# 3D Point Cloud Super-Resolution via Graph Total Variation on Surface Normals

arXiv: https://arxiv.org/abs/1908.06261 · HTML: https://mlsanity.com/paper/1908.06261/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Aug 2019.

## Built on by (most cited first, 8 of 8)

- [PUFA-GAN: A Frequency-Aware Generative Adversarial Network for 3D Point Cloud Upsampling](https://mlsanity.com/paper/2203.00914/) (2022)
- [Joint Point Cloud Upsampling and Cleaning with Octree-based CNNs](https://mlsanity.com/paper/2410.17001/) (2024)
- [Frequency-Selective Geometry Upsampling of Point Clouds](https://mlsanity.com/paper/2205.01458/) (2022)
- [SplatSuRe: Selective Super-Resolution for Multi-view Consistent 3D Gaussian Splatting](https://mlsanity.com/paper/2512.02172/) (2025)
- [Empir3D : A Framework for Multi-Dimensional Point Cloud Assessment](https://mlsanity.com/paper/2306.03660/) (2023)
- [LiSu: A Dataset and Method for LiDAR Surface Normal Estimation](https://mlsanity.com/paper/2503.08601/) (2025)
- [Secure AI-Driven Super-Resolution for Real-Time Mixed Reality Applications](https://mlsanity.com/paper/2512.15823/) (2025)
- [Joint Geometry and Attribute Upsampling of Point Clouds Using Frequency-Selective Models with Overlapped Support](https://mlsanity.com/paper/2301.11630/) (2023)

## Abstract (arXiv)

Point cloud is a collection of 3D coordinates that are discrete geometric samples of an object's 2D surfaces. Using a low-cost 3D scanner to acquire data means that point clouds are often in lower resolution than desired for rendering on high-resolution displays. Building on recent advances in graph signal processing, we design a local algorithm for 3D point cloud super-resolution (SR). First, we initialize new points at centroids of local triangles formed using the low-resolution point cloud, and connect all points using a k-nearestneighbor graph. Then, to establish a linear relationship between surface normals and 3D point coordinates, we perform bipartite graph approximation to divide all nodes into two disjoint sets, which are optimized alternately until convergence. For each node set, to promote piecewise smooth (PWS) 2D surfaces, we design a graph total variation (GTV) objective for nearby surface normals, under the constraint that coordinates of the original points are preserved. We pursue an augmented Lagrangian approach to tackle the optimization, and solve the unconstrained equivalent using the alternating method of multipliers (ADMM). Extensive experiments show that our proposed point cloud SR algorithm outperforms competing schemes objectively and subjectively for a large variety of point clouds.