# Augmenting Implicit Neural Shape Representations with Explicit Deformation Fields

arXiv: https://arxiv.org/abs/2108.08931 · HTML: https://mlsanity.com/paper/2108.08931/

## Key facts

- Cited by 19 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 19 Aug 2021.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [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)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Pixel2Mesh: Generating 3D Mesh Models from Single RGB Images](https://mlsanity.com/paper/1804.01654/) (2018)
- [3D-R2N2: A Unified Approach for Single and Multi-view 3D Object Reconstruction](https://mlsanity.com/paper/1604.00449/) (2016)
- [Learning a Probabilistic Latent Space of Object Shapes via 3D Generative-Adversarial Modeling](https://mlsanity.com/paper/1610.07584/) (2016)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019)
- [DISN: Deep Implicit Surface Network for High-quality Single-view 3D Reconstruction](https://mlsanity.com/paper/1905.10711/) (2019)
- [Neural Unsigned Distance Fields for Implicit Function Learning](https://mlsanity.com/paper/2010.13938/) (2020)
- [Learning Shape Templates with Structured Implicit Functions](https://mlsanity.com/paper/1904.06447/) (2019)
- [Octree Generating Networks: Efficient Convolutional Architectures for High-resolution 3D Outputs](https://mlsanity.com/paper/1703.09438/) (2017)
- [Learning a Predictable and Generative Vector Representation for Objects](https://mlsanity.com/paper/1603.08637/) (2016)
- [3D-CODED : 3D Correspondences by Deep Deformation](https://mlsanity.com/paper/1806.05228/) (2018)
- [SALD: Sign Agnostic Learning with Derivatives](https://mlsanity.com/paper/2006.05400/) (2020)
- [Deep Geometric Prior for Surface Reconstruction](https://mlsanity.com/paper/1811.10943/) (2018)
- [Supervised Fitting of Geometric Primitives to 3D Point Clouds](https://mlsanity.com/paper/1811.08988/) (2018)
- [Controlling Neural Level Sets](https://mlsanity.com/paper/1905.11911/) (2019)
- [3DN: 3D Deformation Network](https://mlsanity.com/paper/1903.03322/) (2019)
- [Multi-view 3D Models from Single Images with a Convolutional Network](https://mlsanity.com/paper/1511.06702/) (2015)
- [LIMP: Learning Latent Shape Representations with Metric Preservation Priors](https://mlsanity.com/paper/2003.12283/) (2020)
- [3D Shape Reconstruction from Sketches via Multi-view Convolutional Networks](https://mlsanity.com/paper/1707.06375/) (2017)
- [Matryoshka Networks: Predicting 3D Geometry via Nested Shape Layers](https://mlsanity.com/paper/1804.10975/) (2018)
- [ShapeFlow: Learnable Deformations Among 3D Shapes](https://mlsanity.com/paper/2006.07982/) (2020)
- [Learning 3D Object Categories by Looking Around Them](https://mlsanity.com/paper/1705.03951/) (2017)
- [Hamiltonian Dynamics for Real-World Shape Interpolation](https://mlsanity.com/paper/2004.05199/) (2020)

## Built on by (most cited first, 19 of 19)

- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Reconstructing Surfaces for Sparse Point Clouds with On-Surface Priors](https://mlsanity.com/paper/2204.10603/) (2022)
- [Frame Averaging for Equivariant Shape Space Learning](https://mlsanity.com/paper/2112.01741/) (2021)
- [Implicit field supervision for robust non-rigid shape matching](https://mlsanity.com/paper/2203.07694/) (2022)
- [GenCorres: Consistent Shape Matching via Coupled Implicit-Explicit Shape Generative Models](https://mlsanity.com/paper/2304.10523/) (2023)
- [UNIF: United Neural Implicit Functions for Clothed Human Reconstruction and Animation](https://mlsanity.com/paper/2207.09835/) (2022)
- [Reduced Representation of Deformation Fields for Effective Non-rigid Shape Matching](https://mlsanity.com/paper/2211.14604/) (2022)
- [Intuitive Shape Editing in Latent Space](https://mlsanity.com/paper/2111.12488/) (2021)
- [BaRe-ESA: A Riemannian Framework for Unregistered Human Body Shapes](https://mlsanity.com/paper/2211.13185/) (2022)
- [RDA-INR: Riemannian Diffeomorphic Autoencoding via Implicit Neural Representations](https://mlsanity.com/paper/2305.12854/) (2023)
- [CanFields: Consolidating Diffeomorphic Flows for Non-Rigid 4D Interpolation from Arbitrary-Length Sequences](https://mlsanity.com/paper/2406.18582/) (2024)
- [Basis restricted elastic shape analysis on the space of unregistered surfaces](https://mlsanity.com/paper/2311.04382/) (2023)
- [Neural Implicit Shape Editing using Boundary Sensitivity](https://mlsanity.com/paper/2304.12951/) (2023)
- [Self Supervised Networks for Learning Latent Space Representations of Human Body Scans and Motions](https://mlsanity.com/paper/2411.03475/) (2024)
- [GenAnalysis: Joint Shape Analysis by Learning Man-Made Shape Generators with Deformation Regularizations](https://mlsanity.com/paper/2503.00807/) (2025)
- [Enhancing Surface Neural Implicits with Curvature-Guided Sampling and Uncertainty-Augmented Representations](https://mlsanity.com/paper/2306.02099/) (2023)
- [Pop-Out Motion: 3D-Aware Image Deformation via Learning the Shape Laplacian](https://mlsanity.com/paper/2203.15235/) (2022)
- [ARAPDiffusion: ARAP Regularization for Diffusion-Based Deformable Shape Space Learning](https://mlsanity.com/paper/2606.06887/) (2026)
- [GenSP: Consistent Spherical Parameterization via Learning Shape Generative Models](https://mlsanity.com/paper/2607.00492/) (2026)

## Abstract (arXiv)

Implicit neural representation is a recent approach to learn shape collections as zero level-sets of neural networks, where each shape is represented by a latent code. So far, the focus has been shape reconstruction, while shape generalization was mostly left to generic encoder-decoder or auto-decoder regularization. In this paper we advocate deformation-aware regularization for implicit neural representations, aiming at producing plausible deformations as latent code changes. The challenge is that implicit representations do not capture correspondences between different shapes, which makes it difficult to represent and regularize their deformations. Thus, we propose to pair the implicit representation of the shapes with an explicit, piecewise linear deformation field, learned as an auxiliary function. We demonstrate that, by regularizing these deformation fields, we can encourage the implicit neural representation to induce natural deformations in the learned shape space, such as as-rigid-as-possible deformations.