How to estimate eye-in-head rotation (degrees of visual angle) from a 2D video of the eye?

Question

I am tracking eye movements in mice passively viewing naturalistic stimuli or experimental stimuli meant to elicit reflexive eye movements. I would like to define a transformation function that translates displacement in pixels (x, y) to degrees of visual angle (azimuth, elevation). Here is an example image:

I have seen this paper referenced several times in other papers that track eye movements in mice, but it seems like the position of my cameras relative to the eye is different than what is shown in the paper and I worry this will affect the validity of the transformation.

I have the ability to track any feature of the eye that is useful. Right now I am tracking the center of the pupil, the corners of the eye, and the center of the top and bottom eyelid.

EDIT #1

Here is a description of the camera's position relative to the animal. The solid black object represents the animal (A=anterior, P=posterior, D=dorsal, V=ventral). The angle from each orientation represents the angle from the animal to the camera.

Answer 1

In theory you can use the geometry of your setup to transform your data to the orientation reffered in the paper you mentioned using Scheimpflug Principle and then use the methods provided in it.

Practically, you can only approximate the geometry of your setup. If you have some idea about angles in something like this

please let me know, I might be able to do the math for you.

EDIT: The lens plane is parallel to image plane in cameras so now it is just the question of orientation of subject plane and lens plane(camera plane).