In lieu of neural networks and deep learning, what are some approaches to computer vision? So much software related to computer vision relies on AI and neural networks, I wonder some of the approaches which don't use those methods. How could some of the mainstays of computer vision (eg. recognition and identification) be achieved without "artificial" means?

I'm reading Vision by David Marr and it talks about the human visual system model and how it could be emulated algorithmically for computer vision. I know of salience mapping and edge detection algorithms which there's significant consensus that the brain processes visual information in a manner not too dissimilar to, but what other methods are there?

Consider something such as facial recognition: I have a headshot of hundreds of individuals, how could a system recognize if a new face was novel or previously recognized without neural networks or deep learning? My interest is in white-box approaches to computer vision rather than these black-box approaches.
I think you could use some type of probabilistic model to solve this issue. I might be completely wrong, though, as I do not know a lot about probabilistic models.

Some time ago, I made use of Markov chains to generate levels for a game called Mega Man, and I remember that the results were promising, so I looked up "Markov Chains and face recognition" and found the following paper:

http://www.anefian.com/research/nefian98_face.pdf

It deals with the specific problem of face recognition.

Markov Chains also work with Optical Character Recognition, and though I know that comparing a letter to a face is a bit of a stretch, the following paper might give you some insight.

http://www.aclweb.org/anthology/N03-1018

I hope that helps!