Results 11 to 20 of about 65,484 (270)
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
doaj +3 more sources
Relative Hausdorff distance for network analysis [PDF]
Applied Network Science, 2019 Similarity measures are used extensively in machine learning and data science algorithms. The newly proposed graph Relative Hausdorff (RH) distance is a lightweight yet nuanced similarity measure for quantifying the closeness of two graphs.
Sinan G. Aksoy +3 more
doaj +3 more sources
Branching Geodesics of the Gromov-Hausdorff Distance
Analysis and Geometry in Metric Spaces, 2022 In this paper, we first evaluate topological distributions of the sets of all doubling spaces, all uniformly disconnected spaces, and all uniformly perfect spaces in the space of all isometry classes of compact metric spaces equipped with the Gromov ...
Ishiki Yoshito
doaj +3 more sources
Hausdorff vs Gromov-Hausdorff distances [PDF]
, 2023 Let $M$ be a closed Riemannian manifold and let $X\subseteq M$. If the sample $X$ is sufficiently dense relative to the curvature of $M$, then the Gromov-Hausdorff distance between $X$ and $M$ is bounded from below by half their Hausdorff distance, namely $d_{GH}(X,M) \ge \frac{1}{2} d_H(X,M)$.
Henry Adams +3 more
openalex +3 more sources
Between shapes, using the Hausdorff distance
Computational Geometry, 2021 Given two shapes $A$ and $B$ in the plane with Hausdorff distance $1$, is there a shape $S$ with Hausdorff distance $1/2$ to and from $A$ and $B$? The answer is always yes, and depending on convexity of $A$ and/or $B$, $S$ may be convex, connected, or disconnected. We show that our result can be generalised to give an interpolated shape between $A$ and
Marc van Kreveld +4 more
openalex +10 more sources
Matricial quantum Gromov-Hausdorff distance [PDF]
Journal of Functional Analysis, 2002 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
openalex +3 more sources
Gromov--Hausdorff Distance to Simplexes [PDF]
, 2019 Geometric characteristics of metric spaces that appear in formulas of the Gromov--Hausdorff distances from these spaces to so-called simplexes, i.e., to the metric spaces, all whose non-zero distances are the same are studied. The corresponding calculations essentially use geometry of partitions of these spaces. In the finite case, it gives the lengths
D. S. Grigor'ev +2 more
openalex +3 more sources
GAN‐LSTM‐3D: An efficient method for lung tumour 3D reconstruction enhanced by attention‐based LSTM
CAAI Transactions on Intelligence Technology, EarlyView., 2023 Abstract Three‐dimensional (3D) image reconstruction of tumours can visualise their structures with precision and high resolution. In this article, GAN‐LSTM‐3D method is proposed for 3D reconstruction of lung cancer tumours from 2D CT images. Our method consists of three phases: lung segmentation, tumour segmentation, and tumour 3D reconstruction. Lung
Lu Hong +12 more
wiley +1 more source
IEEE Access, 2023 The notion of a complex hesitant fuzzy set (CHFS) is one of the better tools in order to deal with complex information. Since distance plays a crucial role in order to differentiate between two things or sets, in this paper, we first develop a priority ...
Muhammad Sajjad Ali Khan +4 more
doaj +1 more source
Borel measures and Hausdorff distance [PDF]
Transactions of the American Mathematical Society, 1988 In this article we study the restriction of Borel measures defined on a metric space X X to the nonempty closed subsets CL ( X ) \operatorname {CL} (X) of X X , topologized by Hausdorff distance. We show that a σ \sigma -finite Radon measure is a
Beer, Gerald, Villar, Luzviminda
openaire +2 more sources