It is common when making a title for something (particularly art) to leave out some or all of the definite or indefinite articles ("the" or "a"/"an"). This is done for two reasons:
- It makes the title shorter, which is often useful
- It can make it feel more "artistic" by making the associated nouns seem to be more about general concepts than concrete things.
The second point can be seen in your first example:
Pines in the fog
This gives the impression of talking about pine trees in the specific fog that's in this photo.
Pines in fog
This gives a feeling more of "fog" as a general concept. The picture is obviously still showing the same specific fog, but the title implies that the fog could, perhaps, be seen as representative of "fog in general", or perhaps a metaphor for other "foggy things".
Note, however, that often when people leave out these articles they're only doing it for reason #1, and reason #2 is not thought about or intended, so it's quite possible the artist didn't actually intend the fog to be representative of anything, they just wanted a nice short title. This is the fun of artistic interpretation :)
So, getting back to your original question:
When making titles for things, it's generally acceptable to leave out definite or indefinite articles whenever you want to. Note that this is only true for definite/indefinite articles ("the"/"a"/"an") and not for prepositions, etc.
This is never required, though. It's just as acceptable to call something "Pines in the fog" as it is to call it "Pines in fog". In many cases, this is just an artistic/aesthetic choice.
In your second example, the "dusk" part is not really the same thing. Here you are not leaving out articles, but actually choosing between two different prepositions, and the two prepositions have slightly different meanings:
Eagle in the dusk
This sounds a bit odd, because most people don't actually talk about things being "in the dusk", but in any case, even if it weren't strange, it would probably imply that you are specifically talking about the eagle being within the (effects of) the dusk (so I would expect to be seeing a dusky sky surrounding the eagle).
Eagle at dusk
This is the way most people would phrase it, just because I think most people would tend to say "at dusk" instead of "in the dusk" anyway, but it also is just saying that the shot was taken at the time of dusk. It could even be that there's no sign of the dusk in the picture at all for some reason, it just happened to be taken at that time (although in that case, I don't know why it would be part of the title, but, you know, sometimes people are strange).