Hausdorff distances between distributions using optimal transport and mathematical morphology
International audience In this paper we address the question of defining and com-puting Hausdorff distances between distributions in a general sense. Weexhibit some links between Prokhorov-Levy distances and dilation-baseddistances. In particular, mathematical morphology provides an elegantway to de...
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ftunivnantes:oai:HAL:hal-01172192v1 2023-05-15T16:48:55+02:00 Hausdorff distances between distributions using optimal transport and mathematical morphology Bloch, Isabelle Atif, J. Image, Modélisation, Analyse, GEométrie, Synthèse (IMAGES) Laboratoire Traitement et Communication de l'Information (LTCI) Institut Mines-Télécom Paris (IMT)-Télécom Paris-Institut Mines-Télécom Paris (IMT)-Télécom Paris Département Traitement du Signal et des Images (TSI) Télécom ParisTech-Centre National de la Recherche Scientifique (CNRS) Université Paris Dauphine-PSL Université Paris sciences et lettres (PSL) Reykjavik, Iceland 2015-07 https://hal-imt.archives-ouvertes.fr/hal-01172192 https://doi.org/10.1007/978-3-319-18720-4_44 en eng HAL CCSD info:eu-repo/semantics/altIdentifier/doi/10.1007/978-3-319-18720-4_44 hal-01172192 https://hal-imt.archives-ouvertes.fr/hal-01172192 doi:10.1007/978-3-319-18720-4_44 12th International Symposium on Mathematical Morphology https://hal-imt.archives-ouvertes.fr/hal-01172192 12th International Symposium on Mathematical Morphology, Jul 2015, Reykjavik, Iceland. pp.522-534, ⟨10.1007/978-3-319-18720-4_44⟩ spatial relations Levy distances Prokhorov Hausdorff fuzzy mathematical morphology Comparison of distributions optimal transport mathemat- ical morphology [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV] [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI] info:eu-repo/semantics/conferenceObject Conference papers 2015 ftunivnantes https://doi.org/10.1007/978-3-319-18720-4_44 2023-03-01T06:35:53Z International audience In this paper we address the question of defining and com-puting Hausdorff distances between distributions in a general sense. Weexhibit some links between Prokhorov-Levy distances and dilation-baseddistances. In particular, mathematical morphology provides an elegantway to deal with periodic distributions. The case of possibility distribu-tions is addressed using fuzzy mathematical morphology. As an illustra-tion, the proposed approaches are applied to the comparison of spatialrelations between objects in an image or a video sequence, when theserelations are represented as distributions. Conference Object Iceland Université de Nantes: HAL-UNIV-NANTES Levy ENVELOPE(-66.567,-66.567,-66.320,-66.320) 522 534 |
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Open Polar |
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Université de Nantes: HAL-UNIV-NANTES |
op_collection_id |
ftunivnantes |
language |
English |
topic |
spatial relations Levy distances Prokhorov Hausdorff fuzzy mathematical morphology Comparison of distributions optimal transport mathemat- ical morphology [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV] [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI] |
spellingShingle |
spatial relations Levy distances Prokhorov Hausdorff fuzzy mathematical morphology Comparison of distributions optimal transport mathemat- ical morphology [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV] [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI] Bloch, Isabelle Atif, J. Hausdorff distances between distributions using optimal transport and mathematical morphology |
topic_facet |
spatial relations Levy distances Prokhorov Hausdorff fuzzy mathematical morphology Comparison of distributions optimal transport mathemat- ical morphology [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV] [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI] |
description |
International audience In this paper we address the question of defining and com-puting Hausdorff distances between distributions in a general sense. Weexhibit some links between Prokhorov-Levy distances and dilation-baseddistances. In particular, mathematical morphology provides an elegantway to deal with periodic distributions. The case of possibility distribu-tions is addressed using fuzzy mathematical morphology. As an illustra-tion, the proposed approaches are applied to the comparison of spatialrelations between objects in an image or a video sequence, when theserelations are represented as distributions. |
author2 |
Image, Modélisation, Analyse, GEométrie, Synthèse (IMAGES) Laboratoire Traitement et Communication de l'Information (LTCI) Institut Mines-Télécom Paris (IMT)-Télécom Paris-Institut Mines-Télécom Paris (IMT)-Télécom Paris Département Traitement du Signal et des Images (TSI) Télécom ParisTech-Centre National de la Recherche Scientifique (CNRS) Université Paris Dauphine-PSL Université Paris sciences et lettres (PSL) |
format |
Conference Object |
author |
Bloch, Isabelle Atif, J. |
author_facet |
Bloch, Isabelle Atif, J. |
author_sort |
Bloch, Isabelle |
title |
Hausdorff distances between distributions using optimal transport and mathematical morphology |
title_short |
Hausdorff distances between distributions using optimal transport and mathematical morphology |
title_full |
Hausdorff distances between distributions using optimal transport and mathematical morphology |
title_fullStr |
Hausdorff distances between distributions using optimal transport and mathematical morphology |
title_full_unstemmed |
Hausdorff distances between distributions using optimal transport and mathematical morphology |
title_sort |
hausdorff distances between distributions using optimal transport and mathematical morphology |
publisher |
HAL CCSD |
publishDate |
2015 |
url |
https://hal-imt.archives-ouvertes.fr/hal-01172192 https://doi.org/10.1007/978-3-319-18720-4_44 |
op_coverage |
Reykjavik, Iceland |
long_lat |
ENVELOPE(-66.567,-66.567,-66.320,-66.320) |
geographic |
Levy |
geographic_facet |
Levy |
genre |
Iceland |
genre_facet |
Iceland |
op_source |
12th International Symposium on Mathematical Morphology https://hal-imt.archives-ouvertes.fr/hal-01172192 12th International Symposium on Mathematical Morphology, Jul 2015, Reykjavik, Iceland. pp.522-534, ⟨10.1007/978-3-319-18720-4_44⟩ |
op_relation |
info:eu-repo/semantics/altIdentifier/doi/10.1007/978-3-319-18720-4_44 hal-01172192 https://hal-imt.archives-ouvertes.fr/hal-01172192 doi:10.1007/978-3-319-18720-4_44 |
op_doi |
https://doi.org/10.1007/978-3-319-18720-4_44 |
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522 |
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534 |
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1766038997430173696 |