( max , min )-convolution and Mathematical Morphology
International audience A formal denition of morphological operators in (max, min)-algebra is introduced and their relevant properties from an algebraic viewpoint are stated. Some previous works in mathematical morphology have already encountered this type of operators but a systematic study of them...
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ftunivnantes:oai:HAL:hal-01257501v1 2023-05-15T16:49:17+02:00 ( max , min )-convolution and Mathematical Morphology Angulo, Jesus Centre de Morphologie Mathématique (CMM) Mines Paris - PSL (École nationale supérieure des mines de Paris) Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL) Reykjavik, Iceland 2015-05 https://hal.archives-ouvertes.fr/hal-01257501 https://hal.archives-ouvertes.fr/hal-01257501/document https://hal.archives-ouvertes.fr/hal-01257501/file/MaxMinConvolution_ISMM15_final.pdf https://doi.org/10.1007/978-3-319-18720-4_41 en eng HAL CCSD info:eu-repo/semantics/altIdentifier/doi/10.1007/978-3-319-18720-4_41 hal-01257501 https://hal.archives-ouvertes.fr/hal-01257501 https://hal.archives-ouvertes.fr/hal-01257501/document https://hal.archives-ouvertes.fr/hal-01257501/file/MaxMinConvolution_ISMM15_final.pdf doi:10.1007/978-3-319-18720-4_41 info:eu-repo/semantics/OpenAccess 12th International Symposium on Mathematical Morphology https://hal.archives-ouvertes.fr/hal-01257501 12th International Symposium on Mathematical Morphology, May 2015, Reykjavik, Iceland. pp.485-496, ⟨10.1007/978-3-319-18720-4_41⟩ Minkowski addition adjunction HamiltonJacobi PDE fuzzy morphology viscous morphology [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV] info:eu-repo/semantics/conferenceObject Conference papers 2015 ftunivnantes https://doi.org/10.1007/978-3-319-18720-4_41 2022-10-19T00:18:50Z International audience A formal denition of morphological operators in (max, min)-algebra is introduced and their relevant properties from an algebraic viewpoint are stated. Some previous works in mathematical morphology have already encountered this type of operators but a systematic study of them has not yet been undertaken in the morphological literature. It is shown in particular that one of their fundamental property is the equivalence with level set processing using Minkowski addition and subtraction. Theory of viscosity solutions of the Hamilton-Jacobi equation with Hamiltonians containing u and Du is summarized, in particular, the corresponding Hopf-Lax-Oleinik formulas as (max, min)-operators. Links between (max, min)-convolutions and some previous approaches of unconventional morphology, in particular fuzzy morphology and viscous morphology, are reviewed. Conference Object Iceland Université de Nantes: HAL-UNIV-NANTES 485 496 |
institution |
Open Polar |
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Université de Nantes: HAL-UNIV-NANTES |
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ftunivnantes |
language |
English |
topic |
Minkowski addition adjunction HamiltonJacobi PDE fuzzy morphology viscous morphology [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV] |
spellingShingle |
Minkowski addition adjunction HamiltonJacobi PDE fuzzy morphology viscous morphology [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV] Angulo, Jesus ( max , min )-convolution and Mathematical Morphology |
topic_facet |
Minkowski addition adjunction HamiltonJacobi PDE fuzzy morphology viscous morphology [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV] |
description |
International audience A formal denition of morphological operators in (max, min)-algebra is introduced and their relevant properties from an algebraic viewpoint are stated. Some previous works in mathematical morphology have already encountered this type of operators but a systematic study of them has not yet been undertaken in the morphological literature. It is shown in particular that one of their fundamental property is the equivalence with level set processing using Minkowski addition and subtraction. Theory of viscosity solutions of the Hamilton-Jacobi equation with Hamiltonians containing u and Du is summarized, in particular, the corresponding Hopf-Lax-Oleinik formulas as (max, min)-operators. Links between (max, min)-convolutions and some previous approaches of unconventional morphology, in particular fuzzy morphology and viscous morphology, are reviewed. |
author2 |
Centre de Morphologie Mathématique (CMM) Mines Paris - PSL (École nationale supérieure des mines de Paris) Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL) |
format |
Conference Object |
author |
Angulo, Jesus |
author_facet |
Angulo, Jesus |
author_sort |
Angulo, Jesus |
title |
( max , min )-convolution and Mathematical Morphology |
title_short |
( max , min )-convolution and Mathematical Morphology |
title_full |
( max , min )-convolution and Mathematical Morphology |
title_fullStr |
( max , min )-convolution and Mathematical Morphology |
title_full_unstemmed |
( max , min )-convolution and Mathematical Morphology |
title_sort |
( max , min )-convolution and mathematical morphology |
publisher |
HAL CCSD |
publishDate |
2015 |
url |
https://hal.archives-ouvertes.fr/hal-01257501 https://hal.archives-ouvertes.fr/hal-01257501/document https://hal.archives-ouvertes.fr/hal-01257501/file/MaxMinConvolution_ISMM15_final.pdf https://doi.org/10.1007/978-3-319-18720-4_41 |
op_coverage |
Reykjavik, Iceland |
genre |
Iceland |
genre_facet |
Iceland |
op_source |
12th International Symposium on Mathematical Morphology https://hal.archives-ouvertes.fr/hal-01257501 12th International Symposium on Mathematical Morphology, May 2015, Reykjavik, Iceland. pp.485-496, ⟨10.1007/978-3-319-18720-4_41⟩ |
op_relation |
info:eu-repo/semantics/altIdentifier/doi/10.1007/978-3-319-18720-4_41 hal-01257501 https://hal.archives-ouvertes.fr/hal-01257501 https://hal.archives-ouvertes.fr/hal-01257501/document https://hal.archives-ouvertes.fr/hal-01257501/file/MaxMinConvolution_ISMM15_final.pdf doi:10.1007/978-3-319-18720-4_41 |
op_rights |
info:eu-repo/semantics/OpenAccess |
op_doi |
https://doi.org/10.1007/978-3-319-18720-4_41 |
container_start_page |
485 |
op_container_end_page |
496 |
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1766039438212726784 |