# Dynamic Neural Surfaces for Elastic 4D Shape Representation and Analysis

arXiv: https://arxiv.org/abs/2503.03132 · HTML: https://mlsanity.com/paper/2503.03132/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 49 references that are in the map.
- First posted on arXiv 5 Mar 2025.

## Builds on (most cited first, 21 of 21)

- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [Expressive Body Capture: 3D Hands, Face, and Body from a Single Image](https://mlsanity.com/paper/1904.05866/) (2019)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [Space-time Neural Irradiance Fields for Free-Viewpoint Video](https://mlsanity.com/paper/2011.12950/) (2020)
- [Generating 3D faces using Convolutional Mesh Autoencoders](https://mlsanity.com/paper/1807.10267/) (2018)
- [Capture, Learning, and Synthesis of 3D Speaking Styles](https://mlsanity.com/paper/1905.03079/) (2019)
- [NeRS: Neural Reflectance Surfaces for Sparse-view 3D Reconstruction in the Wild](https://mlsanity.com/paper/2110.07604/) (2021)
- [Deep Functional Maps: Structured Prediction for Dense Shape Correspondence](https://mlsanity.com/paper/1704.08686/) (2017)
- [Three-D Safari: Learning to Estimate Zebra Pose, Shape, and Texture from Images "In the Wild"](https://mlsanity.com/paper/1908.07201/) (2019)
- [Neural Surface Maps](https://mlsanity.com/paper/2103.16942/) (2021)
- [Learning Parallel Dense Correspondence from Spatio-Temporal Descriptors for Efficient and Robust 4D Reconstruction](https://mlsanity.com/paper/2103.16341/) (2021)
- [Spectral Meets Spatial: Harmonising 3D Shape Matching and Interpolation](https://mlsanity.com/paper/2402.18920/) (2024)
- [Neural Geometry Processing via Spherical Neural Surfaces](https://mlsanity.com/paper/2407.07755/) (2024)
- [Neural Semantic Surface Maps](https://mlsanity.com/paper/2309.04836/) (2023)
- [Numerical Inversion of SRNF Maps for Elastic Shape Analysis of Genus-Zero Surfaces](https://mlsanity.com/paper/1610.04531/) (2016)
- [A Survey on Non-rigid 3D Shape Analysis](https://mlsanity.com/paper/1812.10111/) (2018)
- [4D Atlas: Statistical Analysis of the Spatiotemporal Variability in Longitudinal 3D Shape Data](https://mlsanity.com/paper/2101.09403/) (2021)
- [Fluid Dynamics Network: Topology-Agnostic 4D Reconstruction via Fluid Dynamics Priors](https://mlsanity.com/paper/2303.09871/) (2023)
- [Scalable and Efficient Functional Map Computations on Dense Meshes](https://mlsanity.com/paper/2303.05965/) (2023)
- [ReMatching: Low-Resolution Representations for Scalable Shape Correspondence](https://mlsanity.com/paper/2305.09274/) (2023)

## Built on by (most cited first, 5 of 5)

- [Advances and Trends in the 3D Reconstruction of the Shape and Motion of Animals](https://mlsanity.com/paper/2508.16062/) (2025)
- [Preconditioned Deformation Grids](https://mlsanity.com/paper/2509.18097/) (2025)
- [Neu-PiG: Neural Preconditioned Grids for Fast Dynamic Surface Reconstruction on Long Sequences](https://mlsanity.com/paper/2602.22212/) (2026)
- [PRISM: A 3D Probabilistic Neural Representation for Interpretable Shape Modeling](https://mlsanity.com/paper/2602.11467/) (2026)
- [NeuralSRNF: Neural Square Root Normal Fields for the Statistical Shape Analysis and Generation of Nonrigid 3D and 4D Objects](https://mlsanity.com/paper/2609.27728/) (2026)

## Abstract (arXiv)

We propose a novel framework for the statistical analysis of genus-zero 4D surfaces, i.e., 3D surfaces that deform and evolve over time. This problem is particularly challenging due to the arbitrary parameterizations of these surfaces and their varying deformation speeds, necessitating effective spatiotemporal registration. Traditionally, 4D surfaces are discretized, in space and time, before computing their spatiotemporal registrations, geodesics, and statistics. However, this approach may result in suboptimal solutions and, as we demonstrate in this paper, is not necessary. In contrast, we treat 4D surfaces as continuous functions in both space and time. We introduce Dynamic Spherical Neural Surfaces (D-SNS), an efficient smooth and continuous spatiotemporal representation for genus-0 4D surfaces. We then demonstrate how to perform core 4D shape analysis tasks such as spatiotemporal registration, geodesics computation, and mean 4D shape estimation, directly on these continuous representations without upfront discretization and meshing. By integrating neural representations with classical Riemannian geometry and statistical shape analysis techniques, we provide the building blocks for enabling full functional shape analysis. We demonstrate the efficiency of the framework on 4D human and face datasets. The source code and additional results are available at https://4d-dsns.github.io/DSNS/.