EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 55 / No 3 (May-June 2021) ESAIM: M2AN, 55 3 (2021) 1133-1161 References
Free Access
Issue
ESAIM: M2AN
Volume 55, Number 3, May-June 2021
Page(s) 1133 - 1161
DOI https://doi.org/10.1051/m2an/2021018
Published online 08 June 2021
  1. E. Acerbi, G. Buttazzo and D. Percivale, Thin inclusions in linear elasticity: a variational approach. J. Reine Angew. Math. 386 (1988) 99–115. [Google Scholar]
  2. R.A. Adams and J.J.F. Fournier, Sobolev Spaces, 2nd edition. In: Vol. 140 of Pure and Applied Mathematics (Amsterdam). Elsevier/Academic Press (2003). [Google Scholar]
  3. O. Anza Hafsa and J.-P. Mandallena, Relaxation and 3D–2D passage theorems in hyperelasticity. J. Convex Anal. 19 (2012) 759–794. [Google Scholar]
  4. J.M. Ball, Constitutive inequalities and existence theorems in nonlinear elastostatics. Nonlinear Analysis and Mechanics: Heriot–Watt Symposium, Vol. I. In: Vol. 17 of Research Notes in Math. Pitman (1977) 187–241. [Google Scholar]
  5. J.M. Ball, Global invertibility of Sobolev functions and the interpenetration of matter. Proc. Roy. Soc. Edinburgh Sect. A 88 (1981) 315–328. [Google Scholar]
  6. J.M. Ball, Progress and puzzles in nonlinear elasticity, edited by J. Schröder and P. Neff. In: Poly-, Quasi- and Rank-One Convexity in Applied Mechanics. Springer (2010) 1–15. [Google Scholar]
  7. M. Bauer, M. Bruveris and P.W. Michor, Overview of the geometries of shape spaces and diffeomorphism groups. J. Math. Imaging Vision 50 (2014) 60–97. [Google Scholar]
  8. M. Bauer, M. Bruveris, N. Charon and J. Møller-Andersen, A relaxed approach for curve matching with elastic metrics. ESAIM COCV 25 (2019) 72. [EDP Sciences] [Google Scholar]
  9. M. Bauer, N. Charon, P. Harms and H.-W. Hsieh, A numerical framework for elastic surface matching, comparison, and interpolation. Preprint arXiv:2006.11652 [cs.CV] (2020). [Google Scholar]
  10. A.L. Bessoud, F. Krasucki and G. Michaille, Multi-materials with strong interface: variational modelings. Asymptot. Anal. 61 (2009) 1–19. [Google Scholar]
  11. A. Braides, Γ-Convergence for Beginners. In: Vol. 22 of Oxford Lecture Series in Mathematics and its Applications. Oxford University Press (2002). [Google Scholar]
  12. M. Burger, J. Modersitzki and L. Ruthotto, A hyperelastic regularization energy for image registration. SIAM J. Sci. Comput. 35 (2013) B132–B148. [Google Scholar]
  13. P. Cachier and D. Rey, Symmetrization of the non-rigid registration problem using inversion-invariant energies: application to multiple sclerosis. In: Medical Image Computing and Computer-Assisted Intervention–MICCAI 2000. Springer (2000) 472–481. [Google Scholar]
  14. G. Charpiat, O. Faugeras and R. Keriven, Approximations of shape metrics and application to shape warping and empirical shape statistics. Found. Comput. Math. 5 (2004) 1–58. [Google Scholar]
  15. I. Chavel, Riemannian Geometry, 2nd edition. In: Vol. 98 of Cambridge Studies in Advanced Mathematics. Cambridge University Press (2006). [Google Scholar]
  16. Z. Chen and Z. Huan, On the continuity of the m-th root of a continuous nonnegative definite matrix-valued function. J. Math. Anal. Appl. 209 (1997) 60–66. [Google Scholar]
  17. P.G. Ciarlet, Mathematical Elasticity, Volume III: Theory of Shells. North-Holland (2000). [Google Scholar]
  18. B. Dacorogna, Direct Methods in the Calculus of Variations, 2nd edition. In: Vol. 78 ofApplied Mathematical Sciences. Springer (2008). [Google Scholar]
  19. S. Daneri and A. Pratelli, Smooth approximation of bi-Lipschitz orientation-preserving homeomorphisms. Ann. Inst. H. Poincaré Anal. Non Linéaire 31 (2014) 567–589. [Google Scholar]
  20. N. Debroux, J. Aston, F. Bonardi, A. Forbes, C. Le Guyader, M. Romanchikova and C.-B. Schönlieb, A variational model dedicated to joint segmentation, registration, and atlas generation for shape analysis. SIAM J. Imaging Sci. 13 (2020) 351–380. [Google Scholar]
  21. M.C. Delfour and J.-P. Zolésio, Shape analysis via oriented distance functions. J. Funct. Anal. 123 (1994) 129–201. [Google Scholar]
  22. M.C. Delfour and J.-P. Zolésio, A boundary differential equation for thin shells. J. Differ. Equ. 119 (1995) 426–449. [Google Scholar]
  23. M.C. Delfour and J.-P. Zolésio, Shapes and Geometries, 2nd edition. In: Vol. 22 of Advances in Design and Control. Society for Industrial and Applied Mathematics (SIAM) (2011). [Google Scholar]
  24. F. Demengel and G. Demengel, Functional Spaces for the Theory of Elliptic Partial Differential Equations. Universitext. Springer/EDP Sciences (2012). [CrossRef] [Google Scholar]
  25. M. Droske and M. Rumpf, A variational approach to nonrigid morphological image registration. SIAM J. Appl. Math. 64 (2003/04) 668–687. [Google Scholar]
