# DeepMetaHandles: Learning Deformation Meta-Handles of 3D Meshes with Biharmonic Coordinates

arXiv: https://arxiv.org/abs/2102.09105 · HTML: https://mlsanity.com/paper/2102.09105/

## Key facts

- Cited by 37 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 49 references that are in the map.
- First posted on arXiv 18 Feb 2021.

## Builds on (most cited first, 28 of 28)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [Accelerating 3D Deep Learning with PyTorch3D](https://mlsanity.com/paper/2007.08501/) (2020)
- [Learning a Probabilistic Latent Space of Object Shapes via 3D Generative-Adversarial Modeling](https://mlsanity.com/paper/1610.07584/) (2016)
- [Soft Rasterizer: A Differentiable Renderer for Image-based 3D Reasoning](https://mlsanity.com/paper/1904.01786/) (2019)
- [PolyGen: An Autoregressive Generative Model of 3D Meshes](https://mlsanity.com/paper/2002.10880/) (2020)
- [3D Point Cloud Generative Adversarial Network Based on Tree Structured Graph Convolutions](https://mlsanity.com/paper/1905.06292/) (2019)
- [3D-CODED : 3D Correspondences by Deep Deformation](https://mlsanity.com/paper/1806.05228/) (2018)
- [PQ-NET: A Generative Part Seq2Seq Network for 3D Shapes](https://mlsanity.com/paper/1911.10949/) (2019)
- [SDM-NET: Deep Generative Network for Structured Deformable Mesh](https://mlsanity.com/paper/1908.04520/) (2019)
- [Neural Cages for Detail-Preserving 3D Deformations](https://mlsanity.com/paper/1912.06395/) (2019)
- [Variational Autoencoders for Deforming 3D Mesh Models](https://mlsanity.com/paper/1709.04307/) (2017)
- [Unsupervised Shape and Pose Disentanglement for 3D Meshes](https://mlsanity.com/paper/2007.11341/) (2020)
- [3DN: 3D Deformation Network](https://mlsanity.com/paper/1903.03322/) (2019)
- [Robust Watertight Manifold Surface Generation Method for ShapeNet Models](https://mlsanity.com/paper/1802.01698/) (2018)
- [StructureNet: Hierarchical Graph Networks for 3D Shape Generation](https://mlsanity.com/paper/1908.00575/) (2019)
- [Composite Shape Modeling via Latent Space Factorization](https://mlsanity.com/paper/1901.02968/) (2019)
- [Geometric Disentanglement for Generative Latent Shape Models](https://mlsanity.com/paper/1908.06386/) (2019)
- [DeformNet: Free-Form Deformation Network for 3D Shape Reconstruction from a Single Image](https://mlsanity.com/paper/1708.04672/) (2017)
- [Learning Generative Models of Shape Handles](https://mlsanity.com/paper/2004.03028/) (2020)
- [GRASS: Generative Recursive Autoencoders for Shape Structures](https://mlsanity.com/paper/1705.02090/) (2017)
- [Learning Free-Form Deformations for 3D Object Reconstruction](https://mlsanity.com/paper/1803.10932/) (2018)
- [Learning Local Shape Descriptors from Part Correspondences With Multi-view Convolutional Networks](https://mlsanity.com/paper/1706.04496/) (2017)
- [Synthesizing 3D Shapes from Silhouette Image Collections using Multi-projection Generative Adversarial Networks](https://mlsanity.com/paper/1906.03841/) (2019)
- [ALIGNet: Partial-Shape Agnostic Alignment via Unsupervised Learning](https://mlsanity.com/paper/1804.08497/) (2018)
- [Mesh-based Autoencoders for Localized Deformation Component Analysis](https://mlsanity.com/paper/1709.04304/) (2017)
- [DeformSyncNet: Deformation Transfer via Synchronized Shape Deformation Spaces](https://mlsanity.com/paper/2009.01456/) (2020)

