An Alternative Definition for Digital Convexity


This paper proposes full convexity as an alternative definition of digital convexity, which is valid in arbitrary dimension. It solves many problems related to its usual de nitions, like possible non connectedness or non simple connectedness, while encompassing its desirable features. Fully convex sets are digitally convex, but are connected and simply connected. They have a morphological characterisation, which induces a simple convexity test algorithm. Arithmetic planes are fully convex too. We obtain a natural de nition of tangent subsets to a digital surface, which gives rise to the tangential cover in 2D, and to its extensions in arbitrary dimension. Finally it leads to a simple algorithm for building a polygonal mesh from a set of digital points.

Discrete Geometry and Mathematical Morphology - First International Joint Conference, DGMM 2021, Uppsala, Sweden, May 24-27, 2021, Proceedings, volume 12708 of Lecture Notes in Computer Science, pp 269–282, 2021. Springer
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.