# Neu-PiG: Neural Preconditioned Grids for Fast Dynamic Surface Reconstruction on Long Sequences

arXiv: https://arxiv.org/abs/2602.22212 · HTML: https://mlsanity.com/paper/2602.22212/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 75 references that are in the map.
- First posted on arXiv 25 Feb 2026.

## Builds on (most cited first, 30 of 46)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Expressive Body Capture: 3D Hands, Face, and Body from a Single Image](https://mlsanity.com/paper/1904.05866/) (2019)
- [D-NeRF: Neural Radiance Fields for Dynamic Scenes](https://mlsanity.com/paper/2011.13961/) (2020)
- [TensoRF: Tensorial Radiance Fields](https://mlsanity.com/paper/2203.09517/) (2022)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [Neural Scene Flow Fields for Space-Time View Synthesis of Dynamic Scenes](https://mlsanity.com/paper/2011.13084/) (2020)
- [K-Planes: Explicit Radiance Fields in Space, Time, and Appearance](https://mlsanity.com/paper/2301.10241/) (2023)
- [Keep it SMPL: Automatic Estimation of 3D Human Pose and Shape from a Single Image](https://mlsanity.com/paper/1607.08128/) (2016)
- [HexPlane: A Fast Representation for Dynamic Scenes](https://mlsanity.com/paper/2301.09632/) (2023)
- [Multi-Garment Net: Learning to Dress 3D People from Images](https://mlsanity.com/paper/1908.06903/) (2019)
- [Learning to Regress 3D Face Shape and Expression from an Image without 3D Supervision](https://mlsanity.com/paper/1905.06817/) (2019)
- [Learning to Reconstruct People in Clothing from a Single RGB Camera](https://mlsanity.com/paper/1903.05885/) (2019)
- [4DComplete: Non-Rigid Motion Estimation Beyond the Observable Surface](https://mlsanity.com/paper/2105.01905/) (2021)
- [i3DMM: Deep Implicit 3D Morphable Model of Human Heads](https://mlsanity.com/paper/2011.14143/) (2020)
- [Per-Gaussian Embedding-Based Deformation for Deformable 3D Gaussian Splatting](https://mlsanity.com/paper/2404.03613/) (2024)
- [FaceVerse: a Fine-grained and Detail-controllable 3D Face Morphable Model from a Hybrid Dataset](https://mlsanity.com/paper/2203.14057/) (2022)
- [SIZER: A Dataset and Model for Parsing 3D Clothing and Learning Size Sensitive 3D Clothing](https://mlsanity.com/paper/2007.11610/) (2020)
- [Neural Deformation Graphs for Globally-consistent Non-rigid Reconstruction](https://mlsanity.com/paper/2012.01451/) (2020)
- [CaDeX: Learning Canonical Deformation Coordinate Space for Dynamic Surface Representation via Neural Homeomorphism](https://mlsanity.com/paper/2203.16529/) (2022)
- [WildGS-SLAM: Monocular Gaussian Splatting SLAM in Dynamic Environments](https://mlsanity.com/paper/2504.03886/) (2025)
- [Neural Non-Rigid Tracking](https://mlsanity.com/paper/2006.13240/) (2020)
- [Signal Processing for Implicit Neural Representations](https://mlsanity.com/paper/2210.08772/) (2022)
- [Non-rigid Point Cloud Registration with Neural Deformation Pyramid](https://mlsanity.com/paper/2205.12796/) (2022)
- [Improved Implicit Neural Representation with Fourier Reparameterized Training](https://mlsanity.com/paper/2401.07402/) (2024)
- [Learning Parallel Dense Correspondence from Spatio-Temporal Descriptors for Efficient and Robust 4D Reconstruction](https://mlsanity.com/paper/2103.16341/) (2021)
- [Motion2VecSets: 4D Latent Vector Set Diffusion for Non-rigid Shape Reconstruction and Tracking](https://mlsanity.com/paper/2401.06614/) (2024)
- [Learning Compositional Representation for 4D Captures with Neural ODE](https://mlsanity.com/paper/2103.08271/) (2021)

## Built on by (most cited first, 1 of 1)

- [PiG-Avatar: Hierarchical Neural-Field-Guided Gaussian Avatars](https://mlsanity.com/paper/2605.20185/) (2026)

## Abstract (arXiv)

Temporally consistent surface reconstruction of dynamic 3D objects from unstructured point cloud data remains challenging, especially for very long sequences. Existing methods either optimize deformations incrementally, risking drift and requiring long runtimes, or rely on complex learned models that demand category-specific training. We present Neu-PiG, a fast deformation optimization method based on a novel preconditioned latent-grid encoding that distributes spatial features parameterized on the position and normal direction of a keyframe surface. Our method encodes entire deformations across all time steps at various spatial scales into a multi-resolution latent grid, parameterized by the position and normal direction of a reference surface from a single keyframe. This latent representation is then augmented for time modulation and decoded into per-frame 6-DoF deformations via a lightweight multilayer perceptron (MLP). To achieve high-fidelity, drift-free surface reconstructions in seconds, we employ Sobolev preconditioning during gradient-based training of the latent space, completely avoiding the need for any explicit correspondences or further priors. Experiments across diverse human and animal datasets demonstrate that Neu-PiG outperforms state-the-art approaches, offering both superior accuracy and scalability to long sequences while running at least 60x faster than existing training-free methods and achieving inference speeds on the same order as heavy pretrained models.