x Homepage of Martin Bauer

Publications

     Preprints

  1. M. Bauer, E. Hartman, E. Klassen. The Square Root Normal Field Distance and Unbalanced Optimal Transport. arXiv:2105.06510.
    Code available here
  2. Y. Sukurdeep, M. Bauer, N. Charon. A new variational model for the analysis of shape graphs with partial matching constraints. arXiv:2105.00678.
    Code available here
  3. A. Singh, M. Bauer, S. Joshi. Physics Informed Convex Artificial Neural Networks (PICANNs) for Optimal Transport based Density Estimation. arXiv:2104.01194.
    Code available here
  4. M. Bauer, Y. Lu, C. Maor. A geometric view on the generalized Proudman-Johnson and r-Hunter-Saxton equations. arXiv:2101.03601.
  5. L. Mander, M. Bauer, H. Hang, W. Mio. Geometric and Topological Approaches to Shape Variation in Ginkgo Leaves. bioRxiv:2020.10.23.352476.
  6. M. Bauer, C. Maor, P. W. Michor. Sobolev metrics on spaces of manifold valued curves. arXiv:2007.13315.
  7. M. Bauer, J. Møller-Andersen, S. Preston. Isometric Immersions and the Waving of Flags. arXiv:1905.06378.
  8. M. Bauer, M. Bruveris, P. Harms, P. Michor. Smooth perturbations of the functional calculus and applications to Riemannian geometry on spaces of metrics. arXiv:1810.03169.

