Abstract
To improve our understanding of how deformable objects are transported in flows, it is necessary to develop new experimental tools capable of accurately measuring the evolution of their deformations. We present a reconstruction process for sheet-like objects utilizing Thin-Plate Splines (TPS), providing access to the object’s 3D position and deformation over time. We tested the technique on a simple configuration: a thin-heavy-flexible disc within a vortical flow driven by impellers in a cubic tank. The vortical flow field is characterized using Particle Image Velocimetry (PIV) and is seen to be well approximated as a Lamb–Oseen vortex within the volume of reconstruction. The disc is imaged using three cameras, which are calibrated using the pinhole model. The reconstruction process uses shape-from-silhouette to define an initial 3D reconstruction, which is subsequently refined by minimizing a cost function based on physical and visual criteria. This process is shown to be generalizable to other thin geometries, offering a starting point toward studying the dynamics of more complex sheet-like objects, such as plastic pollutants and vegetation.
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Availability of data and materials
Data used in the production of this paper can be obtained by contacting E. Ibarra or G. Verhille. The MATLAB toolset used to generate Thin-Plate Splines, as written by A. Bartoli, is available under Deformable Image Registration—[GTPSW: Generalized Thin-Plate Spline Warps] at: http://encov.ip.uca.fr/ab/code_and_datasets/.
Notes
Due to the quality of the lenses used and the sphere’s size in combination with its distance from each of the cameras, image distortions and the effect of local perspective are negligible.
References
Agrawal A, Ramalingam S, Taguchi Y, and Chari V (2012) A theory of multi-layer flat refractive geometry. In: 2012 IEEE conference on computer vision and pattern recognition. IEEE, pp 3346–3353. https://doi.org/10.1109/CVPR.2012.6248073
Allende S, Henry C, Bec J (2020) Dynamics and fragmentation of small inextensible fibres in turbulence. Phil Trans R Soc A 378(2175):20190398. https://doi.org/10.1098/rsta.2019.0398
Bartoli A, Perriollat M, Chambon S (2010) Generalized thin-plate spline warps. Int J Comput Vis 88:85–110. https://doi.org/10.1007/s11263-009-0303-4
Bookstein FL (1989) Principal warps: thin-plate splines and the decomposition of deformations. IEEE Trans Pattern Anal Mach Intell 11(6):567–585. https://doi.org/10.1109/34.24792
Brouzet C, Guiné R, Dalbe M-J, Favier B, Vandenberghe N, Villermaux E, Verhille G (2021) Laboratory model for plastic fragmentation in the turbulent ocean. Phys Rev Fluids 6(2):024601. https://doi.org/10.1103/PhysRevFluids.6.024601
Cheung K-M, Baker S, Kanade T (2005) Shape-from-silhouette across time part I: theory and algorithms. Int J Comput Vis 62:221–247. https://doi.org/10.1007/s11263-005-4881-5
De La Rosa Zambrano HM, Verhille G, Le Gal P (2018) Fragmentation of magnetic particle aggregates in turbulence. Phys Rev Fluids 3:084605. https://doi.org/10.1103/PhysRevFluids.3.084605
DiBenedetto MH, Ouellette NT, Koseff JR (2018) Transport of anisotropic particles under waves. J Fluid Mech 837:320–340. https://doi.org/10.1017/jfm.2017.853
Duchon J (1976) Interpolation des fonctions de deux variables suivant le principe de la flexion des plaques minces. Rev Franç d’Automat, Informat, Tech Opérat. Anal Numér 10(R3):5–12
Faugeras, O, Luong QT (2001) The geometry of multiple images: the laws that govern the formation of multiple images of a scene and some of their applications. MIT Press
Hartley R, Zisserman A (2003) Multiple view geometry in computer vision. Cambridge University Press
Heyes A, Jones R, Smith D (2004) Wandering of wing-tip vortices. In: Proceedings of the 12th international symposium on applications of laser techniques to fluid mechanics, pp 35–43
Lamb H (1945) Hydrodynamics. Victoria University of Manchester, Cambridge University Press, Dover Publications Inc., New York, Printed in the USA, Card Number 46-1891. ISBN: 0-486-60256-7
Landau LD, Lifshitz EM, Kosevich AM, Pitaevskii LP (1986) Theory of elasticity: volume 7. Elsevier
Nikolenko SI (2021) Synthetic data for deep learning, vol 174. Springer
Pan B (2018) Digital image correlation for surface deformation measurement: historical developments, recent advances and future goals. Meas Sci Technol 29(8):082001
Powers TR (2010) Dynamics of filaments and membranes in a viscous fluid. Rev Mod Phys 82(2):1607. https://doi.org/10.1103/RevModPhys.82.1607
Ronneberger O, Fischer P, Brox T (2015) U-net: convolutional networks for biomedical image segmentation. In: Medical image computing and computer-assisted intervention—MICCAI 2015: 18th international conference, Munich, Germany, October 5–9, 2015, Proceedings, Part III 18. Springer, pp 234–241. https://doi.org/10.1007/978-3-319-24574-4_28
Rozantsev A, Lepetit V, Fua P (2015) On rendering synthetic images for training an object detector. Comput Vis Image Underst 137:24–37. https://doi.org/10.1016/j.cviu.2014.12.006
Su X, Zhang Q (2010) Dynamic 3-d shape measurement method: a review. Opt Lasers Eng 48(2):191–204
Verbeek P, Van Vliet L (1993) Curvature and bending energy in digitized 2D and 3D images. In: 8th Scandinavian conference on image analysis, Tromso, Norway
Verhille G, Bartoli A (2016) 3D conformation of a flexible fiber in a turbulent flow. Exp Fluids 57(7):117. https://doi.org/10.1007/s00348-016-2201-1
Acknowledgements
The authors would like thank our colleagues Eric Bertrand and Marie-Julie Dalbe for aiding us with the 3D-printing and laser profilometer measurement of our reference disc. This work received support from the French government under the France 2030 investment plan, as part of the Initiative d’Excellence d’Aix-Marseille Université - A*MIDEX - AMX-19-IET-010. This work was carried out in the framework of NetFlex Project (ANR-21-CE30-0040) funded by the French National Research Agency (ANR).
Funding
This work received support from the French government under the France 2030 investment plan, as part of the Initiative d’Excellence d’Aix-Marseille Université - A*MIDEX - AMX-19-IET-010. This work was carried out in the framework of NetFlex Project (ANR-21-CE30-0040) funded by the French National Research Agency (ANR).
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E. Ibarra carried out the experiments and the data analysis, generated figures for the manuscript, and wrote the original manuscript. A. Bartoli and G. Verhille contributed by providing coding toolsets, guidance, and discussions needed for the work presented. All authors contributed by reviewing the manuscript.
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Ibarra, E., Adrien, B. & Gautier, V. 3D reconstruction of a thin flexible disc in a vortical flow. Exp Fluids 64, 172 (2023). https://doi.org/10.1007/s00348-023-03713-9
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DOI: https://doi.org/10.1007/s00348-023-03713-9