Abstract
Surface matching usually provides significant deformations that can lead to structural failure due to the lack of physical policy. In this context, partial surface matching of non-linear deformable bodies is crucial in engineering to govern structure deformations. In this article, we propose to formulate the registration problem as an optimal control problem using an artificial neural network where the unknown is the surface force distribution that applies to the object and the resulting deformation computed using a hyper-elastic model. The optimization problem is solved using an adjoint method where the hyper-elastic problem is solved using the feed-forward neural network and the adjoint problem is obtained through the backpropagation of the network. Our process improves the computation speed by multiple orders of magnitude while providing acceptable registration errors.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Byrd, R.H., Lu, P., Nocedal, J., Zhu, C.: A limited memory algorithm for bound constrained optimization. SIAM J. Sci. Comput. 16(5), 1190–1208 (1995). https://doi.org/10.1137/0916069
Faure, F., et al.: SOFA: a multi-model framework for interactive physical simulation. In: Payan, Y. (ed.) Soft Tissue Biomechanical Modeling for Computer Assisted Surgery. SMTEB, vol. 11, pp. 283–321. Springer, Heidelberg (2012). https://doi.org/10.1007/8415_2012_125
Haouchine, N., et al.: Impact of soft tissue heterogeneity on augmented reality for liver surgery. IEEE Trans. Visual. Comput. Graph. 21(5), 584–597 (2015). https://doi.org/10.1109/TVCG.2014.2377772
He, K., Zhang, X., Ren, S., Sun, J.: Delving deep into rectifiers: surpassing human-level performance on ImageNet classification. In: Proceedings of the IEEE International Conference on Computer Vision (ICCV) (2015)
Heiselman, J.S., Jarnagin, W.R., Miga, M.I.: Intraoperative correction of liver deformation using sparse surface and vascular features via linearized iterative boundary reconstruction. IEEE Trans. Med. Imaging 39(6), 2223–2234 (2020). https://doi.org/10.1109/TMI.2020.2967322
Khan, S., Green, R.: Gravitational-wave surrogate models powered by artificial neural networks. Phys. Rev. D 103, 064015 (2021). https://doi.org/10.1103/PhysRevD.103.064015
Malti, A., Bartoli, A., Hartley, R.: A linear least-squares solution to elastic shape-from-template. In: Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 1629–1637 (2015)
Marchesseau, S., Chatelin, S., Delingette, H.: Nonlinear biomechanical model of the liver. In: Payan, Y., Ohayon, J. (eds.) Biomechanics of Living Organs, Translational Epigenetics, vol. 1, pp. 243–265. Academic Press, Oxford (2017). https://doi.org/10.1016/B978-0-12-804009-6.00011-0
Mestdagh, G., Cotin, S.: An optimal control problem for elastic registration and force estimation in augmented surgery. In: Wang, L., Dou, Q., Fletcher, P.T., Speidel, S., Li, S. (eds.) MICCAI 2022. LNCS, pp. 74–83. Springer, Cham (2022). https://doi.org/10.1007/978-3-031-16449-1_8
Odot, A., Haferssas, R., Cotin, S.: DeepPhysics: a physics aware deep learning framework for real-time simulation. Int. J. Numer. Meth. Eng. 123(10), 2381–2398 (2022). https://doi.org/10.1002/nme.6943
Peterlík, I., et al.: Fast elastic registration of soft tissues under large deformations. Med. Image Anal. 45, 24–40 (2018). ISSN 1361–8415. https://doi.org/10.1016/j.media.2017.12.006
Pfeiffer, M., et al.: Non-rigid volume to surface registration using a data-driven biomechanical model. In: Martel, A.L., et al. (eds.) MICCAI 2020. LNCS, vol. 12264, pp. 724–734. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-59719-1_70
Plantefève, R., Peterlik, I., Haouchine, N., Cotin, S.: Patient-specific biomechanical modeling for guidance during minimally-invasive hepatic surgery. Ann. Biomed. Eng. 44(1), 139–153 (2015). https://doi.org/10.1007/s10439-015-1419-z
Renganathan, S.A., Maulik, R., Ahuja, J.: Enhanced data efficiency using deep neural networks and gaussian processes for aerodynamic design optimization. Aerosp. Sci. Technol. 111, 106522 (2021). https://doi.org/10.1016/j.ast.2021.106522
White, D.A., Arrighi, W.J., Kudo, J., Watts, S.E.: Multiscale topology optimization using neural network surrogate models. Comput. Meth. Appl. Mech. Eng. 346, 1118–1135 (2019). https://doi.org/10.1016/j.cma.2018.09.007
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Odot, A., Mestdagh, G., Privat, Y., Cotin, S. (2023). Real-Time Elastic Partial Shape Matching Using a Neural Network-Based Adjoint Method. In: Dorronsoro, B., Chicano, F., Danoy, G., Talbi, EG. (eds) Optimization and Learning. OLA 2023. Communications in Computer and Information Science, vol 1824. Springer, Cham. https://doi.org/10.1007/978-3-031-34020-8_10
Download citation
DOI: https://doi.org/10.1007/978-3-031-34020-8_10
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-34019-2
Online ISBN: 978-3-031-34020-8
eBook Packages: Computer ScienceComputer Science (R0)