Topological properties of thinning in 2-D pseudomanifolds

Nicolas Passat (1) , Michel Couprie (2) , Loïc Mazo (1) , Gilles Bertrand (2)

1 LSIIT - Laboratoire des Sciences de l'Image, de l'Informatique et de la Télédétection
2 LIGM - Laboratoire d'Informatique Gaspard-Monge

Preserving topological properties of objects during thinning procedures is an important issue in the field of image analysis. In the case of 2-D digital images (i.e. images defined on Z^2) such procedures are usually based on the notion of simple point. In contrast to the situation in Z^n , n>=3, it was proved in the 80s that the exclusive use of simple points in Z^2 was indeed sufficient to develop thinning procedures providing an output that is minimal with respect to the topological characteristics of the object. Based on the recently introduced notion of minimal simple set (generalising the notion of simple point), we establish new properties related to topology-preserving thinning in 2-D spaces which extend, in particular, this classical result to cubical complexes in 2-D pseudomanifolds.

Keywords: simple sets; simple points; topology preservation; confluence; pseudomanifolds; collapse; cubical complexes

Domains: Geometric Topology [math.GT]; Computer Vision and Pattern Recognition [cs.CV]

Nicolas Passat, Michel Couprie, Loïc Mazo, Gilles Bertrand. Topological properties of thinning in 2-D pseudomanifolds. Journal of Mathematical Imaging and Vision, 2010, 37 (1), pp.27-39. ⟨10.1007/s10851-010-0190-x⟩. ⟨hal-00622471⟩