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The Gromov-Hausdorff distance: a brief tutorial on some of its quantitative aspects
Facundo Mémoli1
1 Department of Mathematics The Ohio State University Columbus, OH 43210 United States of America
Actes des rencontres du CIRM, Volume 3 (2013) no. 1, pp. 89-96.

We recall the construction of the Gromov-Hausdorff distance. We concentrate on quantitative aspects of the definition and on quantitative properties of the distance .

Published online:
DOI: 10.5802/acirm.58
Classification: 00X99
Keywords: metric geometry, graph theory, shape recognition, optimal transportation
Facundo Mémoli 1

1 Department of Mathematics The Ohio State University Columbus, OH 43210 United States of America 
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Facundo Mémoli. The Gromov-Hausdorff distance: a brief tutorial on some of its quantitative aspects. Actes des rencontres du CIRM, Volume 3 (2013) no. 1, pp. 89-96. doi : 10.5802/acirm.58. https://acirm.centre-mersenne.org/articles/10.5802/acirm.58/

[1] Alexander M. Bronstein; Michael M. Bronstein; Ron Kimmel Efficient Computation of Isometry-Invariant Distances Between Surfaces, SIAM Journal on Scientific Computing, Volume 28 (2006) no. 5, pp. 1812-1836 http://link.aip.org/link/?SCE/28/1812/1 | DOI | MR | Zbl

[2] D. Burago; Y. Burago; S. Ivanov A Course in Metric Geometry, AMS Graduate Studies in Math., 33, American Mathematical Society, 2001 | MR | Zbl

[3] Eugenio Calabi; Peter J. Olver; Chehrzad Shakiban; Allen Tannenbaum; Steven Haker Differential and Numerically Invariant Signature Curves Applied to Object Recognition, Int. J. Comput. Vision, Volume 26 (1998) no. 2, pp. 107-135 | DOI

[4] Misha Gromov Metric structures for Riemannian and non-Riemannian spaces, Progress in Mathematics, 152, Birkhäuser Boston Inc., Boston, MA, 1999, xx+585 pages | MR | Zbl

[5] N. J. Kalton; M. I. Ostrovskii Distances between Banach spaces, Forum Math., Volume 11:1 (1999), pp. 17-48 | MR | Zbl

[6] Facundo Mémoli Gromov-Hausdorff distances in Euclidean spaces, Computer Vision and Pattern Recognition Workshops, 2008. CVPR Workshops 2008. IEEE Computer Society Conference on (2008), pp. 1-8 | DOI

[7] Facundo Mémoli Gromov-Wasserstein distances and the metric approach to Object Matching, Foundations of computational mathematics, Volume 11 (2011.), pp. 417-487 | DOI | MR | Zbl

[8] Facundo Mémoli Some Properties of Gromov—Hausdorff Distances, Discrete & Computational Geometry (2012), pp. 1-25 (10.1007/s00454-012-9406-8) | MR | Zbl

[9] Facundo Mémoli; Guillermo Sapiro Comparing point clouds, SGP ’04: Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing (2004), pp. 32-40 | DOI

[10] Facundo Mémoli; Guillermo Sapiro A theoretical and computational framework for isometry invariant recognition of point cloud data, Found. Comput. Math., Volume 5 (2005) no. 3, pp. 313-347 | DOI | MR | Zbl

[11] P.J. Olver Joint invariant signatures, Foundations of computational mathematics, Volume 1 (2001) no. 1, pp. 3-68 | DOI | MR

[12] Quadratic assignment and related problems (Panos M. Pardalos; Henry Wolkowicz, eds.), DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 16, American Mathematical Society, Providence, RI, 1994, xii+364 pages (Papers from the workshop held at Rutgers University, New Brunswick, New Jersey, May 20–21, 1993)

[13] Karl-Theodor Sturm On the geometry of metric measure spaces. I, Acta Math., Volume 196 (2006) no. 1, pp. 65-131 | DOI | Zbl

[14] Karl-Theodor Sturm The space of spaces: curvature bounds and gradient flows on the space of metric measure spaces, arXiv preprint arXiv:1208.0434 (2012)

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