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Calculation of the Gromov–Hausdorff Distance Using the Borsuk Number

Moscow University Mathematics Bulletin, 2023
The Gromov-Hausdorff distance is not only a classical invariant in metric geometry, it also proved to be an important tool in Imaging and its related fields. However, its application in any practical context is severely resticted by the difficulty of its computation. Surprisingly enough, the authors showed in [Chebyshevskiĭ Sb. 21, No. 2(74), 169--189 (
Ivanov, A. O., Tuzhilin, A. A.
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Gromov–Hausdorff distance for pointed metric spaces

The Journal of Analysis, 2016
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Gromov-Hausdorff distances in Euclidean spaces

2008 IEEE Computer Society Conference on Computer Vision and Pattern Recognition Workshops, 2008
The purpose of this paper is to study the relationship between measures of dissimilarity between shapes in Euclidean space. We first concentrate on the pair Gromov-Hausdorff distance (GH) versus Hausdorff distance under the action of Euclidean isometries (EH). Then, we (1) show they are comparable in a precise sense that is not the linear behaviour one
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Estimates for Modified (Euclidean) Gromov–Hausdorff Distance

Moscow University Mathematics Bulletin
The Gromov-Hausdorff distance \(d_{\mathrm{GH}(X, Y ) }\) is well-known to be bounded above and below by the diameters of the sets \(X\) and~\(Y\). The main result of the paper under review gives analogous (sharp) bounds for the Euclidean Gromov-Hausdorff distance in the case of the group of all motions \(|r_X - r_Y | \le d_{\mathcal{G}}(X, Y ) \le ...
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Zero asymptotic Lipschitz distance and finite Gromov-Hausdorff distance

Science in China Series A: Mathematics, 2007
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Gromov-Hausdorff Distances

2022
Jihoon Lee, Carlos Morales Rojas
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Gromov–Hausdorff Distance

2004
Rolf Schimmrigk, Steven Duplij, Antoine Van Proeyen, Władysław Marcinek, Gert Roepstorff, Władysław Marcinek, Władysław Marcinek, Steven Duplij, Steven Duplij, Rolf Schimmrigk, Massimo Bianchi, Mikhail Shifman, Robert Marnelius, Giovanni Landi, Władysław Marcinek, Peter Presnajder, Daniel Hernandez Ruiperez, Steven Duplij, Robert Marnelius, Silvia Penati, Steven Duplij, Andrzej Frydryszak, Cosmas Zachos, Sergey Cherkis, Hugo Garcia-Compean, Tamiaki Yoneya, Machiko Hatsuda, Steven Duplij   +27 more
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Hausdorff vs Gromov–Hausdorff Distances

Discrete & Computational Geometry
Henry Adams, Florian Frick, Sushovan Majhi, Nicholas McBride   +3 more
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Hausdorff and Gromov–Hausdorff Distance

2008
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