## Built on by (most cited first, 30 of 37)

- [One-2-3-45: Any Single Image to 3D Mesh in 45 Seconds without Per-Shape Optimization](https://mlsanity.com/paper/2306.16928/) (2023)
- [One-2-3-45++: Fast Single Image to 3D Objects with Consistent Multi-View Generation and 3D Diffusion](https://mlsanity.com/paper/2311.07885/) (2023)
- [Generative Neural Articulated Radiance Fields](https://mlsanity.com/paper/2206.14314/) (2022)
- [TextDeformer: Geometry Manipulation using Text Guidance](https://mlsanity.com/paper/2304.13348/) (2023)
- [Approximate Convex Decomposition for 3D Meshes with Collision-Aware Concavity and Tree Search](https://mlsanity.com/paper/2205.02961/) (2022)
- [Controllable Mesh Generation Through Sparse Latent Point Diffusion Models](https://mlsanity.com/paper/2303.07938/) (2023)
- [Skeleton-free Pose Transfer for Stylized 3D Characters](https://mlsanity.com/paper/2208.00790/) (2022)
- [Neural Jacobian Fields: Learning Intrinsic Mappings of Arbitrary Meshes](https://mlsanity.com/paper/2205.02904/) (2022)
- [Anymate: A Dataset and Baselines for Learning 3D Object Rigging](https://mlsanity.com/paper/2505.06227/) (2025)
- [As-Plausible-As-Possible: Plausibility-Aware Mesh Deformation Using 2D Diffusion Priors](https://mlsanity.com/paper/2311.16739/) (2023)
- [Learning Whole Heart Mesh Generation From Patient Images For Computational Simulations](https://mlsanity.com/paper/2203.10517/) (2022)
- [PASTA: Controllable Part-Aware Shape Generation with Autoregressive Transformers](https://mlsanity.com/paper/2407.13677/) (2024)
- [InstructP2P: Learning to Edit 3D Point Clouds with Text Instructions](https://mlsanity.com/paper/2306.07154/) (2023)
- [Doodle Your 3D: From Abstract Freehand Sketches to Precise 3D Shapes](https://mlsanity.com/paper/2312.04043/) (2023)
- [Weakly-supervised 3D Pose Transfer with Keypoints](https://mlsanity.com/paper/2307.13459/) (2023)
- [LADIS: Language Disentanglement for 3D Shape Editing](https://mlsanity.com/paper/2212.05011/) (2022)
- [Category-Agnostic Neural Object Rigging](https://mlsanity.com/paper/2505.20283/) (2025)
- [Few-Shot Physically-Aware Articulated Mesh Generation via Hierarchical Deformation](https://mlsanity.com/paper/2308.10898/) (2023)
- [CNS-Edit: 3D Shape Editing via Coupled Neural Shape Optimization](https://mlsanity.com/paper/2402.02313/) (2024)
- [Intuitive Shape Editing in Latent Space](https://mlsanity.com/paper/2111.12488/) (2021)
- [Explorable Mesh Deformation Subspaces from Unstructured Generative Models](https://mlsanity.com/paper/2310.07814/) (2023)
- [ParSEL: Parameterized Shape Editing with Language](https://mlsanity.com/paper/2405.20319/) (2024)
- [Neural Pose Representation Learning for Generating and Transferring Non-Rigid Object Poses](https://mlsanity.com/paper/2406.09728/) (2024)
- [Implicit-ARAP: Efficient Handle-Guided Neural Field Deformation via Local Patch Meshing](https://mlsanity.com/paper/2405.12895/) (2024)
- [Multi-hypotheses Conditioned Point Cloud Diffusion for 3D Human Reconstruction from Occluded Images](https://mlsanity.com/paper/2409.18364/) (2024)
- [ARAP-GS: Drag-driven As-Rigid-As-Possible 3D Gaussian Splatting Editing with Diffusion Prior](https://mlsanity.com/paper/2504.12788/) (2025)
- [TutteNet: Injective 3D Deformations by Composition of 2D Mesh Deformations](https://mlsanity.com/paper/2406.12121/) (2024)
- [3D Semantic Subspace Traverser: Empowering 3D Generative Model with Shape Editing Capability](https://mlsanity.com/paper/2307.14051/) (2023)
- [Relational Anatomical Supervision for Accurate 3D Multi-Chamber Cardiac Mesh Reconstruction](https://mlsanity.com/paper/2503.07874/) (2025)
- [Deep Feature Deformation Weights](https://mlsanity.com/paper/2601.12527/) (2026)

## Abstract (arXiv)

We propose DeepMetaHandles, a 3D conditional generative model based on mesh deformation. Given a collection of 3D meshes of a category and their deformation handles (control points), our method learns a set of meta-handles for each shape, which are represented as combinations of the given handles. The disentangled meta-handles factorize all the plausible deformations of the shape, while each of them corresponds to an intuitive deformation. A new deformation can then be generated by sampling the coefficients of the meta-handles in a specific range. We employ biharmonic coordinates as the deformation function, which can smoothly propagate the control points' translations to the entire mesh. To avoid learning zero deformation as meta-handles, we incorporate a target-fitting module which deforms the input mesh to match a random target. To enhance deformations' plausibility, we employ a soft-rasterizer-based discriminator that projects the meshes to a 2D space. Our experiments demonstrate the superiority of the generated deformations as well as the interpretability and consistency of the learned meta-handles.