# Neural Poisson: Indicator Functions for Neural Fields

arXiv: https://arxiv.org/abs/2211.14249 · HTML: https://mlsanity.com/paper/2211.14249/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 34 references that are in the map.
- First posted on arXiv 25 Nov 2022.

## Builds on (most cited first, 16 of 16)

- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Semantic Scene Completion from a Single Depth Image](https://mlsanity.com/paper/1611.08974/) (2016)
- [ARKitScenes: A Diverse Real-World Dataset For 3D Indoor Scene Understanding Using Mobile RGB-D Data](https://mlsanity.com/paper/2111.08897/) (2021)
- [3D-FRONT: 3D Furnished Rooms with layOuts and semaNTics](https://mlsanity.com/paper/2011.09127/) (2020)
- [Implicit Functions in Feature Space for 3D Shape Reconstruction and Completion](https://mlsanity.com/paper/2003.01456/) (2020)
- [Shape Completion using 3D-Encoder-Predictor CNNs and Shape Synthesis](https://mlsanity.com/paper/1612.00101/) (2016)
- [BundleFusion: Real-time Globally Consistent 3D Reconstruction using On-the-fly Surface Re-integration](https://mlsanity.com/paper/1604.01093/) (2016)
- [ScanComplete: Large-Scale Scene Completion and Semantic Segmentation for 3D Scans](https://mlsanity.com/paper/1712.10215/) (2017)
- [NPMs: Neural Parametric Models for 3D Deformable Shapes](https://mlsanity.com/paper/2104.00702/) (2021)
- [SG-NN: Sparse Generative Neural Networks for Self-Supervised Scene Completion of RGB-D Scans](https://mlsanity.com/paper/1912.00036/) (2019)
- [Iso-Points: Optimizing Neural Implicit Surfaces with Hybrid Representations](https://mlsanity.com/paper/2012.06434/) (2020)
- [SPAMs: Structured Implicit Parametric Models](https://mlsanity.com/paper/2201.08141/) (2022)

## Built on by (most cited first, 7 of 7)

- [Towards Better Gradient Consistency for Neural Signed Distance Functions via Level Set Alignment](https://mlsanity.com/paper/2305.11601/) (2023)
- [Unsupervised Inference of Signed Distance Functions from Single Sparse Point Clouds without Learning Priors](https://mlsanity.com/paper/2303.14505/) (2023)
- [GridPull: Towards Scalability in Learning Implicit Representations from 3D Point Clouds](https://mlsanity.com/paper/2308.13175/) (2023)
- [HotSpot: Signed Distance Function Optimization with an Asymptotically Sufficient Condition](https://mlsanity.com/paper/2411.14628/) (2024)
- [Inferring Neural Signed Distance Functions by Overfitting on Single Noisy Point Clouds through Finetuning Data-Driven based Priors](https://mlsanity.com/paper/2410.19680/) (2024)
- [AiSDF: Structure-aware Neural Signed Distance Fields in Indoor Scenes](https://mlsanity.com/paper/2403.01861/) (2024)
- [Surface Reconstruction from Range Scans Under Visibility Constraints](https://mlsanity.com/paper/2610.18005/) (2026)

## Abstract (arXiv)

Implicit neural field generating signed distance field representations (SDFs) of 3D shapes have shown remarkable progress in 3D shape reconstruction and generation. We introduce a new paradigm for neural field representations of 3D scenes; rather than characterizing surfaces as SDFs, we propose a Poisson-inspired characterization for surfaces as indicator functions optimized by neural fields. Crucially, for reconstruction of real scan data, the indicator function representation enables simple and effective constraints based on common range sensing inputs, which indicate empty space based on line of sight. Such empty space information is intrinsic to the scanning process, and incorporating this knowledge enables more accurate surface reconstruction. We show that our approach demonstrates state-of-the-art reconstruction performance on both synthetic and real scanned 3D scene data, with 9.5% improvement in Chamfer distance over state of the art.