# Non-Rigid Structure-from-Motion via Differential Geometry with Recoverable Conformal Scale

arXiv: https://arxiv.org/abs/2510.01665 · HTML: https://mlsanity.com/paper/2510.01665/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 70 references that are in the map.
- First posted on arXiv 2 Oct 2025.

## Builds on (most cited first, 23 of 23)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [ORB-SLAM: a Versatile and Accurate Monocular SLAM System](https://mlsanity.com/paper/1502.00956/) (2015)
- [ORB-SLAM3: An Accurate Open-Source Library for Visual, Visual-Inertial and Multi-Map SLAM](https://mlsanity.com/paper/2007.11898/) (2020)
- [Deep Ordinal Regression Network for Monocular Depth Estimation](https://mlsanity.com/paper/1806.02446/) (2018)
- [Gaussian Splatting SLAM](https://mlsanity.com/paper/2312.06741/) (2023)
- [InterHand2.6M: A Dataset and Baseline for 3D Interacting Hand Pose Estimation from a Single RGB Image](https://mlsanity.com/paper/2008.09309/) (2020)
- [High Quality Monocular Depth Estimation via Transfer Learning](https://mlsanity.com/paper/1812.11941/) (2018)
- [LASR: Learning Articulated Shape Reconstruction from a Monocular Video](https://mlsanity.com/paper/2105.02976/) (2021)
- [C3DPO: Canonical 3D Pose Networks for Non-Rigid Structure From Motion](https://mlsanity.com/paper/1909.02533/) (2019)
- [DefSLAM: Tracking and Mapping of Deforming Scenes from Monocular Sequences](https://mlsanity.com/paper/1908.08918/) (2019)
- [SD-DefSLAM: Semi-Direct Monocular SLAM for Deformable and Intracorporeal Scenes](https://mlsanity.com/paper/2010.09409/) (2020)
- [Scalable Dense Non-rigid Structure-from-Motion: A Grassmannian Perspective](https://mlsanity.com/paper/1803.00233/) (2018)
- [A Benchmark and Evaluation of Non-Rigid Structure from Motion](https://mlsanity.com/paper/1801.08388/) (2018)
- [Jumping Manifolds: Geometry Aware Dense Non-Rigid Structure from Motion](https://mlsanity.com/paper/1902.01077/) (2019)
- [4D Gaussian Splatting SLAM](https://mlsanity.com/paper/2503.16710/) (2025)
- [PAUL: Procrustean Autoencoder for Unsupervised Lifting](https://mlsanity.com/paper/2103.16773/) (2021)
- [Deep Non-rigid Structure-from-Motion: A Sequence-to-Sequence Translation Perspective](https://mlsanity.com/paper/2204.04730/) (2022)
- [Scalable Dense Monocular Surface Reconstruction](https://mlsanity.com/paper/1710.06130/) (2017)
- [Robust Isometric Non-Rigid Structure-from-Motion](https://mlsanity.com/paper/2010.04690/) (2020)
- [Dense Non-rigid Structure-from-Motion Made Easy - A Spatial-Temporal Smoothness based Solution](https://mlsanity.com/paper/1706.08629/) (2017)
- ["Maximizing rigidity" revisited: a convex programming approach for generic 3D shape reconstruction from multiple perspective views](https://mlsanity.com/paper/1707.05009/) (2017)

## Built on by (most cited first, 1 of 1)

- [Exploring 6D Object Pose Estimation with Deformation](https://mlsanity.com/paper/2604.06720/) (2026)

## Abstract (arXiv)

Non-rigid structure-from-motion (NRSfM), a promising technique for addressing the mapping challenges in monocular visual deformable simultaneous localization and mapping (SLAM), has attracted growing attention. We introduce a novel method, called Con-NRSfM, for NRSfM under conformal deformations, encompassing isometric deformations as a subset. Our approach performs point-wise reconstruction using 2D selected image warps optimized through a graph-based framework. Unlike existing methods that rely on strict assumptions, such as locally planar surfaces or locally linear deformations, and fail to recover the conformal scale, our method eliminates these constraints and accurately computes the local conformal scale. Additionally, our framework decouples constraints on depth and conformal scale, which are inseparable in other approaches, enabling more precise depth estimation. To address the sensitivity of the formulated problem, we employ a parallel separable iterative optimization strategy. Furthermore, a self-supervised learning framework, utilizing an encoder-decoder network, is incorporated to generate dense 3D point clouds with texture. Simulation and experimental results using both synthetic and real datasets demonstrate that our method surpasses existing approaches in terms of reconstruction accuracy and robustness. The code for the proposed method will be made publicly available on the project website: https://sites.google.com/view/con-nrsfm.