Digital moments approximate real moments where the accuracy depends upon grid resolution. There are theoretical results about the speed of convergence. However, there is a lack of more detailed studies with respect to selected shapes of regions, or with respect to experimental data about convergence. This paper discusses moments for specific shapes of regions, and provides some initial experimental data about measured convergence of digital moments.
"Toward experimental studies of digital moment convergence", Proc. SPIE 4117, Vision Geometry IX, (23 October 2000); doi: 10.1117/12.404810; https://doi.org/10.1117/12.404810