Publications

     Preprints

  1. M. Bauer, P. Harms, S. Preston. Vanishing distance phenomena and the geometric approach to SQG. arXiv:1805.04401.
  2. M. Bauer, M. Bruveris, N. Charon, J. Møller-Andersen. A relaxed approach for curve matching with elastic metrics. arXiv:1803.10893.

     Peer-reviewed Articles

  1. Z. Su, M. Bauer, E. Klassen. Comparing Curves in Homogeneous Spaces. Differential Geometry and its Applications, (forthcoming)
    arXiv:1712.04586.
  2. M. Bauer, M. Bruveris, B. Kolev. Fractional Sobolev metrics on spaces of immersed curves. Calculus of Variations and Partial Differential Equations, (2018) 57:27.
    doi:10.1007/978-3-319-68445-1_16 , arXiv:1703.03323
  3. M. Bauer, S. Joshi, K. Modin. Diffeomorphic random sampling using optimal information transport. Geometric Science of Information. GSI 2017. Lecture Notes in Computer Science, vol 10589. Springer.
    doi:10.1007/s0052 , arXiv:1704.07897
    Code available here,
  4. M. Bauer, M. Bruveris, P. Harms, P. Michor. Soliton solutions for the elastic metric on spaces of curves. Discrete and Continuous Dynamical Systems Series A, 38(3): 1161-1185.
    doi:10.3934/dcds.2018049 , arXiv:1702.04344
  5. M. Bauer, M. Bruveris, N. Charon and J. Møller-Andersen. Varifold-based matching of curves via Sobolev-type Riemannian metrics. 7th MICCAI workshop on Mathematical Foundations of Computational Anatomy, 2017.
    arXiv:1706.01821
  6. M. Bauer, S. Joshi, K. Modin. On Geodesic Completeness for Riemannian Metrics on Smooth Probability Densities. Calculus of Variations and Partial Differential Equations, (2017) 56:113, 2017.
    doi:10.1007/s00526-017-1195-8, arXiv:1702.08870.
  7. Z. Su, M. Bauer, E. Klassen. The Square Root Velocity Framework for Curves in a Homogeneous Space. 2017 IEEE Conference on Computer Vision and Pattern Recognition Workshops (CVPRW)
    doi:10.1109/CVPRW.2017.97, arXiv:1706.03095.
  8. M. Bauer, M. Eslitzbichler and M. Grasmair. Landmark-Guided Elastic Shape Analysis of Human Character Motions. Inverse Problems and Imaging ,Volume 11, No. 4, 2017, 601-621
    doi:10.3934/ipi.2017028 , arXiv:1502.07666.
    Code available here,
  9. M. Bauer, M. Bruveris, P. Harms and J. Møller-Andersen. A numerical framework for Sobolev metrics on the space of curves. SIAM J. Imaging Sci. , 10(1), 47-73. (2017)
    doi:10.1137/16M1066282, arXiv:1603.03480,
    Code available here
  10. M. Bauer, P. Michor and Olaf Müller. Riemannian geometry of the space of volume preserving immersions. Differential Geometry and its Applications, 49 (2016), Pages 23-42
    doi:10.1016/j.difgeo.2016.07.002, arXiv:1502.03229
  11. M. Bauer, M. Bruveris, P. W. Michor. Uniqueness of the Fisher-Rao metric on the space of smooth densities. Bull. London Math. Soc.
    doi:10.1112/blms/bdw020, arXiv:1411.5577
  12. M. Bauer, B. Kolev and S. Preston. Geometric investigations of a vorticity model equation. Journal of Differential Equations, (1), 260 (2016), Pages 478–516.
    doi:10.1016/j.jde.2015.09.030, arXiv:1504.08029
  13. M. Bauer, M. Bruveris, P. W. Michor. Why use Sobolev metrics on the space of curves. Riemannian Computing in Computer Vision. Editors P. Turaga and A. Srivastava. 223-255, 2016.
    doi:10.1007/978-3-319-22957-7_11, arXiv:1502.03229
  14. M. Bauer, M. Bruveris, P. Harms, J. Møller-Andersen. Second order elastic metrics on the shape space of curves. 1st Workshp on Differential Geometry in Computer Vision for Analysis of Shapes, Images and Trajectories, 2015.
    doi:10.5244/C.29.DIFFCV.9, arXiv:1507.08816
  15. M. Bauer, M. Bruveris, P. Harms, J. Møller-Andersen. Curve matching with applications in medical imaging. 5th MICCAI workshop on Mathematical Foundations of Computational Anatomy, 2015.
    arXiv:1506.08840
  16. C. Rottman, M. Bauer, S. Joshi and K. Modin. Weighted Diffeomorphic Density Matching with Applications to Thoracic Image Registration. 5th MICCAI workshop on Mathematical Foundations of Computational Anatomy, 2015.
    arXiv:1508.02543
  17. M. Bauer, S. Joshi and K. Modin. Diffeomorphic density matching by optimal information transport. SIAM J. Imaging Sci. 8(3):1718-1751, 2015.
    doi:10.1137/151006238, arXiv:1501.07635
  18. M. Bauer and P. Harms. Metrics on Spaces of Surfaces where Horizontality equals Normality. Differential Geometry and its Applications 39 (2015), pp. 166-183.
