The project CoMeDiC is funded by the ANR. CoMeDiC stands for Convergent Metrics for Digital Calculus.
The CoMeDiC project aims at filling the gap between discrete calculus and standard calculus in the case of the digital space Zn. The global idea is to reliably estimate a metric on digital curves and surfaces such that solving PDEs on these domains with discrete calculus converges toward standard calculus solutions. This approach, a kind of digital calculus, is now conceivable due to recent progresses in digital geometry about the multigrid convergence of length, area, normal and even curvature estimators. Such estimators should induce convergent metrics for many different subsets of digital spaces. Digital calculus would then address an important bottleneck faced by most standard numerical discretization schemes: how to handle variational problems involving objects or functions of dimension k < n (e.g. surfaces in R3 or Z3, curves on surfaces, etc). This project focuses on three domains of application for digital calculus — image analysis, digital geometry processing and shape optimization — both to guide and nourish theoretical developments, as well as to serve as testbed for digital calculus.