# DeepDT: Learning Geometry From Delaunay Triangulation for Surface Reconstruction

arXiv: https://arxiv.org/abs/2101.10353 · HTML: https://mlsanity.com/paper/2101.10353/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 35 references that are in the map.
- First posted on arXiv 25 Jan 2021.

## Builds on (most cited first, 10 of 10)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [OctNet: Learning Deep 3D Representations at High Resolutions](https://mlsanity.com/paper/1611.05009/) (2016)
- [Shape Completion using 3D-Encoder-Predictor CNNs and Shape Synthesis](https://mlsanity.com/paper/1612.00101/) (2016)
- [OctNetFusion: Learning Depth Fusion from Data](https://mlsanity.com/paper/1704.01047/) (2017)
- [SSRNet: Scalable 3D Surface Reconstruction Network](https://mlsanity.com/paper/1911.07401/) (2019)
- [Coupling Explicit and Implicit Surface Representations for Generative 3D Modeling](https://mlsanity.com/paper/2007.10294/) (2020)

## Built on by (most cited first, 12 of 12)

- [POCO: Point Convolution for Surface Reconstruction](https://mlsanity.com/paper/2201.01831/) (2022)
- [ALSO: Automotive Lidar Self-supervision by Occupancy estimation](https://mlsanity.com/paper/2212.05867/) (2022)
- [Reconstructing Surfaces for Sparse Point Clouds with On-Surface Priors](https://mlsanity.com/paper/2204.10603/) (2022)
- [Surface Reconstruction from Point Clouds by Learning Predictive Context Priors](https://mlsanity.com/paper/2204.11015/) (2022)
- [Surface Reconstruction from Point Clouds: A Survey and a Benchmark](https://mlsanity.com/paper/2205.02413/) (2022)
- [PoNQ: a Neural QEM-based Mesh Representation](https://mlsanity.com/paper/2403.12870/) (2024)
- [A Survey and Benchmark of Automatic Surface Reconstruction from Point Clouds](https://mlsanity.com/paper/2301.13656/) (2023)
- [What's the Situation with Intelligent Mesh Generation: A Survey and Perspectives](https://mlsanity.com/paper/2211.06009/) (2022)
- [TetWeave: Isosurface Extraction using On-The-Fly Delaunay Tetrahedral Grids for Gradient-Based Mesh Optimization](https://mlsanity.com/paper/2505.04590/) (2025)
- [Procedural Generation of 3D Maize Plant Architecture from LIDAR Data](https://mlsanity.com/paper/2501.13963/) (2025)
- [A Review of Deep Learning-Powered Mesh Reconstruction Methods](https://mlsanity.com/paper/2303.02879/) (2023)
- [Delaunay Canopy: Building Wireframe Reconstruction from Airborne LiDAR Point Clouds via Delaunay Graph](https://mlsanity.com/paper/2604.02497/) (2026)

## Abstract (arXiv)

In this paper, a novel learning-based network, named DeepDT, is proposed to reconstruct the surface from Delaunay triangulation of point cloud. DeepDT learns to predict inside/outside labels of Delaunay tetrahedrons directly from a point cloud and corresponding Delaunay triangulation. The local geometry features are first extracted from the input point cloud and aggregated into a graph deriving from the Delaunay triangulation. Then a graph filtering is applied on the aggregated features in order to add structural regularization to the label prediction of tetrahedrons. Due to the complicated spatial relations between tetrahedrons and the triangles, it is impossible to directly generate ground truth labels of tetrahedrons from ground truth surface. Therefore, we propose a multi-label supervision strategy which votes for the label of a tetrahedron with labels of sampling locations inside it. The proposed DeepDT can maintain abundant geometry details without generating overly complex surfaces, especially for inner surfaces of open scenes. Meanwhile, the generalization ability and time consumption of the proposed method is acceptable and competitive compared with the state-of-the-art methods. Experiments demonstrate the superior performance of the proposed DeepDT.