Unlike in continuous geometry the notion of convexity is not clearly defined in digital geometry. Arguably, the most natural definition of digital convexity is to say that a lattice set S in Z^d is digital convex if S is equal to the intersection of its convex hull with Z^D. The issue with that definition that motivated the investigation of alternate definition is that it does not ensure any connectivity properties for S (in terms of induced grid subgraph). In this talk we study some computational geometry problems such as the potato peeling problem and the recognition problem in the digital world using this definition of digital convexity. We also study unimodular affine transformations (the set of lattice preserving affine transformation) and their consequences on the connectivity of digital convex sets.
Bio: After working 4 years as a software developer and 2 years as a math teacher, Loïc Crombez took his PhD, and then 1 year as an ATER at Université Clermont Auvergne – LIMOS where he worked on algorithmic problems at the intersection of computational and digital geometry. This work rewarded him the best student paper award in DGCI 2019.
Amphithéâtre 260 (ESIEE Paris)