Delete duplicate photos from Library, keep in albums?

Lspremulli wrote: …Is there anyway to delete a duplicate photo from the Library and leave them in their assigned albums

Here's the thing: Pictures aren't really in albums. When you "put a picture into an album," its name is added to a list of pictures from the Library that display together when the album is clicked, kind of like a music playlist, but for pictures. So two albums can both have the same picture name in their lists (like two playlists with the same song,)  and that picture will show up when you click either album, but there's only one picture file-- it's just on multiple lists. And when you remove a picture from an album, its name remains in the lists of other albums, and the file still remains in your Library. 

So albums give a specific view of your pictures. The picture of "Aunt Ethel at the Grand Canyon" can be in the "Aunt Ethel" album with other pictures of Aunt Ethel, and it can also be in the "Grand Canyon"  album with pictures of other people at the Grand Canyon. And it can also be in a the "September 2015" album with other things that happened then. Each album is pointing to a single file stored in the Photos Library, so having pictures in multiple albums takes up no more storage space. As you can imagine, this is very powerful in organizing pictures.

So, to your question: if you have two identical pictures in your Library, and lets say they are each in their own albums, then you can add them to each other's albums, and then delete one of them from the Library. The remaining picture will be in both albums.

The Merge button in the Duplicates view in the Utilities section does exactly that. Merging two pictures that may be in different albums deletes one and puts the other in all the albums that had either of them. Before using Merge, you probably want to be sure that the pictures have the same location, the same caption, the same keywords, and the same title so you don't lose any of that information that might have been with only one of them.

Is this what you wanted to do?

Is there anyway to delete a duplicate photo from the Library and leave them in their assigned albums

Short answer: No. Why? Because it's not a duplicate. It's the same photo, the same file.

Long Answer: Photos, (like iPhoto, Aperture, Music, iTunes) is a database. This means it can be very flexible and powerful, if sometimes a little confusing. The library is the core of the app. Every image is in the library. Albums are virtual, and are just subsets of the library. In fact, Albums are not places, they are lists - instructions to the app to 'display this group of images together'. So images do not get "moved" to Albums, they get added to that particular list. This means that an image can be in more than one album but use no extra disk space. Similarly in the Music app, all the tracks are in the Library and can be added to any number of playlists.

On a Mac:

You can see which items are not in an album simply by filtering using the ‘Not in Any Album’ criterion. Or on earlier versions a simple Smart Album

File -> New Smart Album

Album -> Is Not -> Any

will find these images. As you add them to albums they will disappear from the Smart Album.

On iPad or iPhone, which do not currently support Smart Albums, since iOS 18.3 identify images not in any album using a filter:

On the main screen tap on the up/arrow and select filter: Not in An Album. Further, you can check the bottom of the Info panel of a photograph for any albums that the image is currently added to.