Ordering on the probability simplex of endmembers for hyperspectral morphological image processing
International audience 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 posi...
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ftccsdartic:oai:HAL:hal-01104250v2 2023-05-15T16:49:50+02:00 Ordering on the probability simplex of endmembers for hyperspectral morphological image processing Franchi, Gianni Angulo, Jesus Centre de Morphologie Mathématique (CMM) MINES ParisTech - École nationale supérieure des mines de Paris Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL) Reykjavik, Iceland 2015 https://hal.archives-ouvertes.fr/hal-01104250 https://hal.archives-ouvertes.fr/hal-01104250v2/document https://hal.archives-ouvertes.fr/hal-01104250v2/file/Article_ordre_v1.pdf https://doi.org/10.1007/978-3-319-18720-4_35 en eng HAL CCSD info:eu-repo/semantics/altIdentifier/doi/10.1007/978-3-319-18720-4_35 hal-01104250 https://hal.archives-ouvertes.fr/hal-01104250 https://hal.archives-ouvertes.fr/hal-01104250v2/document https://hal.archives-ouvertes.fr/hal-01104250v2/file/Article_ordre_v1.pdf doi:10.1007/978-3-319-18720-4_35 info:eu-repo/semantics/OpenAccess International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing https://hal.archives-ouvertes.fr/hal-01104250 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⟩ learning an order Hyperspectral image quantum information mathematical morphology [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing [INFO.INFO-IT]Computer Science [cs]/Information Theory [cs.IT] [MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM] [STAT]Statistics [stat] info:eu-repo/semantics/conferenceObject Conference papers 2015 ftccsdartic https://doi.org/10.1007/978-3-319-18720-4_35 2021-11-21T03:12:38Z International audience 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. Conference Object Iceland Archive ouverte HAL (Hyper Article en Ligne, CCSD - Centre pour la Communication Scientifique Directe) 410 421 |
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Archive ouverte HAL (Hyper Article en Ligne, CCSD - Centre pour la Communication Scientifique Directe) |
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language |
English |
topic |
learning an order Hyperspectral image quantum information mathematical morphology [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing [INFO.INFO-IT]Computer Science [cs]/Information Theory [cs.IT] [MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM] [STAT]Statistics [stat] |
spellingShingle |
learning an order Hyperspectral image quantum information mathematical morphology [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing [INFO.INFO-IT]Computer Science [cs]/Information Theory [cs.IT] [MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM] [STAT]Statistics [stat] Franchi, Gianni Angulo, Jesus Ordering on the probability simplex of endmembers for hyperspectral morphological image processing |
topic_facet |
learning an order Hyperspectral image quantum information mathematical morphology [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing [INFO.INFO-IT]Computer Science [cs]/Information Theory [cs.IT] [MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM] [STAT]Statistics [stat] |
description |
International audience 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. |
author2 |
Centre de Morphologie Mathématique (CMM) MINES ParisTech - École nationale supérieure des mines de Paris Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL) |
format |
Conference Object |
author |
Franchi, Gianni Angulo, Jesus |
author_facet |
Franchi, Gianni Angulo, Jesus |
author_sort |
Franchi, Gianni |
title |
Ordering on the probability simplex of endmembers for hyperspectral morphological image processing |
title_short |
Ordering on the probability simplex of endmembers for hyperspectral morphological image processing |
title_full |
Ordering on the probability simplex of endmembers for hyperspectral morphological image processing |
title_fullStr |
Ordering on the probability simplex of endmembers for hyperspectral morphological image processing |
title_full_unstemmed |
Ordering on the probability simplex of endmembers for hyperspectral morphological image processing |
title_sort |
ordering on the probability simplex of endmembers for hyperspectral morphological image processing |
publisher |
HAL CCSD |
publishDate |
2015 |
url |
https://hal.archives-ouvertes.fr/hal-01104250 https://hal.archives-ouvertes.fr/hal-01104250v2/document https://hal.archives-ouvertes.fr/hal-01104250v2/file/Article_ordre_v1.pdf https://doi.org/10.1007/978-3-319-18720-4_35 |
op_coverage |
Reykjavik, Iceland |
genre |
Iceland |
genre_facet |
Iceland |
op_source |
International Symposium on Mathematical Morphology and Its Applications to Signal and Image Processing https://hal.archives-ouvertes.fr/hal-01104250 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⟩ |
op_relation |
info:eu-repo/semantics/altIdentifier/doi/10.1007/978-3-319-18720-4_35 hal-01104250 https://hal.archives-ouvertes.fr/hal-01104250 https://hal.archives-ouvertes.fr/hal-01104250v2/document https://hal.archives-ouvertes.fr/hal-01104250v2/file/Article_ordre_v1.pdf doi:10.1007/978-3-319-18720-4_35 |
op_rights |
info:eu-repo/semantics/OpenAccess |
op_doi |
https://doi.org/10.1007/978-3-319-18720-4_35 |
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410 |
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421 |
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