# Learning Implicit Functions for Dense 3D Shape Correspondence of Generic Objects

arXiv: https://arxiv.org/abs/2212.14276 · HTML: https://mlsanity.com/paper/2212.14276/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 60 of its 96 references that are in the map.
- First posted on arXiv 29 Dec 2022.

## Builds on (most cited first, 30 of 60)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [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)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [PIFu: Pixel-Aligned Implicit Function for High-Resolution Clothed Human Digitization](https://mlsanity.com/paper/1905.05172/) (2019)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [Pixel2Mesh: Generating 3D Mesh Models from Single RGB Images](https://mlsanity.com/paper/1804.01654/) (2018)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [AdaFace: Quality Adaptive Margin for Face Recognition](https://mlsanity.com/paper/2204.00964/) (2022)
- [Implicit Functions in Feature Space for 3D Shape Reconstruction and Completion](https://mlsanity.com/paper/2003.01456/) (2020)
- [DISN: Deep Implicit Surface Network for High-quality Single-view 3D Reconstruction](https://mlsanity.com/paper/1905.10711/) (2019)
- [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)
- [Bayesian SegNet: Model Uncertainty in Deep Convolutional Encoder-Decoder Architectures for Scene Understanding](https://mlsanity.com/paper/1511.02680/) (2015)
- [Texture Fields: Learning Texture Representations in Function Space](https://mlsanity.com/paper/1905.07259/) (2019)
- [On the uncertainty of self-supervised monocular depth estimation](https://mlsanity.com/paper/2005.06209/) (2020)
- [Learning Shape Abstractions by Assembling Volumetric Primitives](https://mlsanity.com/paper/1612.00404/) (2016)
- [Probabilistic Face Embeddings](https://mlsanity.com/paper/1904.09658/) (2019)
- [3D-CODED : 3D Correspondences by Deep Deformation](https://mlsanity.com/paper/1806.05228/) (2018)
- [Deep Functional Maps: Structured Prediction for Dense Shape Correspondence](https://mlsanity.com/paper/1704.08686/) (2017)
- [Data Uncertainty Learning in Face Recognition](https://mlsanity.com/paper/2003.11339/) (2020)
- [Deformed Implicit Field: Modeling 3D Shapes with Learned Dense Correspondence](https://mlsanity.com/paper/2011.13650/) (2020)
- [Learning Accurate Dense Correspondences and When to Trust Them](https://mlsanity.com/paper/2101.01710/) (2021)
- [i3DMM: Deep Implicit 3D Morphable Model of Human Heads](https://mlsanity.com/paper/2011.14143/) (2020)

## Built on by (most cited first, 2 of 2)

- [3D Semantic Subspace Traverser: Empowering 3D Generative Model with Shape Editing Capability](https://mlsanity.com/paper/2307.14051/) (2023)
- [SGSoft: Learning Fused Semantic-Geometric Features for 3D Shape Correspondence via Template-Guided Soft Signals](https://mlsanity.com/paper/2605.18039/) (2026)

## Abstract (arXiv)

The objective of this paper is to learn dense 3D shape correspondence for topology-varying generic objects in an unsupervised manner. Conventional implicit functions estimate the occupancy of a 3D point given a shape latent code. Instead, our novel implicit function produces a probabilistic embedding to represent each 3D point in a part embedding space. Assuming the corresponding points are similar in the embedding space, we implement dense correspondence through an inverse function mapping from the part embedding vector to a corresponded 3D point. Both functions are jointly learned with several effective and uncertainty-aware loss functions to realize our assumption, together with the encoder generating the shape latent code. During inference, if a user selects an arbitrary point on the source shape, our algorithm can automatically generate a confidence score indicating whether there is a correspondence on the target shape, as well as the corresponding semantic point if there is one. Such a mechanism inherently benefits man-made objects with different part constitutions. The effectiveness of our approach is demonstrated through unsupervised 3D semantic correspondence and shape segmentation.