Ordering on the probability simplex of endmembers for hyperspectral morphological image processing

Gianni Franchi (1) , Jesus Angulo (1)

1 CMM - Centre de Morphologie Mathématique

A hyperspectral image can be represented as a set of ma-terials 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 characterize a hyper-spectral 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.

Mots clés: learning an order; Hyperspectral image; quantum information; mathematical morphology

Domaines: Traitement du signal et de l'image [eess.SP]; Théorie de l'information [cs.IT]; Mathématiques générales [math.GM]; Statistiques [stat]

Gianni Franchi, Jesus Angulo. Ordering on the probability simplex of endmembers for hyperspectral morphological image processing. International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing, 2015, Reykjavik, Iceland. pp.410-421, ⟨10.1007/978-3-319-18720-4_35⟩. ⟨hal-01104250v2⟩