# Deformable Surface Reconstruction via Riemannian Metric Preservation

arXiv: https://arxiv.org/abs/2212.11596 · HTML: https://mlsanity.com/paper/2212.11596/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 59 references that are in the map.
- First posted on arXiv 22 Dec 2022.

## Builds on (most cited first, 17 of 17)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [Universal Approximation with Deep Narrow Networks](https://mlsanity.com/paper/1905.08539/) (2019)
- [A Structured Dictionary Perspective on Implicit Neural Representations](https://mlsanity.com/paper/2112.01917/) (2021)
- [DefSLAM: Tracking and Mapping of Deforming Scenes from Monocular Sequences](https://mlsanity.com/paper/1908.08918/) (2019)
- [Shape Reconstruction by Learning Differentiable Surface Representations](https://mlsanity.com/paper/1911.11227/) (2019)
- [State of the Art in Dense Monocular Non-Rigid 3D Reconstruction](https://mlsanity.com/paper/2210.15664/) (2022)
- [Noether Networks: Meta-Learning Useful Conserved Quantities](https://mlsanity.com/paper/2112.03321/) (2021)
- [φ-SfT: Shape-from-Template with a Physics-Based Deformation Model](https://mlsanity.com/paper/2203.11938/) (2022)
- [Pix2Surf: Learning Parametric 3D Surface Models of Objects from Images](https://mlsanity.com/paper/2008.07760/) (2020)
- [Geometry-Aware Network for Non-Rigid Shape Prediction from a Single View](https://mlsanity.com/paper/1809.10305/) (2018)
- [Tailoring: encoding inductive biases by optimizing unsupervised objectives at prediction time](https://mlsanity.com/paper/2009.10623/) (2020)
- [Learning to Reconstruct Texture-less Deformable Surfaces from a Single View](https://mlsanity.com/paper/1803.08908/) (2018)
- [Model Predictive Control for Dynamic Cloth Manipulation: Parameter Learning and Experimental Validation](https://mlsanity.com/paper/2209.05798/) (2022)

## Built on by (most cited first, 2 of 2)

- [Beyond Static Perception: Integrating Temporal Context into VLMs for Cloth Folding](https://mlsanity.com/paper/2505.07600/) (2025)
- [ParCo-SDF: Learning Prior-Free Partial-to-Complete Signed Distance Fields of Deformable Objects](https://mlsanity.com/paper/2605.29417/) (2026)

## Abstract (arXiv)

Estimating the pose of an object from a monocular image is an inverse problem fundamental in computer vision. The ill-posed nature of this problem requires incorporating deformation priors to solve it. In practice, many materials do not perceptibly shrink or extend when manipulated, constituting a powerful and well-known prior. Mathematically, this translates to the preservation of the Riemannian metric. Neural networks offer the perfect playground to solve the surface reconstruction problem as they can approximate surfaces with arbitrary precision and allow the computation of differential geometry quantities. This paper presents an approach to inferring continuous deformable surfaces from a sequence of images, which is benchmarked against several techniques and obtains state-of-the-art performance without the need for offline training.