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arXiv · 2601.07621

Searching point patterns in point clouds describing local topography

Ewa Bednarczuk·Rafał Bieńkowski·Robert Kłopotek·Jan Kryński·Krzysztof Leśsniewski·Krzysztof Rutkowski·Małgorzata Szelachowska
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Abstract

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.

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Ewa Bednarczuk, Rafał Bieńkowski, Robert Kłopotek, Jan Kryński, Krzysztof Leśsniewski, Krzysztof Rutkowski, Małgorzata Szelachowska. 2026-01-12. Searching point patterns in point clouds describing local topography. https://arxiv.org/abs/2601.07621

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