# A Three-Dimensional Reverse-Projection Method for Sparse Point Cloud Completion and Its Application to High-Speed Train Nose Reconstruction

arXiv: https://arxiv.org/abs/2610.05758 · HTML: https://mlsanity.com/paper/2610.05758/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 35 references that are in the map.
- First posted on arXiv 5 Oct 2026.

## Builds on (most cited first, 12 of 12)

- [PU-Net: Point Cloud Upsampling Network](https://mlsanity.com/paper/1801.06761/) (2018)
- [Robot Operating System 2: Design, Architecture, and Uses In The Wild](https://mlsanity.com/paper/2211.07752/) (2022)
- [PU-GAN: a Point Cloud Upsampling Adversarial Network](https://mlsanity.com/paper/1907.10844/) (2019)
- [PU-GCN: Point Cloud Upsampling using Graph Convolutional Networks](https://mlsanity.com/paper/1912.03264/) (2019)
- [PointAttN: You Only Need Attention for Point Cloud Completion](https://mlsanity.com/paper/2203.08485/) (2022)
- [FAST-LIVO2: Fast, Direct LiDAR-Inertial-Visual Odometry](https://mlsanity.com/paper/2408.14035/) (2024)
- [SuperPC: A Single Diffusion Model for Point Cloud Completion, Upsampling, Denoising, and Colorization](https://mlsanity.com/paper/2503.14558/) (2025)
- [GS-LIVM: Real-Time Photo-Realistic LiDAR-Inertial-Visual Mapping with Gaussian Splatting](https://mlsanity.com/paper/2410.17084/) (2024)
- [Arbitrary-Scale Point Cloud Upsampling by Voxel-Based Network with Latent Geometric-Consistent Learning](https://mlsanity.com/paper/2403.05117/) (2024)
- [Robust Hole-Detection in Triangular Meshes Irrespective of the Presence of Singular Vertices](https://mlsanity.com/paper/2311.12466/) (2023)
- [Terrain Point Cloud Inpainting via Signal Decomposition](https://mlsanity.com/paper/2404.03572/) (2024)
- [PU-Gaussian: Point Cloud Upsampling using 3D Gaussian Representation](https://mlsanity.com/paper/2509.20207/) (2025)

## Abstract (arXiv)

Holes in LiDAR scans of environments with glass windows remain an unresolved problem in three-dimensional reconstruction. This study presents a pipeline for point cloud acquisition, filtering, completion, and surface reconstruction to address sparse sampling and missing window regions in scans of a high-speed train nose. FAST-LIVO2 provides the initial point cloud through multisensor odometry and mapping, and moving least squares (MLS) smooths the observations. We then introduce three-axis projection-based subdivision and interpolation with reverse hole boundary identification, referred to as three-axis reverse completion. The method interpolates missing regions from observations around each hole. Greedy projection triangulation, Poisson surface reconstruction, and a Marching Cubes-based pipeline generate meshes from the completed point cloud. Experiments on a proportionally scaled display model of a high-speed train nose show that the proposed method fills missing point cloud regions around the glass windows. Under the evaluation setting used in this study, greedy projection triangulation yields lower geometric distance errors than the other two reconstruction pipelines. The pipeline supports non-contact digital modeling of train nose geometry and provides a practical approach to reconstructing objects with glass windows.