# NeuralMLS: Geometry-Aware Control Point Deformation

arXiv: https://arxiv.org/abs/2201.01873 · HTML: https://mlsanity.com/paper/2201.01873/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 38 references that are in the map.
- First posted on arXiv 5 Jan 2022.

## Builds on (most cited first, 26 of 26)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [CoAtNet: Marrying Convolution and Attention for All Data Sizes](https://mlsanity.com/paper/2106.04803/) (2021)
- [Voxel Transformer for 3D Object Detection](https://mlsanity.com/paper/2109.02497/) (2021)
- [Editing Conditional Radiance Fields](https://mlsanity.com/paper/2105.06466/) (2021)
- [On the Inductive Bias of Neural Tangent Kernels](https://mlsanity.com/paper/1905.12173/) (2019)
- [Frequency Bias in Neural Networks for Input of Non-Uniform Density](https://mlsanity.com/paper/2003.04560/) (2020)
- [A Function Space View of Bounded Norm Infinite Width ReLU Nets: The Multivariate Case](https://mlsanity.com/paper/1910.01635/) (2019)
- [How do infinite width bounded norm networks look in function space?](https://mlsanity.com/paper/1902.05040/) (2019)
- [Neural Cages for Detail-Preserving 3D Deformations](https://mlsanity.com/paper/1912.06395/) (2019)
- [3DN: 3D Deformation Network](https://mlsanity.com/paper/1903.03322/) (2019)
- [KeypointDeformer: Unsupervised 3D Keypoint Discovery for Shape Control](https://mlsanity.com/paper/2104.11224/) (2021)
- [Gradient Dynamics of Shallow Univariate ReLU Networks](https://mlsanity.com/paper/1906.07842/) (2019)
- [Joint Learning of 3D Shape Retrieval and Deformation](https://mlsanity.com/paper/2101.07889/) (2021)
- [Unsupervised cycle-consistent deformation for shape matching](https://mlsanity.com/paper/1907.03165/) (2019)
- [A Revisit of Shape Editing Techniques: from the Geometric to the Neural Viewpoint](https://mlsanity.com/paper/2103.01694/) (2021)
- [Self-Sampling for Neural Point Cloud Consolidation](https://mlsanity.com/paper/2008.06471/) (2020)
- [Deep Hybrid Self-Prior for Full 3D Mesh Generation](https://mlsanity.com/paper/2108.08017/) (2021)
- [Learning to Infer Semantic Parameters for 3D Shape Editing](https://mlsanity.com/paper/2011.04755/) (2020)
- [A function space analysis of finite neural networks with insights from sampling theory](https://mlsanity.com/paper/2004.06989/) (2020)

## Built on by (most cited first, 5 of 5)

- [TextDeformer: Geometry Manipulation using Text Guidance](https://mlsanity.com/paper/2304.13348/) (2023)
- [Neural Shape Deformation Priors](https://mlsanity.com/paper/2210.05616/) (2022)
- [Geometry in Style: 3D Stylization via Surface Normal Deformation](https://mlsanity.com/paper/2503.23241/) (2025)
- [DragD3D: Realistic Mesh Editing with Rigidity Control Driven by 2D Diffusion Priors](https://mlsanity.com/paper/2310.04561/) (2023)
- [PDB: Point-Based Deformation Blending for Facial Animation Retargeting](https://mlsanity.com/paper/2610.08672/) (2026)

## Abstract (arXiv)

We introduce NeuralMLS, a space-based deformation technique, guided by a set of displaced control points. We leverage the power of neural networks to inject the underlying shape geometry into the deformation parameters. The goal of our technique is to enable a realistic and intuitive shape deformation. Our method is built upon moving least-squares (MLS), since it minimizes a weighted sum of the given control point displacements. Traditionally, the influence of each control point on every point in space (i.e., the weighting function) is defined using inverse distance heuristics. In this work, we opt to learn the weighting function, by training a neural network on the control points from a single input shape, and exploit the innate smoothness of neural networks. Our geometry-aware control point deformation is agnostic to the surface representation and quality; it can be applied to point clouds or meshes, including non-manifold and disconnected surface soups. We show that our technique facilitates intuitive piecewise smooth deformations, which are well suited for manufactured objects. We show the advantages of our approach compared to existing surface and space-based deformation techniques, both quantitatively and qualitatively.