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Sobolev metrics on shape space, II: Weighted Sobolev metrics and almost local metrics
1. | Fakultät f¨ur Mathematik, Universität Wien, Nordbergstrasse 15, A-1090 Wien, Austria |
2. | EdLabs, Harvard University, 44 Brattle Street, Cambridge, MA 02138 |
References:
[1] |
M. Bauer and M. Bruveris, A new Riemannian setting for surface registration,, 3nd MICCAI Workshop on Mathematical Foundations of Computational Anatomy, (2011), 182. Google Scholar |
[2] |
M. Bauer, M. Bruveris, C. Cotter, S. Marsland and P. W. Michor, Constructing reparametrization invariant metrics on spaces of plane curves,, \arXiv{1207.5965}., (). Google Scholar |
[3] |
M. Bauer, M. Bruveris, P. Harms and P. W. Michor, Vanishing geodesic distance for the riemannian metric with geodesic equation the KdV-equation,, Ann. Global Analysis Geom., 41 (2012), 461.
doi: 10.1007/s10455-011-9294-9. |
[4] |
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., ().
doi: doi:10.1007/s10455-012-9353-x. |
[5] |
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.
doi: 10.1137/100807983. |
[6] |
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.
doi: 10.1016/j.difgeo.2011.10.002. |
[7] |
M. Bauer, P. Harms and P. W. Michor, Sobolev metrics on shape space of surfaces,, Journal of Geometric Mechanics, 3 (2011), 389.
|
[8] |
M. Bauer, P. Harms and P. W. Michor, Sobolev metrics on the manifold of all Riemannian metrics,, To appear in, (). Google Scholar |
[9] |
M. Bauer, "Almost Local Metrics on Shape Space of Surfaces,", Ph.D thesis, (2010). Google Scholar |
[10] |
A. L. Besse, "Einstein Manifolds,", Classics in Mathematics. Springer-Verlag, (2008).
|
[11] |
P. Harms, "Sobolev Metrics on Shape Space of Surfaces,", Ph.D Thesis, (2010). Google Scholar |
[12] |
P. W. Michor and D. Mumford, Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms,, Doc. Math., 10 (2005), 217.
|
[13] |
P. W. Michor and D. Mumford, Riemannian geometries on spaces of plane curves,, J. Eur. Math. Soc. (JEMS), 8 (2006), 1.
doi: 10.4171/JEMS/37. |
[14] |
P. W. Michor and D. Mumford, An overview of the Riemannian metrics on spaces of curves using the Hamiltonian approach,, Appl. Comput. Harmon. Anal., 23 (2007), 74.
doi: 10.1016/j.acha.2006.07.004. |
[15] |
J. Peetre, Une caractérisation abstraite des opérateurs différentiels,, Math. Scand., 7 (1959), 211.
|
[16] |
J. Peetre, Réctification à l'article "Une caractérisation abstraite des opérateurs différentiels",, Math. Scand., 8 (1960), 116.
|
[17] |
J. Shah, $H^0$-type Riemannian metrics on the space of planar curves,, Quart. Appl. Math., 66 (2008), 123.
|
[18] |
M. A. Shubin, "Pseudodifferential Operators and Spectral Theory,", Springer Series in Soviet Mathematics. Springer-Verlag, (1987).
doi: 10.1007/978-3-642-96854-9. |
[19] |
Jan Slovák, Peetre theorem for nonlinear operators,, Ann. Global Anal. Geom., 6 (1988), 273.
doi: 10.1007/BF00054575. |
[20] |
A. Yezzi and A. Mennucci, Conformal riemannian metrics in space of curves,, EUSIPCO, (2004). Google Scholar |
[21] |
A. Yezzi and A. Mennucci, Metrics in the space of curves,, \arXiv{math/0412454}, (2004). Google Scholar |
[22] |
A. Yezzi and A. Mennucci, Conformal metrics and true "gradient flows" for curves,, in, 1 (2005), 913. Google Scholar |
[23] |
L. Younes, P. W. Michor, J. Shah and D. Mumford, A metric on shape space with explicit geodesics,, Rend. Lincei Mat. Appl., 9 (2008), 25.
