A proper generalized decomposition approach for optical flow estimation
| hal.structure.identifier | Laboratoire des Sciences de l'Ingénieur pour l'Environnement - UMR 7356 [LaSIE] | |
| dc.contributor.author | EL HAMIDI, Abdallah | |
| hal.structure.identifier | Laboratoire des Sciences de l'Ingénieur pour l'Environnement - UMR 7356 [LaSIE] | |
| dc.contributor.author | SALEH, Marwan | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | PAPADAKIS, Nicolas | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | DENIS DE SENNEVILLE, Baudouin | |
| dc.date.accessioned | 2024-04-04T02:48:56Z | |
| dc.date.available | 2024-04-04T02:48:56Z | |
| dc.date.issued | 2020 | |
| dc.identifier.issn | 0170-4214 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191781 | |
| dc.description.abstractEn | This paper introduces the use of the Proper Generalized Decomposition (PGD) method for the optical flow (OF) problem in a classical framework of Sobolev spaces, i.e. optical flow methods including a robust energy for the data fidelity term together with a quadratic penalizer for the regularisation term. A mathematical study of PGD methods is first presented for general regularization problems in the framework of (Hilbert) Sobolev spaces, and their convergence is then illustrated on OF computation. The convergence study is divided in two parts: (i) the weak convergence based on the Brézis-Lieb decomposition, (ii) the strong convergence based on a growth result on the sequence of descent directions. A practical PGD-based OF implementation is then proposed and evaluated on freely available OF data sets. The proposed PGD-based OF approach outperforms the corresponding non-PGD implementation in terms of both accuracy and computation time for images containing a weak level of information, namely low image resolution and/or low Signal-To-Noise Ratio (SNR). | |
| dc.language.iso | en | |
| dc.publisher | Wiley | |
| dc.subject.en | Proper Generalized Decomposition (PGD) | |
| dc.subject.en | Optical Flow | |
| dc.subject.en | Optimization | |
| dc.title.en | A proper generalized decomposition approach for optical flow estimation | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1002/mma.6275 | |
| dc.subject.hal | Mathématiques [math] | |
| dc.subject.hal | Informatique [cs]/Traitement du signal et de l'image | |
| bordeaux.journal | Mathematical Methods in the Applied Sciences | |
| bordeaux.page | 5339-5356 | |
| bordeaux.volume | 43 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 8 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-02471619 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-02471619v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Mathematical%20Methods%20in%20the%20Applied%20Sciences&rft.date=2020&rft.volume=43&rft.issue=8&rft.spage=5339-5356&rft.epage=5339-5356&rft.eissn=0170-4214&rft.issn=0170-4214&rft.au=EL%20HAMIDI,%20Abdallah&SALEH,%20Marwan&PAPADAKIS,%20Nicolas&DENIS%20DE%20SENNEVILLE,%20Baudouin&rft.genre=article |
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