# Preconditioned Deformation Grids

arXiv: https://arxiv.org/abs/2509.18097 · HTML: https://mlsanity.com/paper/2509.18097/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 62 references that are in the map.
- First posted on arXiv 22 Sep 2025.

## Builds on (most cited first, 30 of 34)

- [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)
- [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)
- [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)
- [Keep it SMPL: Automatic Estimation of 3D Human Pose and Shape from a Single Image](https://mlsanity.com/paper/1607.08128/) (2016)
- [Multi-Garment Net: Learning to Dress 3D People from Images](https://mlsanity.com/paper/1908.06903/) (2019)
- [Shape As Points: A Differentiable Poisson Solver](https://mlsanity.com/paper/2106.03452/) (2021)
- [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)
- [Deep Geometric Prior for Surface Reconstruction](https://mlsanity.com/paper/1811.10943/) (2018)
- [i3DMM: Deep Implicit 3D Morphable Model of Human Heads](https://mlsanity.com/paper/2011.14143/) (2020)
- [Neural Actor: Neural Free-view Synthesis of Human Actors with Pose Control](https://mlsanity.com/paper/2106.02019/) (2021)
- [Neural Kernel Surface Reconstruction](https://mlsanity.com/paper/2305.19590/) (2023)
- [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)
- [Non-rigid Point Cloud Registration with Neural Deformation Pyramid](https://mlsanity.com/paper/2205.12796/) (2022)
- [Point2Mesh: A Self-Prior for Deformable Meshes](https://mlsanity.com/paper/2005.11084/) (2020)
- [Learning Parallel Dense Correspondence from Spatio-Temporal Descriptors for Efficient and Robust 4D Reconstruction](https://mlsanity.com/paper/2103.16341/) (2021)
- [Learning Compositional Representation for 4D Captures with Neural ODE](https://mlsanity.com/paper/2103.08271/) (2021)
- [Neural incomplete factorization: learning preconditioners for the conjugate gradient method](https://mlsanity.com/paper/2305.16368/) (2023)
- [Learning from Linear Algebra: A Graph Neural Network Approach to Preconditioner Design for Conjugate Gradient Solvers](https://mlsanity.com/paper/2405.15557/) (2024)
- [Graph Neural Preconditioners for Iterative Solutions of Sparse Linear Systems](https://mlsanity.com/paper/2406.00809/) (2024)
- [4DTAM: Non-Rigid Tracking and Mapping via Dynamic Surface Gaussians](https://mlsanity.com/paper/2505.22859/) (2025)

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

- [Neu-PiG: Neural Preconditioned Grids for Fast Dynamic Surface Reconstruction on Long Sequences](https://mlsanity.com/paper/2602.22212/) (2026)

## Abstract (arXiv)

Dynamic surface reconstruction of objects from point cloud sequences is a challenging field in computer graphics. Existing approaches either require multiple regularization terms or extensive training data which, however, lead to compromises in reconstruction accuracy as well as over-smoothing or poor generalization to unseen objects and motions. To address these lim- itations, we introduce Preconditioned Deformation Grids, a novel technique for estimating coherent deformation fields directly from unstructured point cloud sequences without requiring or forming explicit correspondences. Key to our approach is the use of multi-resolution voxel grids that capture the overall motion at varying spatial scales, enabling a more flexible deformation representation. In conjunction with incorporating grid-based Sobolev preconditioning into gradient-based optimization, we show that applying a Chamfer loss between the input point clouds as well as to an evolving template mesh is sufficient to obtain accurate deformations. To ensure temporal consistency along the object surface, we include a weak isometry loss on mesh edges which complements the main objective without constraining deformation fidelity. Extensive evaluations demonstrate that our method achieves superior results, particularly for long sequences, compared to state-of-the-art techniques.