Computational aspects of the Hausdorff distance in unbounded dimension
Journal of Computational Geometry, 2014 We study the computational complexity of determining the Hausdorff distance oftwo polytopes given in halfspace- or vertex-presentation in arbitrary dimension.
Stefan König
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Hausdorff Measures on Generalized Set Valued Neutrosophic Quadruple Numbers and Decision Making Applications for Adequacy of Online Education [PDF]
Neutrosophic Sets and Systems, 2021 In this paper, we develop a new method of decision-making algorithm with Hausdorff distance and Hausdorff similarity measures based on generalized set-valued neutrosophic quadruple numbers.
Sevilay Şahin +2 more
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Approximating Gromov-Hausdorff distance in Euclidean space
Computational Geometry: Theory and ApplicationsThe 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, Carola Wenk
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Determining the Hausdorff Distance Between Trees in Polynomial Time [PDF]
Discrete Mathematics & Theoretical Computer Science, 2021 The Hausdorff distance is a relatively new measure of similarity of graphs. The notion of the Hausdorff distance considers a special kind of a common subgraph of the compared graphs and depends on the structural properties outside of the common subgraph.
Aleksander Kelenc
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A hybrid Hausdorff distance track correlation algorithm based on time sliding window [PDF]
MATEC Web of Conferences, 2021 In multi-sensor target tracking, track correlation is the key to the unification of global situation. Hausdorff distance has been applied to power fault elimination, point cloud data, medical measurement, image segmentation, vehicle trajectory ...
Li Yinlong, Zhang Tianshu
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The Complexity of the Hausdorff Distance
Discrete & Computational Geometry, 2023 AbstractWe investigate the computational complexity of computing the Hausdorff distance. Specifically, we show that the decision problem of whether the Hausdorff distance of two semi-algebraic sets is bounded by a given threshold is complete for the complexity class $${ \forall \exists _{<}\mathbb {R}} $$ ∀
Paul Jungeblut +2 more
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FPT-Algorithms for computing Gromov-Hausdorff and interleaving distances between trees
Journal of Computational Geometry, 2022 The Gromov-Hausdorff distance is a natural way to measure the distortion between two metric spaces. However, there has been only limited algorithmic development to compute or approximate this distance. We focus on computing the Gromov-Hausdorff distance
Elena Farahbakhsh Touli, Yusu Wang
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Translating Hausdorff is hard: fine-grained lower bounds for Hausdorff distance under translation
Journal of Computational Geometry, 2022 Computing the similarity of two point sets is a ubiquitous task in medical imaging, geometric shape comparison, trajectory analysis, and many more settings.
Karl Bringmann, André Nusser
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Lost-in-space star identification algorithm based on Hausdorff distance with two approaches: Pivot star and celestial sphere segmentation [PDF]
علوم، فناوری و کاربردهای فضایی, 2023 One of the best attitude sensors for space applications is the star sensor. This sensor determines the attitude using stars in the field of view. One of the main advantages of this sensor is attitude initialization using lost-in-space star identification
Mona Zahednamazi +2 more
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Hausdorff vs Gromov-Hausdorff distances
, 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 $d_{GH}(X,M) \ge \frac{1}{2} d_H(X,M)$.
Adams, Henry +3 more
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