research-article

Between shapes, using the Hausdorff distance

Authors:

Marc van Kreveld,

Tillmann Miltzow,

Jordi L. VermeulenAuthors Info & Claims

Volume 100, Issue C

https://doi.org/10.1016/j.comgeo.2021.101817

Published: 01 January 2022 Publication History

Abstract

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 generalized to give an interpolated shape between A and B for any interpolation variable α between 0 and 1, and prove that the resulting morph has a bounded rate of change with respect to α. Finally, we explore a generalization of the concept of a Hausdorff middle to more than two input sets. We show how to approximate or compute this middle shape, and that the properties relating to the connectedness of the Hausdorff middle extend from the case with two input sets. We also give bounds on the Hausdorff distance between the middle set and the input.

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Digital Library

Cited By

Alpar OKrejcar O(2023)Whole Tumor Area Estimation in Incremental Brain MRI Using Dilation and Erosion-Based Binary MorphingBioinformatics and Biomedical Engineering10.1007/978-3-031-34953-9_10(131-142)Online publication date: 12-Jul-2023
https://dl.acm.org/doi/10.1007/978-3-031-34953-9_10

Index Terms

Between shapes, using the Hausdorff distance
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
2. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Computational geometry

Index terms have been assigned to the content through auto-classification.

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cover image Computational Geometry: Theory and Applications

Computational Geometry: Theory and Applications Volume 100, Issue C

Jan 2022

152 pages

ISSN:0925-7721

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Elsevier Science Publishers B. V.

Netherlands

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Published: 01 January 2022

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Cited By

Alpar OKrejcar O(2023)Whole Tumor Area Estimation in Incremental Brain MRI Using Dilation and Erosion-Based Binary MorphingBioinformatics and Biomedical Engineering10.1007/978-3-031-34953-9_10(131-142)Online publication date: 12-Jul-2023
https://dl.acm.org/doi/10.1007/978-3-031-34953-9_10

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