I am working on an estimation problem involving cameras, where the quality of a location of the camera is quantified by multiple factors: such as how many feature points (salient features in a given image) are visible in its field of view, as well as how evenly distributed they are in that space. The points are defined by their 2D coordinates in the image plane and then the challenge is to come up with a parameter that determines how evenly they're distributed throughout the image plane. The dimensions of the image are known.
If 100 points are visible in the image but if they're all in a straight line, or grouped together in a corner, it's not a very good set, but if they're distributed evenly like a checkered pattern, it's perfect. What is a good way to define a parameter for this? The first thing I thought about was a Voronoi diagram, which would intuitively (visually) inform me of the distribution but I am having trouble actually quantifying it as a number that I can pass to my algorithm.
At the end, I am looking for a number that quantifies this 'quality of distribution' of points, which will then be passed to an optimization pipeline that attempts to pick better viewpoints by minimizing (or maximizing) this number.