# Learning Implicit Functions for Topology-Varying Dense 3D Shape Correspondence

arXiv: https://arxiv.org/abs/2010.12320 · HTML: https://mlsanity.com/paper/2010.12320/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Oct 2020.

## Built on by (most cited first, 27 of 27)

- [ImFace: A Nonlinear 3D Morphable Face Model with Implicit Neural Representations](https://mlsanity.com/paper/2203.14510/) (2022)
- [FeatureNeRF: Learning Generalizable NeRFs by Distilling Foundation Models](https://mlsanity.com/paper/2303.12786/) (2023)
- [Unsupervised Learning for Cuboid Shape Abstraction via Joint Segmentation from Point Clouds](https://mlsanity.com/paper/2106.03437/) (2021)
- [AUV-Net: Learning Aligned UV Maps for Texture Transfer and Synthesis](https://mlsanity.com/paper/2204.03105/) (2022)
- [Topology-Preserving Shape Reconstruction and Registration via Neural Diffeomorphic Flow](https://mlsanity.com/paper/2203.08652/) (2022)
- [Template Free Reconstruction of Human-object Interaction with Procedural Interaction Generation](https://mlsanity.com/paper/2312.07063/) (2023)
- [Instant Multi-View Head Capture through Learnable Registration](https://mlsanity.com/paper/2306.07437/) (2023)
- [Learning 3D Dense Correspondence via Canonical Point Autoencoder](https://mlsanity.com/paper/2107.04867/) (2021)
- [Voxel-based 3D Detection and Reconstruction of Multiple Objects from a Single Image](https://mlsanity.com/paper/2111.03098/) (2021)
- [NCP: Neural Correspondence Prior for Effective Unsupervised Shape Matching](https://mlsanity.com/paper/2301.05839/) (2023)
- [EFEM: Equivariant Neural Field Expectation Maximization for 3D Object Segmentation Without Scene Supervision](https://mlsanity.com/paper/2303.15440/) (2023)
- [Back to 3D: Few-Shot 3D Keypoint Detection with Back-Projected 2D Features](https://mlsanity.com/paper/2311.18113/) (2023)
- [Fully Understanding Generic Objects: Modeling, Segmentation, and Reconstruction](https://mlsanity.com/paper/2104.00858/) (2021)
- [Point2SSM: Learning Morphological Variations of Anatomies from Point Cloud](https://mlsanity.com/paper/2305.14486/) (2023)
- [Zero-shot Pose Transfer for Unrigged Stylized 3D Characters](https://mlsanity.com/paper/2306.00200/) (2023)
- [GenCorres: Consistent Shape Matching via Coupled Implicit-Explicit Shape Generative Models](https://mlsanity.com/paper/2304.10523/) (2023)
- [ImFace++: A Sophisticated Nonlinear 3D Morphable Face Model with Implicit Neural Representations](https://mlsanity.com/paper/2312.04028/) (2023)
- [Correspondence Distillation from NeRF-based GAN](https://mlsanity.com/paper/2212.09735/) (2022)
- [Deep Deformable Models: Learning 3D Shape Abstractions with Part Consistency](https://mlsanity.com/paper/2309.01035/) (2023)
- [Adjoint Rigid Transform Network: Task-conditioned Alignment of 3D Shapes](https://mlsanity.com/paper/2102.01161/) (2021)
- [TEGLO: High Fidelity Canonical Texture Mapping from Single-View Images](https://mlsanity.com/paper/2303.13743/) (2023)
- [Learning SO(3)-Invariant Semantic Correspondence via Local Shape Transform](https://mlsanity.com/paper/2404.11156/) (2024)
- [Learning Implicit Functions for Dense 3D Shape Correspondence of Generic Objects](https://mlsanity.com/paper/2212.14276/) (2022)
- [Laplacian ICP for Progressive Registration of 3D Human Head Meshes](https://mlsanity.com/paper/2302.02194/) (2023)
- [3D Semantic Subspace Traverser: Empowering 3D Generative Model with Shape Editing Capability](https://mlsanity.com/paper/2307.14051/) (2023)
- [Trustworthy Representation Learning Across Domains](https://mlsanity.com/paper/2308.12315/) (2023)
- [Mitigating Prior Shape Bias in Point Clouds via Differentiable Center Learning](https://mlsanity.com/paper/2402.02088/) (2024)

## Abstract (arXiv)

The goal of this paper is to learn dense 3D shape correspondence for topology-varying 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 part embedding vector for each 3D point, which is assumed to be similar to its densely corresponded point in another 3D shape of the same object category. Furthermore, we implement dense correspondence through an inverse function mapping from the part embedding to a corresponded 3D point. Both functions are jointly learned with several effective 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.