Grain Buiding Ordering

Jean Serra (1)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge

Given a set E, the partitions of E are usually ordered by merging of classes. In segmentation procedures, this ordering often generates small parasite classes. A new ordering, called "grain building ordering", or GBO, is proposed. It requires a connection over E and states that A 4 B, with A,B ⊆ E, when each connected component of B contains a connected component of A. TheGBO applies to sets, partitions, and numerical functions. Thickenings with respect to the GBO are introduced as extensive idempotent operators that do not create connected components. The composition product of a connected opening by a thickening is still a thickening. Moreover, when {i, i ∈ I} is a granulometric family, then the two sequences { i, i ∈ I} and { i , i ∈ I}generate hierarchies, from which semi-groups can be derived. In addition,the approach allows us to combine any set of partitions or of tessellations into a synthetic one.

Domaines: Traitement des images [eess.IV]

Jean Serra. Grain Buiding Ordering. ISMM 2011, Jul 2011, Verbania-Intra, Italy. pp.37-48, ⟨10.1007/978-3-642-21569-8_4⟩. ⟨hal-00624388⟩