Approximating Gromov-Hausdorff Distance in Euclidean Space [PDF]
Computational Geometry, 2019 The Gromov-Hausdorff distance $(d_{GH})$ proves to be a useful distance measure between shapes. In order to approximate $d_{GH}$ for compact subsets $X,Y\subset\mathbb{R}^d$, we look into its relationship with $d_{H,iso}$, the infimum Hausdorff distance under Euclidean isometries.
Sushovan Majhi +2 more
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The Hausdorff Algebra Fuzzy Distance and its Basic Properties [PDF]
Engineering and Technology Journal, 2021 In this article we recall the definition of algebra fuzzy metric space and its basic properties. In order to introduced the Hausdorff algebra fuzzy metric from fuzzy compact set to another fuzzy compact set we define the algebra fuzzy distance between ...
Zainab Khudhair, Jehad Kider
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A (p,q)-Averaged Hausdorff Distance for Arbitrary Measurable Sets
Mathematical and Computational Applications, 2018 The Hausdorff distance is a widely used tool to measure the distance between different sets. For the approximation of certain objects via stochastic search algorithms this distance is, however, of limited use as it punishes single outliers.
Johan M. Bogoya +3 more
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Chordal Hausdorff Convergence and Quasihyperbolic Distance [PDF]
Analysis and Geometry in Metric Spaces, 2020 We study Hausdorff convergence (and related topics) in the chordalization of a metric space to better understand pointed Gromov-Hausdorff convergence of quasihyperbolic distances (and other conformal distances).
Herron David A. +2 more
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Efficient and Accurate Hausdorff Distance Computation Based on Diffusion Search
IEEE Access, 2018 The Hausdorff distance (HD) between two point sets is widely used in similarity measures, but the high computational cost of HD algorithms restrict their practical use.
Dejun Zhang +3 more
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Development of hamming and hausdorff distance metrics for cubic intuitionistic fuzzy hypersoft set in cement storage quality control: Development and evaluation. [PDF]
PLoS One, 2023 Saeed M, Saeed MH, Khalid M, Mekawy I.
europepmc +3 more sources
A cohomology-based Gromov–Hausdorff metric approach for quantifying molecular similarity [PDF]
Scientific ReportsWe introduce a cohomology-based Gromov–Hausdorff ultrametric method to analyze 1-dimensional and higher-dimensional (co)homology groups, focusing on loops, voids, and higher-dimensional cavity structures in simplicial complexes, to address typical ...
JunJie Wee +3 more
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Target Detection Based on Improved Hausdorff Distance Matching Algorithm for Millimeter-Wave Radar and Video Fusion. [PDF]
Sensors (Basel), 2022 Xu D, Liu Y, Wang Q, Wang L, Liu R.
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Quantized Gromov–Hausdorff distance
Journal of Functional Analysis, 2006 A quantized metric space is a matrix order unit space equipped with an operator space version of Rieffel's Lip-norm. We develop for quantized metric spaces an operator space version of quantum Gromov-Hausdorff distance. We show that two quantized metric spaces are completely isometric if and only if their quantized Gromov-Hausdorff distance is zero. We
Wei Wu
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Matricial quantum Gromov–Hausdorff distance [PDF]
Journal of Functional Analysis, 2003 We develop a matricial version of Rieffel's Gromov-Hausdorff distance for compact quantum metric spaces within the setting of operator systems and unital C*-algebras. Our approach yields a metric space of ``isometric'' unital complete order isomorphism classes of metrized operator systems which in many cases exhibits the same convergence properties as ...
David Kerr
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