For a given image I one can compute connected components and define a graph structure G on those components. Each connected component is one node in the graph and the nodes are connected if they share a pixel boundary. This operation is for example called "connected component labeling". Let's call this L: I -> G.
Now assume one starts with a graph G with some reasonable properties. How can one compute an image I such that L(I) = G?
This "inverse" is most definitely not uniquely defined so I assume there has to be some additional constraints like a random seed. Moreover I would believe that the graph has to be at least planar for there to be a solution. Any hints on methods or algorithms would be of great help.