    doi:10.1016/j.difgeo.2014.12.008, arXiv:1403.1436
  19. M. Bauer, J. Escher and B. Kolev. Local and Global Well-posedness of the fractional order EPDiff equation on R^d. Journal of Differential Equations (6) 258 (2015), p. 2010-2053.
    doi:10.1016/j.jde.2014.11.021, arXiv:1411.4081
  20. M. Bauer, M. Grasmair and C. Kirisits. Optical Flow on Moving Manifolds. SIAM J. Imaging Sci. 2015, Vol. 8, No. 1, pp. 484-512.
    doi:10.1137/140965235, arXiv:1404.3885
  21. M. Bauer, M. Bruveris, S. Marsland and P. W. Michor. Constructing reparametrization invariant metrics on spaces of plane curves. Differ. Geom. Appl., 34C, 139-165, 2014.
    doi:10.1016/j.difgeo.2014.04.008, arXiv:1207:5965
  22. M. Bauer, M. Bruveris, P. W. Michor. R-transforms for H^2-metrics on spaces of plane curves. Geom. Imaging Comput., 1(1), 1-56, 2014.
    doi:10.4310/GIC.2014.v1.n1.a1, arXiv:1311.3526
  23. M. Bauer, M. Bruveris, P. W. Michor. The homogeneous Sobolev metric of order one on diffeomorphism groups on the real line. J. Nonlinear Sci, 24(5), 769-808, 2014.
    doi:10.1007/s00332-014-9204-y, arXiv:1209.2836
  24. M. Bauer, M. Bruveris, P. W. Michor. Overview of the geometries of shape spaces and diffeomorphism groups. J. Math. Imaging Vis., 50(1-2), 60-97, 2014.
    doi:10.1007/s10851-013-0490-z, arXiv:1305.1150
  25. M. Bauer, M. Bruveris, P. W. Michor. Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group. II. Ann. Glob. Anal. Geom., 44(4), 361-368, 2013.
    doi:10.1007/s10455-013-9370-4, arXiv:1211.7254
  26. M. Bauer, M. Bruveris, P. Harms and P. W. Michor. Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group. Ann. Glob. Anal. Geom., 44(1), 5-21, 2013.
    doi:10.1007/s10455-012-9353-x, arXiv:1105.0327
  27. M. Bauer, P. Harms and P. W. Michor. Sobolev metrics on the manifold of all Riemannian metrics. Journal of Differential Geometry 94, 2 (2013), 187-208.
    Euclid, arXiv:1102.3347
  28. M. Bauer, T. Fidler and M. Grasmair. Local Uniqueness of the Circular Integral Invariant. Inverse Problems and Imaging 7,1 (2013) 107-122.
    doi:10.3934/ipi.2013.7.107, arXiv:1107.4257
  29. M. Bauer, P. Harms and P. W. Michor. Sobolev Metrics on Shape Space, II: Weighted Sobolev Metrics and Almost Local Metrics. Journal of Geometric Mechanics 3, 4, 4 (2012), 365-383.
    doi:10.3934/jgm.2012.4.365, arXiv:1009.3616
  30. M. Bauer, M. Bruveris, P. Harms and P. W. Michor. Vanishing geodesic distance for the Riemannian metric with geodesic equation the KdV-equation. Ann. Glob. Anal. Geom., 41(4), 461-472, 2012.
    doi:10.1007/s10455-011-9294-9, arXiv:1102.0236
  31. M. Bauer, M. Bruveris. A new Riemannian setting for surface registration. 3rd MICCAI workshop on Mathematical Foundations of Computational Anatomy, 2011.
    hal:inria-00624210, arXiv:1106.0620
  32. M. Bauer, P. Harms and P. W. Michor. Curvature weighted metrics on shape space of hypersurfaces in n-space. Differential Geometry and its Applications , 30 (2012), 33-41.
    doi:10.1016/j.difgeo.2011.10.002, arXiv:1102.0678
  33. M. Bauer, P. Harms and P. W. Michor. Sobolev metrics on shape space of surfaces. Journal of Geometric Mechanics 3, 4 (2011), 389-438.
    doi:10.3934/jgm.2011.3.389, arXiv:1009.3616
  34. M. Bauer, P. Harms and P. W. Michor. Almost local metrics on shape space of hypersurfaces in n-space. SIAM J. Imaging Sci. 5 (2012), 244-310.
    doi:10.1137/100807983, arXiv:1001.0717

     Technical Reports

  1. M. Bauer and P. Harms. Metrics with prescribed horizontal bundle on spaces of curves. Proceedings of Math at the Rocks - Shape Analysis Workshop in Grundsund, 2015. doi:zenodo.33558, arXiv:1511.05889
  2. M. Bauer and P. Harms. Hörmander's condition for normal bundles on spaces of immersions. Proceedings of Math at the Rocks - Shape Analysis Workshop in Grundsund, 2015. doi:zenodo.33558, arXiv:1511.05883
  3. M. Bauer. Riemannian Metrics on spaces of densities, Kahler potentials, Riemannian metrics and diffeomorphisms Proceedings of Math in the Cabin - Shape Analysis Workshop in Gastein, 2014. hal-01076953

     Theses

  1. M. Bauer. Riemannian Geometry of Shape Spaces and Diffeomorphism Groups. habilitation thesis, University of Vienna, 2015.
  2. M. Bauer. Almost local metrics on shape space. doctoral thesis, University of Vienna, 2010.
  3. M. Bauer. Geodesics in Subriemannian Geometry. master thesis, Vienna University of Technology, 2008.