# Deformed Implicit Field: Modeling 3D Shapes with Learned Dense Correspondence

arXiv: https://arxiv.org/abs/2011.13650 · HTML: https://mlsanity.com/paper/2011.13650/

## Key facts

- Cited by 119 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Nov 2020.

## Built on by (most cited first, 30 of 119)

- [LION: Latent Point Diffusion Models for 3D Shape Generation](https://mlsanity.com/paper/2210.06978/) (2022)
- [Deep Marching Tetrahedra: a Hybrid Representation for High-Resolution 3D Shape Synthesis](https://mlsanity.com/paper/2111.04276/) (2021)
- [NeRF-Editing: Geometry Editing of Neural Radiance Fields](https://mlsanity.com/paper/2205.04978/) (2022)
- [Neural Descriptor Fields: SE(3)-Equivariant Object Representations for Manipulation](https://mlsanity.com/paper/2112.05124/) (2021)
- [Native and Compact Structured Latents for 3D Generation](https://mlsanity.com/paper/2512.14692/) (2025)
- [NeuMesh: Learning Disentangled Neural Mesh-based Implicit Field for Geometry and Texture Editing](https://mlsanity.com/paper/2207.11911/) (2022)
- [SINE: Semantic-driven Image-based NeRF Editing with Prior-guided Editing Field](https://mlsanity.com/paper/2303.13277/) (2023)
- [Towards Implicit Text-Guided 3D Shape Generation](https://mlsanity.com/paper/2203.14622/) (2022)
- [ImFace: A Nonlinear 3D Morphable Face Model with Implicit Neural Representations](https://mlsanity.com/paper/2203.14510/) (2022)
- [CaDeX: Learning Canonical Deformation Coordinate Space for Dynamic Surface Representation via Neural Homeomorphism](https://mlsanity.com/paper/2203.16529/) (2022)
- [Self-supervised Neural Articulated Shape and Appearance Models](https://mlsanity.com/paper/2205.08525/) (2022)
- [SE(3)-Equivariant Relational Rearrangement with Neural Descriptor Fields](https://mlsanity.com/paper/2211.09786/) (2022)
- [Registering Explicit to Implicit: Towards High-Fidelity Garment mesh Reconstruction from Single Images](https://mlsanity.com/paper/2203.15007/) (2022)
- [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)
- [PartNeRF: Generating Part-Aware Editable 3D Shapes without 3D Supervision](https://mlsanity.com/paper/2303.09554/) (2023)
- [Neural Template: Topology-aware Reconstruction and Disentangled Generation of 3D Meshes](https://mlsanity.com/paper/2206.04942/) (2022)
- [Mesh2Tex: Generating Mesh Textures from Image Queries](https://mlsanity.com/paper/2304.05868/) (2023)
- [EditableNeRF: Editing Topologically Varying Neural Radiance Fields by Key Points](https://mlsanity.com/paper/2212.04247/) (2022)
- [Topologically-Aware Deformation Fields for Single-View 3D Reconstruction](https://mlsanity.com/paper/2205.06267/) (2022)
- [Neural Shape Deformation Priors](https://mlsanity.com/paper/2210.05616/) (2022)
- [Neural Capture of Animatable 3D Human from Monocular Video](https://mlsanity.com/paper/2208.08728/) (2022)
- [SP-GAN: Sphere-Guided 3D Shape Generation and Manipulation](https://mlsanity.com/paper/2108.04476/) (2021)
- [Learning Whole Heart Mesh Generation From Patient Images For Computational Simulations](https://mlsanity.com/paper/2203.10517/) (2022)
- [Neural Correspondence Field for Object Pose Estimation](https://mlsanity.com/paper/2208.00113/) (2022)
- [SDF4CHD: Generative Modeling of Cardiac Anatomies with Congenital Heart Defects](https://mlsanity.com/paper/2311.00332/) (2023)
- [Neural Parameterization for Dynamic Human Head Editing](https://mlsanity.com/paper/2207.00210/) (2022)
- [Novel-view Synthesis and Pose Estimation for Hand-Object Interaction from Sparse Views](https://mlsanity.com/paper/2308.11198/) (2023)
- [AniPortraitGAN: Animatable 3D Portrait Generation from 2D Image Collections](https://mlsanity.com/paper/2309.02186/) (2023)

## Abstract (arXiv)

We propose a novel Deformed Implicit Field (DIF) representation for modeling 3D shapes of a category and generating dense correspondences among shapes. With DIF, a 3D shape is represented by a template implicit field shared across the category, together with a 3D deformation field and a correction field dedicated for each shape instance. Shape correspondences can be easily established using their deformation fields. Our neural network, dubbed DIF-Net, jointly learns a shape latent space and these fields for 3D objects belonging to a category without using any correspondence or part label. The learned DIF-Net can also provides reliable correspondence uncertainty measurement reflecting shape structure discrepancy. Experiments show that DIF-Net not only produces high-fidelity 3D shapes but also builds high-quality dense correspondences across different shapes. We also demonstrate several applications such as texture transfer and shape editing, where our method achieves compelling results that cannot be achieved by previous methods.