dorsal/arxiv
View SchemaSearching point patterns in point clouds describing local topography
| Authors | Ewa Bednarczuk, Rafał Bieńkowski, Robert Kłopotek, Jan Kryński, Krzysztof Leśsniewski, Krzysztof Rutkowski, Małgorzata Szelachowska |
|---|---|
| Categories | |
| ArXiv ID | 2601.07621vv1 |
| URL | https://arxiv.org/abs/2601.07621 |
| License | http://creativecommons.org/licenses/by/4.0/ |
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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"record": {
"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.",
"arxiv_id": "2601.07621",
"authors": [
"Ewa Bednarczuk",
"Rafa\u0142 Bie\u0144kowski",
"Robert K\u0142opotek",
"Jan Kry\u0144ski",
"Krzysztof Le\u015bsniewski",
"Krzysztof Rutkowski",
"Ma\u0142gorzata Szelachowska"
],
"categories": [
"cs.CG",
"math.OC"
],
"license": "http://creativecommons.org/licenses/by/4.0/",
"title": "Searching point patterns in point clouds describing local topography",
"url": "https://arxiv.org/abs/2601.07621",
"version": "v1"
},
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"source": {
"execution_id": "eb6ad89a-caa6-4263-8eb7-1fbc19319f53",
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