Binary Partition Trees-based spectral-spatial permutation ordering

Miguel Angel Veganzones (1, 2) , Mauro Dalla Mura (1) , Guillaume Tochon (1) , Jocelyn Chanussot (1)

1 GIPSA-SIGMAPHY - GIPSA - Signal Images Physique
2 GIPSA-CICS - GIPSA - Communication Information and Complex Systems

Mathematical Morphology (MM) is founded on the mathematical branch of Lattice Theory. Morphological operations can be described as mappings between complete lattices, and complete lattices are a type of partially-ordered sets (poset). Thus, the most elementary requirement to define morphological operators on a data domain is to establish an ordering of the data. MM has been very successful defining image operators and filters for binary and gray-scale images, where it can take advantage of the natural ordering of the sets {0, 1} and Z +. For multivariate data, i.e. RGB or hyperspectral images, other orderings such as reduced orderings (R-orderings) have been proposed. Anyway, all these orderings are based solely on sorting the spectral set of values. Here, we propose to define an ordering based on both, the spectral and the spatial information, by means of a binary partition tree (BPT) representation of images. This novel ordering takes into account not only the spectral ordering but also the hierarchies of spatial structures encoded in the BPT.

Mots clés: Binary Partition Trees; Lattice Theory; Spectral Spatial analysis; Ordering; Mathematical Morphology

Domaines: Traitement du signal et de l'image [eess.SP]

Miguel Angel Veganzones, Mauro Dalla Mura, Guillaume Tochon, Jocelyn Chanussot. Binary Partition Trees-based spectral-spatial permutation ordering. ISMM 2015 - 12th International Symposium on Mathematical Morphology, May 2015, Reykjavik, Iceland. pp.434-445, ⟨10.1007/978-3-319-18720-4_37⟩. ⟨hal-01121187⟩