First off sorry to hear about it, that totally sucks! Your best bet is to call the police if you haven't already. Leaving the scene of an accident is a crime.
Contour-wise it's theoretically possible to figure this out, but extremely difficult even if all the information is available. A 3D map of the damage would have to be created, and then run through some sort of computer based modeling software which would determine the possible shape of the offending car based on estimates of collision speed, direction and the deformation mechanics of your car's bumper materials. That would then produce an approximate 3D shape of the object that hit your car, which would then be matched to a database of car shapes to find candidate cars, presuming such a database exists. A method such as this could come up with many candidates, and would require a great deal of expertise in computer science - not to mention special equipment. It's unlikely anyone would do this for a simple hit and run with nobody hurt.
From a forensics perspective it's more likely something could be done with paint transfer, at least to get a color. That's not trivial exercise either, so again not something the police are likely to do.
More likely you'll have someone familiar with accident damage look and be able to rattle off the cars it was likely to have been. People whose job it is to analyze traffic accidents all day get a nose for these things.