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

arXiv: https://arxiv.org/abs/2604.21519 · HTML: https://mlsanity.com/paper/2604.21519/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 45 references that are in the map.
- First posted on arXiv 23 Apr 2026.

## Builds on (most cited first, 5 of 5)

- [TEASER: Fast and Certifiable Point Cloud Registration](https://mlsanity.com/paper/2001.07715/) (2020)
- [Neural Shape Mating: Self-Supervised Object Assembly with Adversarial Shape Priors](https://mlsanity.com/paper/2205.14886/) (2022)
- [Breaking Bad: A Dataset for Geometric Fracture and Reassembly](https://mlsanity.com/paper/2210.11463/) (2022)
- [LSG-CPD: Coherent Point Drift with Local Surface Geometry for Point Cloud Registration](https://mlsanity.com/paper/2103.15039/) (2021)
- [A New Outlier Removal Strategy Based on Reliability of Correspondence Graph for Fast Point Cloud Registration](https://mlsanity.com/paper/2205.07404/) (2022)

## Abstract (arXiv)

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.