  26. D. Ezuz, B. Heeren, O. Azencot, M. Rumpf and M. Ben-Chen, Elastic correspondence between triangle meshes. Comput. Graph. Forum 38 (2019) 121–134. [Google Scholar]
  27. R.L. Foote, Regularity of the distance function. Proc. Am. Math. Soc. 92 (1984) 153–155. [Google Scholar]
  28. S. Friedland, Variation of tensor powers and spectra. Linear Multilinear Algebra 12 (1982/83) 81–98. [Google Scholar]
  29. G. Friesecke, R.D. James and S. Müller, A hierarchy of plate models derived from nonlinear elasticity by Gamma-convergence. Arch. Ration. Mech. Anal. 180 (2006) 183–236. [CrossRef] [MathSciNet] [Google Scholar]
  30. M. Fuchs, B. Jüttler, O. Scherzer and H. Yang, Shape metrics based on elastic deformations. J. Math. Imaging Vision 35 (2009) 86–102. [Google Scholar]
  31. D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order. In: Classics in Mathematics. Springer-Verlag (2001). Reprint of the 1998 edition. [Google Scholar]
  32. S. Hencl and P. Koskela, Lectures on Mappings of Finite Distortion. In: Vol. 2096 of Lecture Notes in Mathematics. Springer(2014). [CrossRef] [Google Scholar]
  33. J.A. Iglesias, B. Berkels, M. Rumpf and O. Scherzer, A thin shell approach to the registration of implicit surfaces. In: Proceedings of the Vision, Modeling, and Visualization Workshop 2013. Eurographics Association (2013) 89–96. [Google Scholar]
  34. J.A. Iglesias, M. Rumpf and O. Scherzer, Shape-aware matching of implicit surfaces based on thin shell energies. Found. Comput. Math. 18 (2018) 891–927. [Google Scholar]
  35. T. Iwaniec and J. Onninen, Hyperelastic deformations of smallest total energy. Arch. Ration. Mech. Anal. 194 (2009) 927–986. [Google Scholar]
  36. T. Iwaniec, L.V. Kovalev and J. Onninen, Diffeomorphic approximation of Sobolev homeomorphisms. Arch. Ration. Mech. Anal. 201 (2011) 1047–1067. [CrossRef] [Google Scholar]
  37. P. Knabner, S. Korotov and G. Summ, Conditions for the invertibility of the isoparametric mapping for hexahedral finite elements. Finite Elem. Anal. Des. 40 (2003) 159–172. [Google Scholar]
  38. S. Kolouri, D. Slepčev and G.K. Rohde, A symmetric deformation-based similarity measure for shape analysis. In: IEEE 12th International Symposium on Biomedical Imaging (ISBI). IEEE (2015) 314–318. [Google Scholar]
  39. H. Le Dret, Nonlinear Elliptic Partial Differential Equations. Universitext. Springer (2018). [Google Scholar]
  40. H. Le Dret and A. Raoult, The nonlinear membrane model as variational limit of nonlinear three-dimensional elasticity. J. Math. Pures Appl. 74 (1995) 549–578. [Google Scholar]
  41. H. Le Dret and A. Raoult, The membrane shell model in nonlinear elasticity: a variational asymptotic derivation. J. Nonlinear Sci. 6 (1996) 59–84. [CrossRef] [MathSciNet] [Google Scholar]
  42. N. Litke, M. Droske, M. Rumpf and P. Schröder, An image processing approach to surface matching. In: Symposium on Geometry Processing, edited by M. Desbrun and H. Pottmann (2005) 207–216. [Google Scholar]
  43. P. Marcellini, Approximation of quasiconvex functions, and lower semicontinuity of multiple integrals. Manuscripta Math. 51 (1985) 1–28. [Google Scholar]
  44. J. Milnor, Morse Theory. In: Annals of Mathematics Studies, No. 51. Princeton University Press (1963). [Google Scholar]
  45. L. Nirenberg, An extended interpolation inequality. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 20 (1966) 733–737. [Google Scholar]
  46. Quocmesh library, AG rumpf, Institute for Numerical Simulation, Universität Bonn. http://numod.ins.uni-bonn.de/software/quocmesh/index.html. [Google Scholar]
  47. M. Rumpf and B. Wirth, A nonlinear elastic shape averaging approach. SIAM J. Imaging Sci. 2 (2009) 800–833. [Google Scholar]
  48. M. Rumpf and B. Wirth, Variational methods in shape analysis. In: Handbook of Mathematical Methods in Imaging, edited by O. Scherzer. Springer (2011) 1363–1401. [Google Scholar]
  49. M. Rumpf and B. Wirth, Discrete geodesic calculus in shape space and applications in the space of viscous fluidic objects. SIAM J. Imaging Sci. 6 (2013) 2581–2602. [Google Scholar]
  50. M. Rumpf and B. Wirth, Variational time discretization of geodesic calculus. IMA J. Numer. Anal. 35 (2015) 1011–1046. [CrossRef] [Google Scholar]
  51. J.A. Sethian, Level Set Methods and Fast Marching Methods, 2nd edition. Cambridge University Press (1999). [Google Scholar]
  52. T. Windheuser, U. Schlickewei, F.R. Schmidt and D. Cremers, Geometrically consistent elastic matching of 3D shapes: a linear programming solution. In: International Conference on Computer Vision (2011) 2134–2141. [Google Scholar]
  53. W.P. Ziemer, Weakly Differentiable Functions. In: Vol. 120 of Graduate Texts in Mathematics. Springer-Verlag (1989). [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you