This reminds me of the way TD Possum always analyzed the backgrounds of photos in the sexy janeway thread.
I'm so used to watching the show I never stop to look at the set decoration... although I do like the Leonardo DaVinci drawing (I assume "he" did it) in her ready room.
I notice such details. It's not like I'm looking for such things and analyzing every frame. When a certain detail catches my eye I wonder what it is. In Star Trek we can often see such details, like models of ships, shuttles, paintings, or artwork. For example, the observation lounge of the Enterprise D (and E) had sculptures of all previous Enterprise ships on the wall, which I think was a nice little detail.
I want to hear what Dix thinks these things are. Unless an object's specifically referred to, we can assume it's just there to add interest to a wall, whether for the characters or the camera.
Well, I already said what I think it is. My guess is that it's some abstract art. It looks like a decoration. But I couldn't find any specific information about it. There's only this on Memory Alpha:
The briefing room of the USS Voyager was decorated with various objects of art.