Full convexity for polyhedral models in digital spaces


In a recent work, full convexity has been proposed as an alternative definition of digital convexity. It solves many problems related to its usual definitions, for instance: fully convex sets are digitally convex in the usual sense, but are also connected and simply connected. However, full convexity is not a monotone property hence intersections of fully convex sets may be neither fully convex nor connected. This defect might forbid digital polyhedral models with fully convex faces and edges. This can be detrimental since classical standard and naive planes are fully convex. We propose in this paper an envelope operator which solves in arbitrary dimension the problem of extending a digital set into a fully convex set. This extension naturally leads to digital polyhedra whose cells are fully convex. We present first a generic envelope operator which add points in required directions in parallel and prove that it builds a fully convex set. Then a relative envelope operator is proposed, which can be used to force digital planarity of fully convex sets. We provide experiments showing that our method produces coherent polyhedral models for any polyhedron in arbitrary dimension.

Discrete Geometry and Mathematical Morphology - Second International Joint Conference, DGMM 2022, Strasbourg, France, Oct 24-27, 2022, Proceedings, pp 98-109, volume 13493 of Lecture Notes in Computer Science, 2022, Springer, Cham.
Jacques-Olivier Lachaud
Jacques-Olivier Lachaud
Professor of Computer Science

My research interests include digital geometry, geometry processing, image analysis, variational models and discrete calculus.