Fill selection regions with the average color inside them

I'm trying to design stained glass. Photoshop has the "Stained Glass" filter, but I need a bit more flexibility than it allows.

I've used it to create the came structure:

Now I want to take my original image:

And color the regions according to it, such that there is only one color per region.

Here's the expected result:

Of course, I know I can select each region individually and posterize it, but I was hoping for something that made use of the computer a bit more.

If this is not possible within Photoshop, I'm happy to use any other graphic software for the task