Coincidentally, I had exactly just that thought about a week ago whilst I was staring out at a nearby mountain.
I have very little knowledge about this kind of problem, but to me, it seems like a solvable problem - there has been some interesting work in reconstructing 3D models from photographs of objects (I have a friend who did his masters in something similar) and I don't doubt that people working on that type of problem would likely have some ideas for approaching this one.
Though to make it tractable one would perhaps want to "weight" the algorithm / start the search from likely vantage points (i.e. from inside cities / on top of buildings, and along roads), and take some discrete samples of what the mountain range would look like at various angles from that point.
I wonder if it would be possible to do something similar to a binary search or Newton's method type thing where if you have two nearby points looking at the same mountain range, you could figure out the probability that the actual vantage point lies somewhere in the vague area between those points, and so get a better idea of where to take more precise samples after you've started with a few discrete samples.
This should be a tractable problem. Cruise missiles navigate by matching the terrain they're flying by with a 3d model.
Doing it with 2d video and not having precise starting coordinates, speed/heading/altitude makes the search space larger but I think that is more than made up for by the fact that you're not trying to do it all on embedded hardware from the 80s.
Makes me wonder if that 2D mountain range projection could be used to 'search' through a 3D map for a match.