Constructing a braid of partitions from hierarchies of partitions

From LRDE

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 workwe 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. Howeverwe 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.

Documents

Bibtex (lrde.bib)

@InProceedings{	  tochon.19.ismm,
  author	= {Guillaume Tochon and Mauro {Dalla Mura} and Jocelyn
		  Chanussot},
  title		= {Constructing a braid of partitions from hierarchies of
		  partitions},
  booktitle	= {Mathematical Morphology and Its Application to Signal and
		  Image Processing -- Proceedings of the 14th International
		  Symposium on Mathematical Morphology (ISMM)},
  year		= 2019,
  series	= {Lecture Notes in Computer Science Series},
  address	= {Saarbr\"ucken, Germany},
  publisher	= {Springer},
  pages		= {1--12},
  month		= jul,
  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.}
}