How to Peel Fully Convex Digital Sets

Full convexity is an interesting alternative to classical digital convexity since it guarantees connectedness and even simple connectedness in digital spaces $\mathbb{Z}^d$, for any dimension $d$. This paper aims at giving a better understanding of the monotonicity properties of fully convex digital sets, since earlier works showed that the question was difficult for thin fully convex sets. To decipher the hierarchy of fully convex sets ordered by inclusion, we study how we can peel a fully convex set pro- gressively while keeping its full convexity. We provide a characterization of peelable points and fast algorithms to identify them. Furthermore we show that fully convex set can be peeled one point at a time till reduced to the empty set, similarly to digitally convex sets in the classical sense. The peeling of a fully convex set can be seen as an analog to homotopic thinning processes, but with an additional geometric property.

Discrete Geometry and Mathematical Morphology - 4th International Joint Conference, {DGMM} 2025, Groningen, The Netherlands, November 3-6, 2025, Proceedings, volume 16296 of Lecture Notes in Computer Science, pp 77–89, 2025. Springer