How many unique images are mathematically possible given the perceptive ability of the human eye?
If you have a combination lock like this
you have 4 spaces (r) and 10 possible options on each of those spaces (n). The formula to get this is called a permutation with repetition, in this case nr
Let's say we have a big 4k monitor 4096x2160 displaying 24bit images.
Let's say the total number of rods is 110,000,000 but some people say that the human eye cannot distinguish more than 30-40 shades of gray, so this would be:
(50)110,000,000 for black and white images.
and (100,000,000) 6,400,000 for colour images. (100 shades of r, g, b, and 6,400,000 cones.)
I'm not an anathomist, so I don't know if all the cells are taking into account when seeing an image, or details like that. But you can do your own math with the medical references you choose.
Another method would be taking into account the angular resolution of the human vision and what is the neccesary coverage angle to see all the presented image as an environmental surrounding, density, psychology, etc.
I'm sure the images are less than those numbers because when you see a face with 1 pixel variation, it is the same face.
When people see pictures of similar photos of persons of a race different from their own or that they are not used to it is hard to distinguish from one to another.
Your question is unanswerable, other than a vague "extremely large number".
Defining "uniquely discernable" is not possible. If I show you an all-black 512x512 image, how much white do I need to add until 10 people say "it's different"? If I use Lena instead, and shift the feathers from purple to bluish-purple, where is the change line? If it's a gamma change will viewers see it as the same image?
If I start with black and raise the luminance over an hour the threshold of "different" will be much higher than if 2 images are side-by-side.
The human sensory system is a bit complicated to summarize in a Q&A format. But here goes:
First you have to realize that there's quite a lot of variation in humans. Hell some people can actually see four colors (see this, for a light explanation), while others only one or two. So to answer the question properly you would have to define what is a human you want to mathematically model.
Second human senses are relative to change. This means essentially that sometimes humans can sense a change while sometimes not. The sensory apparatus is also prone to interpretation error. A good example is the blue or white dress, discussion.
Third human eyes and optic are extremely sophisticated information processing units (yes that's right processing starts immediately on the retina). So while you could say that the human can discern a bit over 300 PPI* that's not exactly a true measure of the sensitivity. Because human eye has cell groupings that sense straight lines so the kind of matrix grid we use is sometimes seen even if it over exceeds our resolution target.
Once you can answer these and many more questions your ready to answer your question. Some estimates exist, but in general this is a topic that's worth a PHD or two.
* somebody had a great answer with exact breakdown of ranges, dpi and human vusal resolution on GD.SE can you find it?