The Gromov-Hausdorff distance: a brief tutorial on some of its quantitative aspects

Facundo Mémoli[1]

  • [1] Department of Mathematics The Ohio State University Columbus, OH 43210 United States of America

Actes des rencontres du CIRM (2013)

  • Volume: 3, Issue: 1, page 89-96
  • ISSN: 2105-0597

Abstract

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

How to cite

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Mémoli, Facundo. "The Gromov-Hausdorff distance: a brief tutorial on some of its quantitative aspects." Actes des rencontres du CIRM 3.1 (2013): 89-96. <http://eudml.org/doc/275383>.

@article{Mémoli2013,
abstract = {We recall the construction of the Gromov-Hausdorff distance. We concentrate on quantitative aspects of the definition and on quantitative properties of the distance .},
affiliation = {Department of Mathematics The Ohio State University Columbus, OH 43210 United States of America},
author = {Mémoli, Facundo},
journal = {Actes des rencontres du CIRM},
keywords = {metric geometry; graph theory; shape recognition; optimal transportation},
language = {eng},
month = {11},
number = {1},
pages = {89-96},
publisher = {CIRM},
title = {The Gromov-Hausdorff distance: a brief tutorial on some of its quantitative aspects},
url = {http://eudml.org/doc/275383},
volume = {3},
year = {2013},
}

TY - JOUR
AU - Mémoli, Facundo
TI - The Gromov-Hausdorff distance: a brief tutorial on some of its quantitative aspects
JO - Actes des rencontres du CIRM
DA - 2013/11//
PB - CIRM
VL - 3
IS - 1
SP - 89
EP - 96
AB - We recall the construction of the Gromov-Hausdorff distance. We concentrate on quantitative aspects of the definition and on quantitative properties of the distance .
LA - eng
KW - metric geometry; graph theory; shape recognition; optimal transportation
UR - http://eudml.org/doc/275383
ER -

References

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  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 26 (1998), 107-135 
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  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), 1-8 Zbl1254.54033
  7. Facundo Mémoli, Gromov-Wasserstein distances and the metric approach to Object Matching, Foundations of computational mathematics 11 (2011.), 417-487 Zbl1244.68078MR2811584
  8. Facundo Mémoli, Some Properties of Gromov—Hausdorff Distances, Discrete & Computational Geometry (2012), 1-25 Zbl1254.54033MR2946454
  9. Facundo Mémoli, Guillermo Sapiro, Comparing point clouds, SGP ’04: Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing (2004), 32-40, ACM, New York, NY, USA Zbl1079.65020
  10. Facundo Mémoli, Guillermo Sapiro, A theoretical and computational framework for isometry invariant recognition of point cloud data, Found. Comput. Math. 5 (2005), 313-347 Zbl1101.53022MR2168679
  11. P.J. Olver, Joint invariant signatures, Foundations of computational mathematics 1 (2001), 3-68 Zbl1001.53004MR1829236
  12. Quadratic assignment and related problems, (1994), PardalosPanos M.P. M., Providence, RI MR1290344
  13. Karl-Theodor Sturm, On the geometry of metric measure spaces. I, Acta Math. 196 (2006), 65-131 Zbl1105.53035MR2237206
  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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