Gmd: Gaussian mixture descriptor for pair matching of 3D fragments

2026-04-23

AI Summary

This study addresses the challenge of matching fractured surfaces in automatic 3D fragment reassembly from laser scans by proposing a novel local descriptor based on Gaussian Mixture Models (GMMs). The method partitions local regions of fracture surfaces into concave and convex components, models each separately, and fuses them to generate a Gaussian Mixture Descriptor (GMD). Similarity between descriptors is measured using L2 distance, and robust alignment is achieved through a combination of RANSAC and ICP. The key innovation lies in explicitly characterizing point cloud distributions via GMMs and enhancing descriptor discriminability through geometric semantic segmentation. Experimental results demonstrate that the proposed approach significantly outperforms existing methods on both public benchmarks and real-world Terracotta Warrior scan data, substantially improving fragment matching accuracy.

Technology Category

• Computer Vision: 3D Computer Vision
• Search and Optimization: Mixed Discrete/Continuous Search
• Intelligent Robots: Localization, Mapping, and Navigation

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

In the automatic reassembly of fragments acquired using laser scanners to reconstruct objects, a crucial step is the matching of fractured surfaces. In this paper, we propose a novel local descriptor that uses the Gaussian Mixture Model (GMM) to fit the distribution of points, allowing for the description and matching of fractured surfaces of fragments. Our method involves dividing a local surface patch into concave and convex regions for estimating the k value of GMM. Then the final Gaussian Mixture Descriptor (GMD) of the fractured surface is formed by merging the regional GMDs. To measure the similarities between GMDs for determining adjacent fragments, we employ the L2 distance and align the fragments using Random Sample Consensus (RANSAC) and Iterative Closest Point (ICP). The extensive experiments on real-scanned public datasets and Terracotta datasets demonstrate the effectiveness of our approach; furthermore, the comparisons with several existing methods also validate the advantage of the proposed method.

Problem

• 3D fragment reassembly
• fractured surface matching
• local descriptor
• Gaussian Mixture Model
• pair matching

Innovation

• Gaussian Mixture Model
• 3D fragment reassembly
• local surface descriptor
• fractured surface matching
• RANSAC-ICP alignment