. If I only want to get one central edge, is there another approach I can use?

Detecting thick edges

How can I detect thick edges in an image, without detecting double edges?

How can I get from this image description

as close as possible to this:

image description

I realise why Canny, Sobel or Laplace will not work in this case. They will all find two edges, from black to white, and from white to black. If I only want to get one central edge, is there another approach I can use?