Binary Partition Trees-based spectral-spatial permutation ordering

• Main Authors: Veganzones, Miguel Angel, Dalla Mura, Mauro, Tochon, Guillaume, Chanussot, Jocelyn
• Other Authors: GIPSA - Signal Images Physique (GIPSA-SIGMAPHY), Département Images et Signal (GIPSA-DIS), Grenoble Images Parole Signal Automatique (GIPSA-lab), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Stendhal - Grenoble 3-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Stendhal - Grenoble 3-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Grenoble Images Parole Signal Automatique (GIPSA-lab), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Stendhal - Grenoble 3-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Stendhal - Grenoble 3-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), GIPSA - Communication Information and Complex Systems (GIPSA-CICS)
• Format: Conference Object
• Language: English
• Published: HAL CCSD 2015
• Subjects: Binary Partition Trees; Lattice Theory; Spectral Spatial analysis; Ordering; Mathematical Morphology; [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing; Iceland
• Online Access: https://hal.science/hal-01121187; https://hal.science/hal-01121187/document; https://hal.science/hal-01121187/file/ISMM2015_veganzones.pdf; https://doi.org/10.1007/978-3-319-18720-4_37

International audience 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.