# Reducing the Gap Between Spatial and Space-Filling Curve Neighbors in 3D Point Cloud Segmentation

arXiv: https://arxiv.org/abs/2610.19530 · HTML: https://mlsanity.com/paper/2610.19530/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 31 references that are in the map.
- First posted on arXiv 14 Oct 2026.

## Builds on (most cited first, 23 of 23)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [ScanNet: Richly-annotated 3D Reconstructions of Indoor Scenes](https://mlsanity.com/paper/1702.04405/) (2017)
- [PointPillars: Fast Encoders for Object Detection from Point Clouds](https://mlsanity.com/paper/1812.05784/) (2018)
- [Point Transformer](https://mlsanity.com/paper/2011.00931/) (2020)
- [4D Spatio-Temporal ConvNets: Minkowski Convolutional Neural Networks](https://mlsanity.com/paper/1904.08755/) (2019)
- [PCT: Point cloud transformer](https://mlsanity.com/paper/2012.09688/) (2020)
- [Multi-View 3D Object Detection Network for Autonomous Driving](https://mlsanity.com/paper/1611.07759/) (2016)
- [Point Transformer V3: Simpler, Faster, Stronger](https://mlsanity.com/paper/2312.10035/) (2023)
- [Semantic Scene Completion from a Single Depth Image](https://mlsanity.com/paper/1611.08974/) (2016)
- [PointNeXt: Revisiting PointNet++ with Improved Training and Scaling Strategies](https://mlsanity.com/paper/2206.04670/) (2022)
- [Point Transformer V2: Grouped Vector Attention and Partition-based Pooling](https://mlsanity.com/paper/2210.05666/) (2022)
- [Rethinking Network Design and Local Geometry in Point Cloud: A Simple Residual MLP Framework](https://mlsanity.com/paper/2202.07123/) (2022)
- [Deep Learning for LiDAR Point Clouds in Autonomous Driving: A Review](https://mlsanity.com/paper/2005.09830/) (2020)
- [Swin3D: A Pretrained Transformer Backbone for 3D Indoor Scene Understanding](https://mlsanity.com/paper/2304.06906/) (2023)
- [OctFormer: Octree-based Transformers for 3D Point Clouds](https://mlsanity.com/paper/2305.03045/) (2023)
- [Vehicle Detection from 3D Lidar Using Fully Convolutional Network](https://mlsanity.com/paper/1608.07916/) (2016)
- [FlatFormer: Flattened Window Attention for Efficient Point Cloud Transformer](https://mlsanity.com/paper/2301.08739/) (2023)
- [Semantic Segmentation for Real Point Cloud Scenes via Bilateral Augmentation and Adaptive Fusion](https://mlsanity.com/paper/2103.07074/) (2021)
- [DALES: A Large-scale Aerial LiDAR Data Set for Semantic Segmentation](https://mlsanity.com/paper/2004.11985/) (2020)
- [Efficient 3D Semantic Segmentation with Superpoint Transformer](https://mlsanity.com/paper/2306.08045/) (2023)
- [PanopticNDT: Efficient and Robust Panoptic Mapping](https://mlsanity.com/paper/2309.13635/) (2023)

## Abstract (arXiv)

As a lightweight and highly accurate method for nearest-neighbor search in 3D point clouds, approaches based on space-filling curves (SFC) have been proposed. However, due to the inherent properties of SFC, a gap arises between proximity relationships along the SFC and those in the original Euclidean space. In this study, we propose a loss function that reduces the influence of this gap. Specifically, we compute the distances between adjacent points along the SFC and train the model to optimize feature similarity between pairs of points that are distant from each other in the original 3D space. We incorporate the proposed method into a high-performing 3D point cloud segmentation model and evaluate its effectiveness on three datasets. The results demonstrate that the proposed method outperforms conventional methods on both indoor and outdoor point cloud datasets.