# PET-NeuS: Positional Encoding Tri-Planes for Neural Surfaces

arXiv: https://arxiv.org/abs/2305.05594 · HTML: https://mlsanity.com/paper/2305.05594/

## Key facts

- Cited by 37 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 50 references that are in the map.
- First posted on arXiv 9 May 2023.

## Builds on (most cited first, 30 of 31)

- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [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)
- [Mip-NeRF: A Multiscale Representation for Anti-Aliasing Neural Radiance Fields](https://mlsanity.com/paper/2103.13415/) (2021)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [Plenoxels: Radiance Fields without Neural Networks](https://mlsanity.com/paper/2112.05131/) (2021)
- [TensoRF: Tensorial Radiance Fields](https://mlsanity.com/paper/2203.09517/) (2022)
- [Efficient Geometry-aware 3D Generative Adversarial Networks](https://mlsanity.com/paper/2112.07945/) (2021)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Volume Rendering of Neural Implicit Surfaces](https://mlsanity.com/paper/2106.12052/) (2021)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Differentiable Volumetric Rendering: Learning Implicit 3D Representations without 3D Supervision](https://mlsanity.com/paper/1912.07372/) (2019)
- [KiloNeRF: Speeding up Neural Radiance Fields with Thousands of Tiny MLPs](https://mlsanity.com/paper/2103.13744/) (2021)
- [Common Objects in 3D: Large-Scale Learning and Evaluation of Real-life 3D Category Reconstruction](https://mlsanity.com/paper/2109.00512/) (2021)
- [UNISURF: Unifying Neural Implicit Surfaces and Radiance Fields for Multi-View Reconstruction](https://mlsanity.com/paper/2104.10078/) (2021)
- [Ref-NeRF: Structured View-Dependent Appearance for Neural Radiance Fields](https://mlsanity.com/paper/2112.03907/) (2021)
- [Stand-Alone Self-Attention in Vision Models](https://mlsanity.com/paper/1906.05909/) (2019)
- [Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapes](https://mlsanity.com/paper/2101.10994/) (2021)
- [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019)
- [Implicit Functions in Feature Space for 3D Shape Reconstruction and Completion](https://mlsanity.com/paper/2003.01456/) (2020)
- [Neural Unsigned Distance Fields for Implicit Function Learning](https://mlsanity.com/paper/2010.13938/) (2020)
- [Neural Volumes: Learning Dynamic Renderable Volumes from Images](https://mlsanity.com/paper/1906.07751/) (2019)
- [Modulated Periodic Activations for Generalizable Local Functional Representations](https://mlsanity.com/paper/2104.03960/) (2021)
- [Improving neural implicit surfaces geometry with patch warping](https://mlsanity.com/paper/2112.09648/) (2021)
- [HF-NeuS: Improved Surface Reconstruction Using High-Frequency Details](https://mlsanity.com/paper/2206.07850/) (2022)
- [ACORN: Adaptive Coordinate Networks for Neural Scene Representation](https://mlsanity.com/paper/2105.02788/) (2021)
- [SAPE: Spatially-Adaptive Progressive Encoding for Neural Optimization](https://mlsanity.com/paper/2104.09125/) (2021)

