Digital convexity preserving pixelwise deformation

Convexity is one of useful geometric properties of digital sets in digital image processing. There are various applications which require deforming digital convex sets while preserving their convexity. In this talk, we first present various definitions of digital convexity and their relationships. We then choose one of them with the aim of deforming a digital convex set by adding and/or removing digital points one by one while preserving its digital convexity. For realizing such pixelwise deformations, we introduce the notions of removable and insertable pixels, which are characterized using combinatorics on the boundary words of digital convex shapes. These characterizations enable us to choose one of removable and insertable pixels for each deformation step with some additional geometric constraint and to update each digital convex shape efficiently. We also show that, given any pair of digital convex sets, there always exists at least one sequence of digital convex sets, which is a deformation between them.

In collaboration with: Lama Tarssisi (LIGM), David Coeurjolly (LIRIS), Pascal Romon (LAMA), Jean-Pierre Borel (XLIM), Hadjer Djerroumi (LIGM).

Attention à la salle ! c’est la salle de séminaire S3 247, couloir de Math, 2ème étage. (car la salle S3 351 qui vient d’être repeinte n’a pas encore de tableau ni d’écran…)