The problem
I have a collection of digital photos of a mountain in Japan. However the mountain is often obscured by clouds or fog.
What techniqu
I think you are working on too low a level. A quick pass through an edge detection filter partitioned the image set very distinctly into (1, 3) and (2, 4). Especially if these images come from a fixed camera viewpoint, finding a match against the prototypical shape in (1) would be relatively easy algorithmically. Even your case of (4) could give you a domain of partial matching which you could heuristically determine if there was enough mountain there to consider.