     Peer-reviewed Articles

  1. M. Bauer, N. Charon, P. Harms, H. Hsieh. A numerical framework for elastic surface matching, comparison, and interpolation. To appear in International Journal of Computer Vision
    arXiv:2006.11652.
    Code available here
  2. E. Hartman, Y. Sukurdeep, N. Charon, E. Klassen, M. Bauer. Supervised deep learning of elastic SRV distances on the shape space of curves. To appear in 2021 IEEE Conference on Computer Vision and Pattern Recognition Workshops (CVPRW)
    arXiv:2101.04929.
  3. K. Campbell, H. Dai, Z. Su, M. Bauer, T. Fletcher, S. Joshi. Structural Connectome Atlas Construction in the Space of Riemannian Metrics. To appear in Information Processing in Medical Imaging 2021 (IPMI 2021)
    arXiv:2103.05730.
  4. M. Bauer, C. Maor. Can we run to infinity? The diameter of the diffeomorphism group with respect to right-invariant Sobolev metrics. Calculus of Variations and Partial Differential Equations, 60:54, 2021.
    doi:10.1007/s00526-021-01918-6, arXiv:1910.04834.
  5. M. Bauer, N. Charon, E. Klassen, A. Le Brigant. Intrinsic Riemannian metrics on spaces of curves: theory and computation. In: Chen K., Schönlieb CB., Tai XC., Younces L. (eds): Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging. Springer, Cham.
    doi:10.1007/978-3-030-03009-4_87-1, arXiv:2003.05590.
  6. M. Bauer, E. Klassen, S. Preston, Z. Su. A diffeomorphism-invariant metric on the space of vector-valued one-forms. To appear in Pure and Applied Mathematics Quarterly
    arXiv:1812.10867.
  7. Z. Su, M. Bauer, K. Gallivan, E. Klassen. Simplifying Transformations for a Family of Elastic Metrics on the Space of Surfaces. 2020 IEEE Conference on Computer Vision and Pattern Recognition Workshops (CVPRW)
  8. Z. Su, M. Bauer, S. Preston, H. Laga, and E. Klassen. Shape analysis of surfaces using general elastic metrics. Journal of Mathematical Imaging and Vision, (2020).
    doi:10.1007%2Fs10851-020-00959-4, arXiv:1910.02045.
  9. M. Bauer, B. Kolev, S. Preston. Geodesic completeness of the H^(3/2) metric on Diff(S^1). Monatshefte für Mathematik, 1-13 (2020).
    doi:10.1007/s00605-020-01405-8, arXiv:1904.12523.
  10. M. Bauer, K. Modin. Semi-invariant Riemannian metrics in hydrodynamics. Calculus of Variations and Partial Differential Equations, 59:65 (2020).
    doi:10.1007/s00526-020-1722-x, arXiv:1810.03424.
  11. M. Bauer, P. Harms, P. Michor. Fractional Sobolev metrics on spaces of immersions. Calculus of Variations and Partial Differential Equations, 59:62 (2020).
    doi:10.1007/s00526-020-1719-5, arXiv:1909.08657.
  12. Y. Sukurdeep, M. Bauer, N. Charon. An inexact matching approach for the comparison of plane curves with general elastic metrics. Proceedings of the Asilomar Conference on Signals, Systems, & Computers, 2019.
    doi:10.1109/IEEECONF44664.2019.9049031, arXiv:2001.02858.
  13. M. Bauer, M. Bruveris, E. Cismas, J. Escher, B. Kolev. Well-posedness of the EPDiff equation with a pseudo-differential inertia operator. Journal of Differential Equations, 269.1 (2020) 288-325.
    doi:10.1016/j.jde.2019.12.008, arXiv:1911.03238.
  14. M. Bauer, P. Harms, S. Preston. Vanishing distance phenomena and the geometric approach to SQG. Arch Rational Mech Anal, 235, 1445–1466 (2020).
    doi:10.1007/s00205-019-01449-7, arXiv:1805.04401.
  15. M. Bauer, N Charon, P Harms. Inexact elastic shape matching in the square root normal field framework. In: Geometric Science of Information. Lecture Notes in Computer Science (Springer), pages 13-21, (2019). Editors: F. Nielsen and F. Barbaresco.
    ISBN 978-3-030-26980-7, arXiv:1903.00855.
  16. M. Bauer, N. Charon, L. Younes.Metric Registration of Curves and Surfaces using Optimal Control. Handbook of Numerical Analysis Volume 20, 2019, Pages 613-646. Editors: Ron Kimmel and Xue-Cheng Tai.
    doi:10.1016/bs.hna.2019.03.001, arXiv:1809.06422.
  17. M. Bauer, S. Joshi, K. Modin. Diffeomorphic density matching. In: Riemannian Geometric Statistics in Medical Image Analysis; Academic Press, 2020. pages 577-603. Editors: X. Pennec, S. Sommer and T. Fletcher.
    doi:0.1016/B978-0-12-814725-2.00025-X, arXiv:1807.05505.
  18. M. Bauer, M. Bruveris, N. Charon, J. Møller-Andersen. A relaxed approach for curve matching with elastic metrics. ESAIM: COCV, 25 (2019) 72
    doi:10.1051/cocv/2018053 , arXiv:1803.10893.
  19. Z. Su, M. Bauer, E. Klassen. Comparing Curves in Homogeneous Spaces. Differential Geometry and its Applications, 60 (2018), 9–32.
    doi:10.1016/j.difgeo.2018.05.001 , arXiv:1712.04586.
  20. 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
  21. 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,
  22. 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
  23. 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
  24. 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.
  25. 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.
  26. 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,
  27. 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
  28. 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:1603.05916
  29. M. Bauer, M. Bruveris, P. W. Michor. Uniqueness of the Fisher-Rao metric on the space of smooth densities. Bull. London Math. Soc. 48.3 (2016): 499-506.
    doi:10.1112/blms/bdw020, arXiv:1411.5577
  30. 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
  31. 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
  32. 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
  33. 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
  34. 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
  35. 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
  36. 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
  37. 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
  38. 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
  39. 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
  40. 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
  41. 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
  42. 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
  43. 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
  44. 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
  45. 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
  46. 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
  47. 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
  48. 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
  49. 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
  50. 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
  51. 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
  52. 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.