Elastic Analysis of Augmented Curves and Constrained Surfaces

1. Ambellan, F., Hanik, M., von Tycowicz, C.: Morphomatics: geometric morphometrics in non-Euclidean shape spaces (2021). https://doi.org/10.12752/8544. https://morphomatics.github.io/

2. Bauer, M., Bruveris, M., Marsland, S., Michor, P.: Constructing reparametrization invariant metrics on spaces of plane curves. Differential Geometry (2012). https://arxiv.org/pdf/1207.5965.pdf

3. Bauer, M., Bruveris, M., Charon, N., Møller-Andersen, J.: A relaxed approach for curve matching with elastic metrics. ESAIM: Control Optim. Calc. Var. 25, (March 2018). https://doi.org/10.1051/cocv/2018053

4. Bauer, M., Bruveris, M., Harms, Philipp Michor, P.W.: Soliton solutions for the elastic metric on spaces of curves. Discret. Contin. Dyn. Syst. A 38, 1161–1185 (2018). https://doi.org/10.3934/dcds.2018049

5. Bauer, M., Bruveris, M., Michor, P.W.: Overview of the geometries of shape spaces and diffeomorphism groups. J. Math. Imaging Vis. 50(1–2), 60–97 (2014)

   Article  MathSciNet  Google Scholar 

6. Bauer, M., Charon, N., Klassen, E., Brigant, A.L.: Intrinsic Riemannian metrics on spaces of curves: theory and computation. arXiv preprint (2020). https://arxiv.org/abs/2003.05590

7. Bauer, M., Harms, P., Michor, P.W., et al.: Sobolev metrics on the manifold of all Riemannian metrics. J. Differ. Geom. 94(2), 187–208 (2013)

   MathSciNet  Google Scholar 

8. do Carmo, M.P.: Riemannian Geometry. Mathematics: Theory and Applications, 2nd edn. Birkhäuser, Boston (1992)

   Google Scholar 

9. Celledoni, E., Eidnes, S., Schmeding, A.: Shape analysis on homogeneous spaces: a generalised SRVT framework. In: Celledoni, E., Di Nunno, G., Ebrahimi-Fard, K., Munthe-Kaas, H.Z. (eds.) Abelsymposium 2016. AS, vol. 13, pp. 187–220. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-01593-0_7

   Chapter  Google Scholar 

10. Gallot, S., Hullin, D., Lafontaine, J.: Riemannian Geometry. Universitext, 3rd edn. Springer, Berlin (2004)

    Book  Google Scholar 

11. Huang, W., Gallivan, K.A., Srivastava, A., Absil, P.A.: Riemannian optimization for registration of curves in elastic shape analysis. J. Math. Imaging Vis. 54(3), 320–343 (2016)

    Article  MathSciNet  Google Scholar 

12. Kendall, D., Barden, D., Carne, T., Le, H.: Shape and Shape Theory. Wiley, New York (1999)

    Book  Google Scholar 

13. Le Brigant, A.: Computing distances and geodesics between manifold-valued curves in the SRV framework. J. Geom. Mech. 9(2), (2017)

    Google Scholar 

14. Liu, W., Srivastava, A., Zhang, J.: Protein structure alignment using elastic shape analysis. In: Proceedings of the First ACM International Conference on Bioinformatics and Computational Biology, pp. 62–70 (2010)

    Google Scholar 

15. Michor, P., Mumford, D., Shah, J., Younes, L.: A metric on shape space with explicit geodesics. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 19, (July 2007). https://doi.org/10.4171/RLM/506

16. Michor, P.W., Mumford, D.: Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms. Doc. Math. 10, 217–245 (2005)

    Article  MathSciNet  Google Scholar 

17. Michor, P.W., Mumford, D.: An overview of the Riemannian metrics on spaces of curves using the Hamiltonian approach. Appl. Comput. Harmon. Anal. 23(1), 74–113 (2007)

    Article  MathSciNet  Google Scholar 

18. Mio, W., Srivastava, A., Joshi, S.H.: On shape of plane elastic curves. Int. J. Comput. Vis. 73, 307–324 (2006)

    Article  Google Scholar 

19. Mio, W., Srivastava, A., Joshi, S.: On shape of plane elastic curves. Int. J. Comput. Vis. 73, 307–324 (2007). https://doi.org/10.1007/s11263-006-9968-0

20. Nava-Yazdani, E., Ambellan, F., Hanik, M., von Tycowicz, C.: Sasaki metric for spline models of manifold-valued trajectories. Comput. Aided Geom. Des. 104, 102220 (2023). https://doi.org/10.1016/j.cagd.2023.102220

    Article  MathSciNet  Google Scholar 

21. Nava-Yazdani, E., Hege, H.C., Sullivan, T.J., von Tycowicz, C.: Geodesic analysis in Kendall’s shape space with epidemiological applications. J. Math. Imaging Vis. 1–11 (2020)

    Google Scholar 

22. Nava-Yazdani, E., Hege, H.C., von Tycowicz, C.: A hierarchical geodesic model for longitudinal analysis on manifolds. J. Math. Imaging Vis. 64(4), 395–407 (2022). https://doi.org/10.1007/s10851-022-01079-x

    Article  MathSciNet  Google Scholar 

23. Needham, T., Kurtek, S.: Simplifying transforms for general elastic metrics on the space of plane curves. SIAM J. Imaging Sci. 13(1), 445–473 (2020). https://doi.org/10.1137/19M1265132

24. Srivastava, A., Klassen, E.P.: Functional and Shape Data Analysis, vol. 1. Springer, New York (2016)

    Book  Google Scholar 

25. Su, Z., Klassen, E., Bauer, M.: The square root velocity framework for curves in a homogeneous space. In: 2017 IEEE Conference on Computer Vision and Pattern Recognition Workshops (CVPRW), pp. 680–689 (2017)

    Google Scholar 

26. Su, Z., Klassen, E., Bauer, M.: Comparing curves in homogeneous spaces. Differ. Geom. Appl. 60, 9–32 (2018)

    Article  MathSciNet  Google Scholar 

27. Zhang, Z., Su, J., Klassen, E., Le, H., Srivastava, A.: Rate-invariant analysis of covariance trajectories. J. Math. Imaging Vis. 60, 1306–1323 (2018)

    Article  MathSciNet  Google Scholar 

Download references