doi: 10.4171/RLM/506. |
show all references
References:
[1] |
M. Bauer and M. Bruveris, A new Riemannian setting for surface registration,, 3nd MICCAI Workshop on Mathematical Foundations of Computational Anatomy, (2011), 182. Google Scholar |
[2] |
M. Bauer, M. Bruveris, C. Cotter, S. Marsland and P. W. Michor, Constructing reparametrization invariant metrics on spaces of plane curves,, \arXiv{1207.5965}., (). Google Scholar |
[3] |
M. Bauer, M. Bruveris, P. Harms and P. W. Michor, Vanishing geodesic distance for the riemannian metric with geodesic equation the KdV-equation,, Ann. Global Analysis Geom., 41 (2012), 461.
doi: 10.1007/s10455-011-9294-9. |
[4] |
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., ().
doi: doi:10.1007/s10455-012-9353-x. |
[5] |
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.
doi: 10.1137/100807983. |
[6] |
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.
doi: 10.1016/j.difgeo.2011.10.002. |
[7] |
M. Bauer, P. Harms and P. W. Michor, Sobolev metrics on shape space of surfaces,, Journal of Geometric Mechanics, 3 (2011), 389.
|
[8] |
M. Bauer, P. Harms and P. W. Michor, Sobolev metrics on the manifold of all Riemannian metrics,, To appear in, (). Google Scholar |
[9] |
M. Bauer, "Almost Local Metrics on Shape Space of Surfaces,", Ph.D thesis, (2010). Google Scholar |
[10] |
A. L. Besse, "Einstein Manifolds,", Classics in Mathematics. Springer-Verlag, (2008).
|
[11] |
P. Harms, "Sobolev Metrics on Shape Space of Surfaces,", Ph.D Thesis, (2010). Google Scholar |
[12] |
P. W. Michor and D. Mumford, Vanishing geodesic distance on spaces of submanifolds and diffeomorphisms,, Doc. Math., 10 (2005), 217.
|
[13] |
P. W. Michor and D. Mumford, Riemannian geometries on spaces of plane curves,, J. Eur. Math. Soc. (JEMS), 8 (2006), 1.
doi: 10.4171/JEMS/37. |
[14] |
P. W. Michor and D. Mumford, An overview of the Riemannian metrics on spaces of curves using the Hamiltonian approach,, Appl. Comput. Harmon. Anal., 23 (2007), 74.
doi: 10.1016/j.acha.2006.07.004. |
[15] |
J. Peetre, Une caractérisation abstraite des opérateurs différentiels,, Math. Scand., 7 (1959), 211.
|
[16] |
J. Peetre, Réctification à l'article "Une caractérisation abstraite des opérateurs différentiels",, Math. Scand., 8 (1960), 116.
|
[17] |
J. Shah, $H^0$-type Riemannian metrics on the space of planar curves,, Quart. Appl. Math., 66 (2008), 123.
|
[18] |
M. A. Shubin, "Pseudodifferential Operators and Spectral Theory,", Springer Series in Soviet Mathematics. Springer-Verlag, (1987).
doi: 10.1007/978-3-642-96854-9. |
[19] |
Jan Slovák, Peetre theorem for nonlinear operators,, Ann. Global Anal. Geom., 6 (1988), 273.
doi: 10.1007/BF00054575. |
[20] |
A. Yezzi and A. Mennucci, Conformal riemannian metrics in space of curves,, EUSIPCO, (2004). Google Scholar |
[21] |
A. Yezzi and A. Mennucci, Metrics in the space of curves,, \arXiv{math/0412454}, (2004). Google Scholar |
[22] |
A. Yezzi and A. Mennucci, Conformal metrics and true "gradient flows" for curves,, in, 1 (2005), 913. Google Scholar |
[23] |
L. Younes, P. W. Michor, J. Shah and D. Mumford, A metric on shape space with explicit geodesics,, Rend. Lincei Mat. Appl., 9 (2008), 25.
doi: 10.4171/RLM/506. |
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