Zobrazeno 1 - 10
of 29
pro vyhledávání: '"Antonio Leaci"'
Autor:
Antonio Leaci, Franco Tomarelli
Publikováno v:
Axioms, Vol 11, Iss 1, p 30 (2022)
We establish some properties of the bilateral Riemann–Liouville fractional derivative Ds. We set the notation, and study the associated Sobolev spaces of fractional order s, denoted by Ws,1(a,b), and the fractional bounded variation spaces of fract
Externí odkaz:
https://doaj.org/article/b0ee1aea0e0d44f3bc40a8e03e689e43
Autor:
Antonio Leaci, Franco Tomarelli
Publikováno v:
Advances in Continuous and Discrete Models. 2023
We introduce and study a variational model for signal and image analysis based on Riemann–Liouville fractional derivatives. Both the one-dimensional and two-dimensional cases are studied. The model exploits a quadratic fitting data term together wi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::244d161dba98543a2f1867c711fdb5d5
https://doi.org/10.1186/s13662-023-03762-8
https://doi.org/10.1186/s13662-023-03762-8
Publikováno v:
Fractional Calculus & Applied Analysis
Fractional Calculus & Applied Analysis, 2017, ⟨10.1515/fca-2017-0049⟩
Fractional Calculus & Applied Analysis, 2017, ⟨10.1515/fca-2017-0049⟩
International audience; We investigate the 1D Riemann-Liouville fractional derivative focusing on the connections with fractional Sobolev spaces, the space BV of functions of bounded variation, whose derivatives are not functions but measures andthe
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::110707a3cb06141c7ce6407afaf1b8ec
https://hal.archives-ouvertes.fr/hal-01287725
https://hal.archives-ouvertes.fr/hal-01287725
Publikováno v:
Journal de Mathématiques Pures et Appliquées. 96(1):58-87
We show Euler equations fulfilled by strong minimizers of Blake and Zisserman functional. We prove an Almansi-type decomposition and provide explicit coefficients of asymptotic expansion for bi-harmonic functions in a disk with a cut from center to b
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e1e67ea60a0d7ab98a115d4cbe11857a
Publikováno v:
Discrete & Continuous Dynamical Systems - A. 31:1129-1150
We prove density estimates and elimination properties for minimizing triplets of functionals which are related to contour detection in image segmentation and depend on free discontinuities, free gradient discontinuities and second order derivatives.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::63e6529d430b4d035f4b4efcf74cd0c6
https://doi.org/10.3934/dcds.2011.31.1129
https://doi.org/10.3934/dcds.2011.31.1129
Publikováno v:
Calculus of Variations and Partial Differential Equations. 32:81-110
We derive many necessary conditions for minimizers of a functional depending on free discontinuities, free gradient discontinuities and second derivatives, which is related to image segmentation. The results are obtained by using different kind of va
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::35f17993aaeccc614f0e252c4e15fde2
https://doi.org/10.1007/s00526-007-0129-2
https://doi.org/10.1007/s00526-007-0129-2
In a previous paper, focused on the analysis of Blake & Zisserman functional in image segmentation, we showed an Almansi-type decomposition and explicit coefficients of asymptotic expansion for bi-harmonic functions in a disk with a cut from center t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::678f43e41459790bf9760339b175dcfc
http://hdl.handle.net/11311/968008
http://hdl.handle.net/11311/968008
The aim of this work is to provide a concise survey of results about the Blake–Zisserman functional for image segmentation and inpainting. Moreover a refinement of the Almansi decomposition is shown for biharmonic functions in 2-dimensional open di
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::65eda980d88e6461fc6d001e71947a64
http://hdl.handle.net/11311/968004
http://hdl.handle.net/11311/968004
Publikováno v:
Comptes Rendus Mathematique. 334:343-348
We show some necessary conditions for minimizers of a functional depending on free discontinuities, free gradient discontinuities and second derivatives, which is related to image segmentation. A candidate for minimality of main part of the functiona
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::284bd670872c8e6b28dc8403de58b30a
https://doi.org/10.1016/s1631-073x(02)02231-8
https://doi.org/10.1016/s1631-073x(02)02231-8
We study the variational approximation of an inpainting model for 2-dimensional images which are locally damaged. The scheme provides Γ-convergence of elliptic functionals to a Dirichlet problem with free discontinuity and free gradient discontinuit
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d6606d555a355f1df826307426719c48
http://hdl.handle.net/11311/827131
http://hdl.handle.net/11311/827131