# NeuralSRNF: Neural Square Root Normal Fields for the Statistical Shape Analysis and Generation of Nonrigid 3D and 4D Objects

arXiv: https://arxiv.org/abs/2609.27728 · HTML: https://mlsanity.com/paper/2609.27728/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 49 references that are in the map.
- First posted on arXiv 23 Sep 2026.

## Builds on (most cited first, 24 of 24)

- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [pi-GAN: Periodic Implicit Generative Adversarial Networks for 3D-Aware Image Synthesis](https://mlsanity.com/paper/2012.00926/) (2020)
- [3D Morphable Face Models -- Past, Present and Future](https://mlsanity.com/paper/1909.01815/) (2019)
- [Generating 3D faces using Convolutional Mesh Autoencoders](https://mlsanity.com/paper/1807.10267/) (2018)
- [NeuroMorph: Unsupervised Shape Interpolation and Correspondence in One Go](https://mlsanity.com/paper/2106.09431/) (2021)
- [Unsupervised Learning of Robust Spectral Shape Matching](https://mlsanity.com/paper/2304.14419/) (2023)
- [LIMP: Learning Latent Shape Representations with Metric Preservation Priors](https://mlsanity.com/paper/2003.12283/) (2020)
- [Animal3D: A Comprehensive Dataset of 3D Animal Pose and Shape](https://mlsanity.com/paper/2308.11737/) (2023)
- [Cyclic Functional Mapping: Self-supervised correspondence between non-isometric deformable shapes](https://mlsanity.com/paper/1912.01249/) (2019)
- [Spectral Meets Spatial: Harmonising 3D Shape Matching and Interpolation](https://mlsanity.com/paper/2402.18920/) (2024)
- [Understanding and Improving Features Learned in Deep Functional Maps](https://mlsanity.com/paper/2303.16527/) (2023)
- [Neural Geometry Processing via Spherical Neural Surfaces](https://mlsanity.com/paper/2407.07755/) (2024)
- [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)
- [4Deform: Neural Surface Deformation for Robust Shape Interpolation](https://mlsanity.com/paper/2502.20208/) (2025)
- [Stable-SCore: A Stable Registration-based Framework for 3D Shape Correspondence](https://mlsanity.com/paper/2503.21766/) (2025)
- [Implicit Neural Surface Deformation with Explicit Velocity Fields](https://mlsanity.com/paper/2501.14038/) (2025)
- [Scalable and Efficient Functional Map Computations on Dense Meshes](https://mlsanity.com/paper/2303.05965/) (2023)
- [Dynamic Neural Surfaces for Elastic 4D Shape Representation and Analysis](https://mlsanity.com/paper/2503.03132/) (2025)
- [Geodesic Calculus on Implicitly Defined Latent Manifolds](https://mlsanity.com/paper/2510.09468/) (2025)

## Abstract (arXiv)

We introduce NeuralSRNF, a novel framework for the statistical shape analysis and generation of genus-zero 3D and 4D objects that undergo nonrigid deformations. Traditional methods rely on complex and computationally expensive nonlinear elastic metrics that measure bending and stretching. Recent advances in elastic shape analysis achieve computational efficiency by mapping input 3D shapes to the space of Square Root Normal Fields (SRNFs) where the L2 metric approximates the partial elastic metric, significantly facilitating the process of computing geodesics and summary statistics. SRNFs, however, are not invertible, and the numerical algorithms used to map SRNFs back to the original space of surfaces remain computationally very expensive and often lead to approximate results. This paper addresses this fundamental SRNF inversion problem using a novel neural representation, termed NeuralSRNF. Unlike the commonly used numerical SRNF, NeuralSRNF is (1) continuous, and thus resolution-agnostic, enabling full functional shape analysis, (2) more accurate, and (3) computationally more efficient as it can compute inverse SRNF maps along a geodesic path in less than 3 s compared to over 10 min for the numerical SRNF. We demonstrate, using various datasets, the utility and efficiency of the proposed NeuralSRNF in multiple elastic 3D and 4D shape analysis tasks such as geodesic computation, deformation transfer, statistical summaries computation, and 3D shape generation. We show that it outperforms competing methods on most evaluated datasets and metrics by a wide margin in both accuracy and computational efficiency. The source code and additional results are available at https://awaisnizamani16.github.io/awais/NeuralSRNF/.