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| Main Authors: | , , , , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.07621 |
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| _version_ | 1866908760006459392 |
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| author | Bednarczuk, Ewa Bieńkowski, Rafał Kłopotek, Robert Kryński, Jan Leśsniewski, Krzysztof Rutkowski, Krzysztof Szelachowska, Małgorzata |
| author_facet | Bednarczuk, Ewa Bieńkowski, Rafał Kłopotek, Robert Kryński, Jan Leśsniewski, Krzysztof Rutkowski, Krzysztof Szelachowska, Małgorzata |
| contents | We address the problem of comparing and aligning spatial point configurations in $\mathbb{R}^3$ arising from structured geometric patterns. Each pattern is decomposed into arms along which we define a normalized finite-difference operator measuring local variations of the height component with respect to the planar geometry of the pattern. This quantity provides a parametrization-independent local descriptor that complements global similarity measures. In particular, it integrates naturally with Wasserstein-type distances for comparing point distributions and with Procrustes analysis for rigid alignment of geometric structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_07621 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Searching point patterns in point clouds describing local topography Bednarczuk, Ewa Bieńkowski, Rafał Kłopotek, Robert Kryński, Jan Leśsniewski, Krzysztof Rutkowski, Krzysztof Szelachowska, Małgorzata Computational Geometry Optimization and Control We address the problem of comparing and aligning spatial point configurations in $\mathbb{R}^3$ arising from structured geometric patterns. Each pattern is decomposed into arms along which we define a normalized finite-difference operator measuring local variations of the height component with respect to the planar geometry of the pattern. This quantity provides a parametrization-independent local descriptor that complements global similarity measures. In particular, it integrates naturally with Wasserstein-type distances for comparing point distributions and with Procrustes analysis for rigid alignment of geometric structures. |
| title | Searching point patterns in point clouds describing local topography |
| topic | Computational Geometry Optimization and Control |
| url | https://arxiv.org/abs/2601.07621 |