# Graph-based Point Cloud Surface Reconstruction using B-Splines

arXiv: https://arxiv.org/abs/2509.16050 · HTML: https://mlsanity.com/paper/2509.16050/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 37 references that are in the map.
- First posted on arXiv 19 Sep 2025.

## Builds on (most cited first, 13 of 13)

- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [Large-scale Point Cloud Semantic Segmentation with Superpoint Graphs](https://mlsanity.com/paper/1711.09869/) (2017)
- [Point-GNN: Graph Neural Network for 3D Object Detection in a Point Cloud](https://mlsanity.com/paper/2003.01251/) (2020)
- [What Do Single-view 3D Reconstruction Networks Learn?](https://mlsanity.com/paper/1905.03678/) (2019)
- [Morphing and Sampling Network for Dense Point Cloud Completion](https://mlsanity.com/paper/1912.00280/) (2019)
- [Density-aware Chamfer Distance as a Comprehensive Metric for Point Cloud Completion](https://mlsanity.com/paper/2111.12702/) (2021)
- [ParSeNet: A Parametric Surface Fitting Network for 3D Point Clouds](https://mlsanity.com/paper/2003.12181/) (2020)
- [DeepFit: 3D Surface Fitting via Neural Network Weighted Least Squares](https://mlsanity.com/paper/2003.10826/) (2020)
- [Surface Reconstruction from Point Clouds: A Survey and a Benchmark](https://mlsanity.com/paper/2205.02413/) (2022)
- [GraphFit: Learning Multi-scale Graph-Convolutional Representation for Point Cloud Normal Estimation](https://mlsanity.com/paper/2207.11484/) (2022)
- [p-Poisson surface reconstruction in curl-free flow from point clouds](https://mlsanity.com/paper/2310.20095/) (2023)
- [Differentiable Spline Approximations](https://mlsanity.com/paper/2110.01532/) (2021)

## Abstract (arXiv)

Generating continuous surfaces from discrete point cloud data is a fundamental task in several 3D vision applications. Real-world point clouds are inherently noisy due to various technical and environmental factors. Existing data-driven surface reconstruction algorithms rely heavily on ground truth normals or compute approximate normals as an intermediate step. This dependency makes them extremely unreliable for noisy point cloud datasets, even if the availability of ground truth training data is ensured, which is not always the case. B-spline reconstruction techniques provide compact surface representations of point clouds and are especially known for their smoothening properties. However, the complexity of the surfaces approximated using B-splines is directly influenced by the number and location of the spline control points. Existing spline-based modeling methods predict the locations of a fixed number of control points for a given point cloud, which makes it very difficult to match the complexity of its underlying surface. In this work, we develop a Dictionary-Guided Graph Convolutional Network-based surface reconstruction strategy where we simultaneously predict both the location and the number of control points for noisy point cloud data to generate smooth surfaces without the use of any point normals. We compare our reconstruction method with several well-known as well as recent baselines by employing widely-used evaluation metrics, and demonstrate that our method outperforms all of them both qualitatively and quantitatively.