# ShapeFlow: Learnable Deformations Among 3D Shapes

arXiv: https://arxiv.org/abs/2006.07982 · HTML: https://mlsanity.com/paper/2006.07982/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Jun 2020.

## Built on by (most cited first, 28 of 28)

- [HyperNeRF: A Higher-Dimensional Representation for Topologically Varying Neural Radiance Fields](https://mlsanity.com/paper/2106.13228/) (2021)
- [NeuroMorph: Unsupervised Shape Interpolation and Correspondence in One Go](https://mlsanity.com/paper/2106.09431/) (2021)
- [Towards Implicit Text-Guided 3D Shape Generation](https://mlsanity.com/paper/2203.14622/) (2022)
- [CaDeX: Learning Canonical Deformation Coordinate Space for Dynamic Surface Representation via Neural Homeomorphism](https://mlsanity.com/paper/2203.16529/) (2022)
- [Neural Surface Reconstruction of Dynamic Scenes with Monocular RGB-D Camera](https://mlsanity.com/paper/2206.15258/) (2022)
- [Joint Learning of 3D Shape Retrieval and Deformation](https://mlsanity.com/paper/2101.07889/) (2021)
- [Locally Aware Piecewise Transformation Fields for 3D Human Mesh Registration](https://mlsanity.com/paper/2104.08160/) (2021)
- [NODEO: A Neural Ordinary Differential Equation Based Optimization Framework for Deformable Image Registration](https://mlsanity.com/paper/2108.03443/) (2021)
- [SPAGHETTI: Editing Implicit Shapes Through Part Aware Generation](https://mlsanity.com/paper/2201.13168/) (2022)
- [Neural Jacobian Fields: Learning Intrinsic Mappings of Arbitrary Meshes](https://mlsanity.com/paper/2205.02904/) (2022)
- [ACID: Action-Conditional Implicit Visual Dynamics for Deformable Object Manipulation](https://mlsanity.com/paper/2203.06856/) (2022)
- [Augmenting Implicit Neural Shape Representations with Explicit Deformation Fields](https://mlsanity.com/paper/2108.08931/) (2021)
- [Towards Efficient Graph Convolutional Networks for Point Cloud Handling](https://mlsanity.com/paper/2104.05706/) (2021)
- [Implicit field supervision for robust non-rigid shape matching](https://mlsanity.com/paper/2203.07694/) (2022)
- [PREF: Predictability Regularized Neural Motion Fields](https://mlsanity.com/paper/2209.10691/) (2022)
- [Symplectic Adjoint Method for Exact Gradient of Neural ODE with Minimal Memory](https://mlsanity.com/paper/2102.09750/) (2021)
- [Towards Self-Supervised Category-Level Object Pose and Size Estimation](https://mlsanity.com/paper/2203.02884/) (2022)
- [DPF-Net: Combining Explicit Shape Priors in Deformable Primitive Field for Unsupervised Structural Reconstruction of 3D Objects](https://mlsanity.com/paper/2308.13225/) (2023)
- [Generative Deformable Radiance Fields for Disentangled Image Synthesis of Topology-Varying Objects](https://mlsanity.com/paper/2209.04183/) (2022)
- [Reduced Representation of Deformation Fields for Effective Non-rigid Shape Matching](https://mlsanity.com/paper/2211.14604/) (2022)
- [Representing Shape Collections with Alignment-Aware Linear Models](https://mlsanity.com/paper/2109.01605/) (2021)
- [Proximal Implicit ODE Solvers for Accelerating Learning Neural ODEs](https://mlsanity.com/paper/2204.08621/) (2022)
- [Explorable Mesh Deformation Subspaces from Unstructured Generative Models](https://mlsanity.com/paper/2310.07814/) (2023)
- [CorticalFlow: A Diffeomorphic Mesh Deformation Module for Cortical Surface Reconstruction](https://mlsanity.com/paper/2206.02374/) (2022)
- [Fast Point Cloud to Mesh Reconstruction for Deformable Object Tracking](https://mlsanity.com/paper/2311.02749/) (2023)
- [Mesh Draping: Parametrization-Free Neural Mesh Transfer](https://mlsanity.com/paper/2110.05433/) (2021)
- [Cloud Sphere: A 3D Shape Representation via Progressive Deformation](https://mlsanity.com/paper/2112.11133/) (2021)
- [Development of a deep learning platform for optimising sheet stamping geometries subject to manufacturing constraints](https://mlsanity.com/paper/2202.03422/) (2022)

## Abstract (arXiv)

We present ShapeFlow, a flow-based model for learning a deformation space for entire classes of 3D shapes with large intra-class variations. ShapeFlow allows learning a multi-template deformation space that is agnostic to shape topology, yet preserves fine geometric details. Different from a generative space where a latent vector is directly decoded into a shape, a deformation space decodes a vector into a continuous flow that can advect a source shape towards a target. Such a space naturally allows the disentanglement of geometric style (coming from the source) and structural pose (conforming to the target). We parametrize the deformation between geometries as a learned continuous flow field via a neural network and show that such deformations can be guaranteed to have desirable properties, such as be bijectivity, freedom from self-intersections, or volume preservation. We illustrate the effectiveness of this learned deformation space for various downstream applications, including shape generation via deformation, geometric style transfer, unsupervised learning of a consistent parameterization for entire classes of shapes, and shape interpolation.