## Built on by (most cited first, 30 of 37)

- [Advances in 3D Generation: A Survey](https://mlsanity.com/paper/2401.17807/) (2024)
- [SemCity: Semantic Scene Generation with Triplane Diffusion](https://mlsanity.com/paper/2403.07773/) (2024)
- [Collaborative Semantic Occupancy Prediction with Hybrid Feature Fusion in Connected Automated Vehicles](https://mlsanity.com/paper/2402.07635/) (2024)
- [ResFields: Residual Neural Fields for Spatiotemporal Signals](https://mlsanity.com/paper/2309.03160/) (2023)
- [Anti-Aliased Neural Implicit Surfaces with Encoding Level of Detail](https://mlsanity.com/paper/2309.10336/) (2023)
- [Learning-based Multi-View Stereo: A Survey](https://mlsanity.com/paper/2408.15235/) (2024)
- [G3PT: Unleash the power of Autoregressive Modeling in 3D Generation via Cross-scale Querying Transformer](https://mlsanity.com/paper/2409.06322/) (2024)
- [Factored-NeuS: Reconstructing Surfaces, Illumination, and Materials of Possibly Glossy Objects](https://mlsanity.com/paper/2305.17929/) (2023)
- [Is Vanilla MLP in Neural Radiance Field Enough for Few-shot View Synthesis?](https://mlsanity.com/paper/2403.06092/) (2024)
- [Neural Processing of Tri-Plane Hybrid Neural Fields](https://mlsanity.com/paper/2310.01140/) (2023)
- [SliceOcc: Indoor 3D Semantic Occupancy Prediction with Vertical Slice Representation](https://mlsanity.com/paper/2501.16684/) (2025)
- [Stochastic Preconditioning for Neural Field Optimization](https://mlsanity.com/paper/2505.20473/) (2025)
- [Color-NeuS: Reconstructing Neural Implicit Surfaces with Color](https://mlsanity.com/paper/2308.06962/) (2023)
- [GSurf: Learning Signed Distance Fields from Splatting Opaque Gaussians for High-quality 3D Reconstruction](https://mlsanity.com/paper/2411.15723/) (2024)
- [Spiking NeRF: Representing the Real-World Geometry by a Discontinuous Representation](https://mlsanity.com/paper/2311.09077/) (2023)
- [Sur2f: A Hybrid Representation for High-Quality and Efficient Surface Reconstruction from Multi-view Images](https://mlsanity.com/paper/2401.03704/) (2024)
- [Structure from Duplicates: Neural Inverse Graphics from a Pile of Objects](https://mlsanity.com/paper/2401.05236/) (2024)
- [SAID-NeRF: Segmentation-AIDed NeRF for Depth Completion of Transparent Objects](https://mlsanity.com/paper/2403.19607/) (2024)
- [3D Representation Methods: A Survey](https://mlsanity.com/paper/2410.06475/) (2024)
- [SplatSDF: Boosting SDF-NeRF via Architecture-Level Fusion with Gaussian Splats](https://mlsanity.com/paper/2411.15468/) (2024)
- [PG-NeuS: Robust and Efficient Point Guidance for Multi-View Neural Surface Reconstruction](https://mlsanity.com/paper/2310.07997/) (2023)
- [Improving Neural Surface Reconstruction with Feature Priors from Multi-View Image](https://mlsanity.com/paper/2408.02079/) (2024)
- [MultimodalStudio: A Heterogeneous Sensor Dataset and Framework for Neural Rendering across Multiple Imaging Modalities](https://mlsanity.com/paper/2503.19673/) (2025)
- [PGAHum: Prior-Guided Geometry and Appearance Learning for High-Fidelity Animatable Human Reconstruction](https://mlsanity.com/paper/2404.13862/) (2024)
- [Spatial Annealing for Efficient Few-shot Neural Rendering](https://mlsanity.com/paper/2406.07828/) (2024)
- [Local Occupancy-Enhanced Object Grasping with Multiple Triplanar Projection](https://mlsanity.com/paper/2407.15771/) (2024)
- [Spiking GS: Towards High-Accuracy and Low-Cost Surface Reconstruction via Spiking Neuron-based Gaussian Splatting](https://mlsanity.com/paper/2410.07266/) (2024)
- [GNF: Gaussian Neural Fields for Multidimensional Signal Representation and Reconstruction](https://mlsanity.com/paper/2503.06762/) (2025)
- [FreBIS: Frequency-Based Stratification for Neural Implicit Surface Representations](https://mlsanity.com/paper/2504.20222/) (2025)
- [NePF: Neural Photon Field for Single-Stage Inverse Rendering](https://mlsanity.com/paper/2311.11555/) (2023)

## Abstract (arXiv)

A signed distance function (SDF) parametrized by an MLP is a common ingredient of neural surface reconstruction. We build on the successful recent method NeuS to extend it by three new components. The first component is to borrow the tri-plane representation from EG3D and represent signed distance fields as a mixture of tri-planes and MLPs instead of representing it with MLPs only. Using tri-planes leads to a more expressive data structure but will also introduce noise in the reconstructed surface. The second component is to use a new type of positional encoding with learnable weights to combat noise in the reconstruction process. We divide the features in the tri-plane into multiple frequency scales and modulate them with sin and cos functions of different frequencies. The third component is to use learnable convolution operations on the tri-plane features using self-attention convolution to produce features with different frequency bands. The experiments show that PET-NeuS achieves high-fidelity surface reconstruction on standard datasets. Following previous work and using the Chamfer metric as the most important way to measure surface reconstruction quality, we are able to improve upon the NeuS baseline by 57% on Nerf-synthetic (0.84 compared to 1.97) and by 15.5% on DTU (0.71 compared to 0.84). The qualitative evaluation reveals how our method can better control the interference of high-frequency noise. Code available at urlhttps://github.com/yiqun-wang/PET-NeuS.