Constructing a braid of partitions from hierarchies of partitions

Abstract

Braids of partitions have been introduced in a theoretical framework as a generalization of hierarchies of partitions, but practical guidelines to derive such structures remained an open question. In a previous work, we proposed a methodology to build a braid of partitions by experimentally composing cuts extracted from two hierarchies of partitions, notably paving the way for the hierarchical representation of multimodal images. However, we did not provide the formal proof that our proposed methodology was yielding a braid structure. We remedy to this point in the present paper and give a brief insight on the structural properties of the resulting braid of partitions.