Searching point patterns in point clouds describing local topography
Ewa Bednarczuk, Rafa{\l} Bie\'nkowski, Robert K{\l}opotek, Jan Kry\'nski, Krzysztof Le\'ssniewski, Krzysztof Rutkowski, Ma{\l}gorzata Szelachowska

TL;DR
This paper introduces a novel local descriptor for comparing and aligning 3D point patterns based on height variations, enhancing geometric analysis in topographical data.
Contribution
The work presents a new normalized finite-difference operator that serves as a local descriptor, integrating with Wasserstein distances and Procrustes analysis for improved pattern comparison and alignment.
Findings
Provides a parametrization-independent local descriptor
Enables natural integration with Wasserstein distances
Facilitates rigid alignment of geometric structures
Abstract
We address the problem of comparing and aligning spatial point configurations in 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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Taxonomy
Topics3D Shape Modeling and Analysis · Computational Geometry and Mesh Generation · Topological and Geometric Data Analysis
