[Formulation en transformation finie du principe d’écart d’équilibre discret : application à la régularisation mécanique pour le suivi de mouvement]
Le principe de l’écart d’équilibre offre un bon compromis entre la robustesse et la précision pour la régularisation du suivi du mouvement, car il impose simplement que le mouvement suivi corresponde à celui d’un corps se déformant sous l’effet de charges arbitraires. Cet article présente une extension du principe de l’écart d’équilibre dans le cadre des grandes déformations, un nouveau terme de régularisation pour contrôler les tractions de surface, les deux dans le contexte du suivi de mouvement par éléments finis, et une reformulation « problème inverse » cohérente du problème de suivi de mouvement avec régularisation mécanique. Les performances de suivi de la méthode proposée, avec une résolution de déplacement allant jusqu’à la taille du pixel de l’image, sont démontrées sur des images synthétiques représentant divers mouvements avec différents rapports signal-sur-bruit.
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The equilibrium gap principle offers a good trade-off between robustness and accuracy for regularizing motion tracking, as it simply enforces that the tracked motion corresponds to a body deforming under arbitrary loadings. This paper introduces an extension of the equilibrium gap principle in the large deformation setting, a novel regularization term to control surface tractions, both in the context of finite element motion tracking, and an inverse problem consistent reformulation of the tracking problem. Tracking performance of the proposed method, with displacement resolution down to the pixel size, is demonstrated on synthetic images representing various motions with various signal-to-noise ratios.
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Mot clés : Suivi de mouvement, Régularisation mécanique, Principe de l’écart d’équilibre, Méthode des éléments finis, Problèmes inverses
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@article{CRMECA_2023__351_G2_429_0,
author = {Martin Genet},
title = {Finite strain formulation of the discrete equilibrium gap principle: application to mechanically consistent regularization for large motion tracking},
journal = {Comptes Rendus. M\'ecanique},
pages = {429--458},
publisher = {Acad\'emie des sciences, Paris},
volume = {351},
year = {2023},
doi = {10.5802/crmeca.228},
language = {en},
}
TY - JOUR AU - Martin Genet TI - Finite strain formulation of the discrete equilibrium gap principle: application to mechanically consistent regularization for large motion tracking JO - Comptes Rendus. Mécanique PY - 2023 SP - 429 EP - 458 VL - 351 PB - Académie des sciences, Paris DO - 10.5802/crmeca.228 LA - en ID - CRMECA_2023__351_G2_429_0 ER -
%0 Journal Article %A Martin Genet %T Finite strain formulation of the discrete equilibrium gap principle: application to mechanically consistent regularization for large motion tracking %J Comptes Rendus. Mécanique %D 2023 %P 429-458 %V 351 %I Académie des sciences, Paris %R 10.5802/crmeca.228 %G en %F CRMECA_2023__351_G2_429_0
Martin Genet. Finite strain formulation of the discrete equilibrium gap principle: application to mechanically consistent regularization for large motion tracking. Comptes Rendus. Mécanique, Volume 351 (2023), pp. 429-458. doi : 10.5802/crmeca.228. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.228/
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