Abstract
In this paper, we propose an implementation of both Large Deformation Diffeomorphic Metric Mapping (LDDMM) and Metamorphosis image registration using a semi-Lagrangian scheme for geodesic shooting. We propose to solve both problems as an inexact matching providing a single and unifying cost function. We demonstrate that for image registration the use of a semi-Lagrangian scheme is more stable than a standard Eulerian scheme. Our GPU implementation is based on PyTorch, which greatly simplifies and accelerates the computations thanks to its powerful automatic differentiation engine. It will be freely available at https://github.com/antonfrancois/Demeter_metamorphosis.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Arsigny, V., Commowick, O., Pennec, X., Ayache, N.: A log-euclidean framework for statistics on diffeomorphisms. In: Larsen, R., Nielsen, M., Sporring, J. (eds.) MICCAI 2006. LNCS, vol. 4190, pp. 924–931. Springer, Heidelberg (2006). https://doi.org/10.1007/11866565_113
Ashburner, J.: A fast diffeomorphic image registration algorithm. NeuroImage 38(1), 95–113 (2007)
Ashburner, J., Friston, K.J.: Diffeomorphic registration using geodesic shooting and Gauss–Newton optimisation. NeuroImage 55(3), 954–967 (2011)
Avants, B.B., Schoenemann, P.T., Gee, J.C.: Lagrangian frame diffeomorphic image registration: morphometric comparison of human and chimpanzee cortex. Med. Image Anal. 10(3), 397–412 (2006)
Beg, M.F., Miller, M.I., Trouvé, A., Younes, L.: Computing large deformation metric mappings via geodesic flows of diffeomorphisms. IJCV 61(2), 139–157 (2005). https://doi.org/10.1023/B:VISI.0000043755.93987.aa
Dupuis, P., Grenander, U., Miller, M.I.: Variational problems on flows of diffeomorphisms for image matching. Q. Appl. Math. 56(3), 587–600 (1998)
Efremov, A., Karepova, E., Shaydurov, V., Vyatkin, A.: A computational realization of a semi-lagrangian method for solving the advection equation. JAM 2014, 1–12 (2014)
Gooya, A., Pohl, K.M., Bilello, M., Cirillo, L., Biros, G., Melhem, E.R., Davatzikos, C.: GLISTR: Glioma image segmentation and registration. IEEE Trans. Med. Imaging 31(10), 1941–1954 (2012)
Gris, B., Chen, C., Öktem, O.: Image reconstruction through metamorphosis. Inverse Prob. 36(2), 025001 (2020)
Holm, D.D., Trouvé, A., Younes, L.: The Euler-Poincaré theory of metamorphosis. QAL 67(4), 661–685 (2009)
Liu, X., Niethammer, M., Kwitt, R., Singh, N., McCormick, M., Aylward, S.: Low-rank atlas image analyses in the presence of pathologies. IEEE Trans. Med. Imaging 34(12), 2583–2591 (2015)
Miller, M.I., Trouvé, A., Younes, L.: Geodesic shooting for computational anatomy. J. Math. Imaging Vis. 24(2), 209–228 (2006)
Richardson, C.L., Younes, L.: Metamorphosis of images in reproducing kernel Hilbert spaces. Adv. Comput. Math. 42(3), 573–603 (2015). https://doi.org/10.1007/s10444-015-9435-y
Ripollés, P., et al.: Analysis of automated methods for spatial normalization of lesioned brains. NeuroImage 60(2), 1296–1306 (2012)
Sdika, M., Pelletier, D.: Nonrigid registration of multiple sclerosis brain images using lesion inpainting for morphometry or lesion mapping. Hum. Brain Mapp. 30(4), 1060–1067 (2009)
Trouvé, A., Younes, L.: Local geometry of deformable templates. SIAM 37(1), 17–59 (2005)
Vialard, F.X., Risser, L., Rueckert, D., Cotter, C.J.: Diffeomorphic 3D image registration via geodesic shooting using an efficient adjoint calculation. IJCV 97(2), 229–241 (2011). https://doi.org/10.1007/s11263-011-0481-8
Younes, L.: Shapes and Diffeomorphisms. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-12055-8
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this paper
Cite this paper
François, A., Gori, P., Glaunès, J. (2021). Metamorphic Image Registration Using a Semi-lagrangian Scheme. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2021. Lecture Notes in Computer Science(), vol 12829. Springer, Cham. https://doi.org/10.1007/978-3-030-80209-7_84
Download citation
DOI: https://doi.org/10.1007/978-3-030-80209-7_84
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-80208-0
Online ISBN: 978-3-030-80209-7
eBook Packages: Computer ScienceComputer Science (R0)