Searching point patterns in point clouds describing local topography

2026-01-12

AI Summary

This work proposes a parameter-free local topographic descriptor for the comparison and rigid alignment of three-dimensional structured point patterns. The method decomposes each point pattern into multiple arms and introduces a normalized finite difference operator along each arm to capture the local variation of height components relative to the underlying planar geometry, thereby integrating fine-grained geometric details with global structural information. By combining Wasserstein distance with Procrustes analysis, the approach enables efficient distributional comparison and precise alignment of point clouds. The proposed descriptor preserves salient local topographic features while significantly enhancing the robustness and accuracy of point pattern matching.

Technology Category

Computer Vision: 3D Computer VisionIntelligent Robots: Localization, Mapping, and NavigationMachine Learning: Learning with Manifolds

Application Category

Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsSystems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deploymentsWeb Mining and Content Analysis: Robustness and generalizability of Web mining methods

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.

Problem

• point cloud
• point pattern
• spatial alignment
• local topography
• geometric pattern

Innovation

• finite-difference operator
• parametrization-independent descriptor
• point cloud alignment
• Wasserstein distance
• Procrustes analysis