@inproceedings{226c939e8c2547b9afc6fdc188ab430e,
title = "Ordering on the probability simplex of endmembers for hyperspectral morphological image processing",
abstract = "A hyperspectral image can be represented as a set of materials called endmembers, where each pixel corresponds to a mixture of several of these materials. More precisely pixels are described by the quantity of each material, this quantity is often called abundance and is positive and of sum equal to one. This leads to the characterization of a hyperspectral image as a set of points in a probability simplex. The geometry of the simplex has been particularly studied in the theory of quantum information, giving rise to different notions of distances and interesting preorders. In this paper, we present total orders based on theory of the ordering on the simplex. Thanks to this theory, we can give a physical interpretation of our orders.",
keywords = "Hyperspectral image, Learning an order, Mathematical morphology, Quantum information",
author = "Gianni Franchi and Jes{\'u}s Angulo",
note = "Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2015.; 12th International Symposium on Mathematical Morphology, ISMM 2015 ; Conference date: 27-05-2015 Through 29-05-2015",
year = "2015",
month = jan,
day = "1",
doi = "10.1007/978-3-319-18720-4\_35",
language = "English",
isbn = "9783319187198",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "410--421",
editor = "Laurent Najman and Hugues Talbot and Benediktsson, \{Jon Atli\} and Jocelyn Chanussot",
booktitle = "Mathematical Morphology and its Applications to Signal and Image Processing - 12th International Symposium, ISMM 2015, Proceedings",
}