# Implicit field supervision for robust non-rigid shape matching

arXiv: https://arxiv.org/abs/2203.07694 · HTML: https://mlsanity.com/paper/2203.07694/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 54 of its 89 references that are in the map.
- First posted on arXiv 15 Mar 2022.

## Builds on (most cited first, 30 of 54)

- [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)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (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)
- [End-to-end Recovery of Human Shape and Pose](https://mlsanity.com/paper/1712.06584/) (2017)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [GIRAFFE: Representing Scenes as Compositional Generative Neural Feature Fields](https://mlsanity.com/paper/2011.12100/) (2020)
- [GRAF: Generative Radiance Fields for 3D-Aware Image Synthesis](https://mlsanity.com/paper/2007.02442/) (2020)
- [DensePose: Dense Human Pose Estimation In The Wild](https://mlsanity.com/paper/1802.00434/) (2018)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Simple Baselines for Human Pose Estimation and Tracking](https://mlsanity.com/paper/1804.06208/) (2018)
- [Geometric deep learning on graphs and manifolds using mixture model CNNs](https://mlsanity.com/paper/1611.08402/) (2016)
- [Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapes](https://mlsanity.com/paper/2101.10994/) (2021)
- [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019)
- [Learning from Synthetic Humans](https://mlsanity.com/paper/1701.01370/) (2017)
- [3D Menagerie: Modeling the 3D shape and pose of animals](https://mlsanity.com/paper/1611.07700/) (2016)
- [Learning Shape Templates with Structured Implicit Functions](https://mlsanity.com/paper/1904.06447/) (2019)
- [Neural Body Fitting: Unifying Deep Learning and Model-Based Human Pose and Shape Estimation](https://mlsanity.com/paper/1808.05942/) (2018)
- [DIST: Rendering Deep Implicit Signed Distance Function with Differentiable Sphere Tracing](https://mlsanity.com/paper/1911.13225/) (2019)
- [Panoptic Studio: A Massively Multiview System for Social Interaction Capture](https://mlsanity.com/paper/1612.03153/) (2016)
- [DiffusionNet: Discretization Agnostic Learning on Surfaces](https://mlsanity.com/paper/2012.00888/) (2020)
- [3D-CODED : 3D Correspondences by Deep Deformation](https://mlsanity.com/paper/1806.05228/) (2018)
- [SMPLicit: Topology-aware Generative Model for Clothed People](https://mlsanity.com/paper/2103.06871/) (2021)
- [Deep Functional Maps: Structured Prediction for Dense Shape Correspondence](https://mlsanity.com/paper/1704.08686/) (2017)
- [Deep Geometric Functional Maps: Robust Feature Learning for Shape Correspondence](https://mlsanity.com/paper/2003.14286/) (2020)
- [4DComplete: Non-Rigid Motion Estimation Beyond the Observable Surface](https://mlsanity.com/paper/2105.01905/) (2021)
- [PQ-NET: A Generative Part Seq2Seq Network for 3D Shapes](https://mlsanity.com/paper/1911.10949/) (2019)
- [Deformed Implicit Field: Modeling 3D Shapes with Learned Dense Correspondence](https://mlsanity.com/paper/2011.13650/) (2020)
- [SDM-NET: Deep Generative Network for Structured Deformable Mesh](https://mlsanity.com/paper/1908.04520/) (2019)

## Built on by (most cited first, 13 of 13)

- [Spectral Meets Spatial: Harmonising 3D Shape Matching and Interpolation](https://mlsanity.com/paper/2402.18920/) (2024)
- [Self-Supervised Learning for Multimodal Non-Rigid 3D Shape Matching](https://mlsanity.com/paper/2303.10971/) (2023)
- [SE-ORNet: Self-Ensembling Orientation-aware Network for Unsupervised Point Cloud Shape Correspondence](https://mlsanity.com/paper/2304.05395/) (2023)
- [Denoising Functional Maps: Diffusion Models for Shape Correspondence](https://mlsanity.com/paper/2503.01845/) (2025)
- [Zero-shot Pose Transfer for Unrigged Stylized 3D Characters](https://mlsanity.com/paper/2306.00200/) (2023)
- [CCuantuMM: Cycle-Consistent Quantum-Hybrid Matching of Multiple Shapes](https://mlsanity.com/paper/2303.16202/) (2023)
- [GenCorres: Consistent Shape Matching via Coupled Implicit-Explicit Shape Generative Models](https://mlsanity.com/paper/2304.10523/) (2023)
- [Self-supervised Learning of Implicit Shape Representation with Dense Correspondence for Deformable Objects](https://mlsanity.com/paper/2308.12590/) (2023)
- [Unsupervised Template-assisted Point Cloud Shape Correspondence Network](https://mlsanity.com/paper/2403.16412/) (2024)
- [Kissing to Find a Match: Efficient Low-Rank Permutation Representation](https://mlsanity.com/paper/2308.13252/) (2023)
- [Occlusion-aware Non-Rigid Point Cloud Registration via Unsupervised Neural Deformation Correntropy](https://mlsanity.com/paper/2502.10704/) (2025)
- [Semantic-Aware Implicit Template Learning via Part Deformation Consistency](https://mlsanity.com/paper/2308.11916/) (2023)
- [Matching Shapes Under Different Topologies: A Topology-Adaptive Deformation Guided Approach](https://mlsanity.com/paper/2509.06862/) (2025)

## Abstract (arXiv)

Establishing a correspondence between two non-rigidly deforming shapes is one of the most fundamental problems in visual computing. Existing methods often show weak resilience when presented with challenges innate to real-world data such as noise, outliers, self-occlusion etc. On the other hand, auto-decoders have demonstrated strong expressive power in learning geometrically meaningful latent embeddings. However, their use in shape analysis has been limited. In this paper, we introduce an approach based on an auto-decoder framework, that learns a continuous shape-wise deformation field over a fixed template. By supervising the deformation field for points on-surface and regularising for points off-surface through a novel Signed Distance Regularisation (SDR), we learn an alignment between the template and shape volumes. Trained on clean water-tight meshes, without any data-augmentation, we demonstrate compelling performance on compromised data and real-world scans.