Representing 2 dimensional data for facial recognition
You are describing is a Cartesian coordinate system where each point is an ordered pair of signed numbers.

In order to compare across people, you need to define the same origin (0,0) and define all points relative to that. Typically, the origin of a face is the tip of the nose.

The input to a model would be a collection of these Cartesian coordinate pairs for each training instance. 

Google's Firebase ML-Kit has a very specific API for Face Detection  with specific facial landmarks and each point is a VisionPoint. Given the predefined, rigid, and hierarchical structure, it would be more useful to store the data as JSON to preserve the relationship between label and coordinate pair.