# Organic Priors in Non-Rigid Structure from Motion

arXiv: https://arxiv.org/abs/2207.06262 · HTML: https://mlsanity.com/paper/2207.06262/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 52 references that are in the map.
- First posted on arXiv 13 Jul 2022.

## Builds on (most cited first, 13 of 13)

- [Monocular Dense 3D Reconstruction of a Complex Dynamic Scene from Two Perspective Frames](https://mlsanity.com/paper/1708.04398/) (2017)
- [Superpixel Soup: Monocular Dense 3D Reconstruction of a Complex Dynamic Scene](https://mlsanity.com/paper/1911.09092/) (2019)
- [Scalable Dense Non-rigid Structure-from-Motion: A Grassmannian Perspective](https://mlsanity.com/paper/1803.00233/) (2018)
- [Non-Rigid Structure from Motion: Prior-Free Factorization Method Revisited](https://mlsanity.com/paper/1902.10274/) (2019)
- [Multi-body Non-rigid Structure-from-Motion](https://mlsanity.com/paper/1607.04515/) (2016)
- [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)
- [Robust Single Rotation Averaging](https://mlsanity.com/paper/2004.00732/) (2020)
- [Partial Sum Minimization of Singular Values in Robust PCA: Algorithm and Applications](https://mlsanity.com/paper/1503.01444/) (2015)
- [Scalable Dense Monocular Surface Reconstruction](https://mlsanity.com/paper/1710.06130/) (2017)
- [Dense Depth Estimation of a Complex Dynamic Scene without Explicit 3D Motion Estimation](https://mlsanity.com/paper/1902.03791/) (2019)
- [Accurate Optimization of Weighted Nuclear Norm for Non-Rigid Structure from Motion](https://mlsanity.com/paper/2003.10281/) (2020)
- [Dense Non-Rigid Structure from Motion: A Manifold Viewpoint](https://mlsanity.com/paper/2006.09197/) (2020)

## Built on by (most cited first, 15 of 15)

- [Recent Trends in 3D Reconstruction of General Non-Rigid Scenes](https://mlsanity.com/paper/2403.15064/) (2024)
- [Fast Encoder-Based 3D from Casual Videos via Point Track Processing](https://mlsanity.com/paper/2404.07097/) (2024)
- [Learning Robust Multi-Scale Representation for Neural Radiance Fields from Unposed Images](https://mlsanity.com/paper/2311.04521/) (2023)
- [Robust Single Rotation Averaging Revisited](https://mlsanity.com/paper/2309.05388/) (2023)
- [Fast Non-Rigid Radiance Fields from Monocularized Data](https://mlsanity.com/paper/2212.01368/) (2022)
- [Uncertainty-Driven Dense Two-View Structure from Motion](https://mlsanity.com/paper/2302.00523/) (2023)
- [Learning Better Keypoints for Multi-Object 6DoF Pose Estimation](https://mlsanity.com/paper/2308.07827/) (2023)
- [Shape-from-Template with Generalised Camera](https://mlsanity.com/paper/2508.13791/) (2025)
- [Time-Archival Camera Virtualization for Sports and Visual Performances](https://mlsanity.com/paper/2602.15181/) (2026)
- [Convex Relaxations for Isometric and Equiareal NRSfM](https://mlsanity.com/paper/2211.16005/) (2022)
- [Non-rigid Structure-from-Motion: Temporally-smooth Procrustean Alignment and Spatially-variant Deformation Modeling](https://mlsanity.com/paper/2405.04309/) (2024)
- [Next-Future: Sample-Efficient Policy Learning for Robotic-Arm Tasks](https://mlsanity.com/paper/2504.11247/) (2025)
- [SSR: A Training-Free Approach for Streaming 3D Reconstruction](https://mlsanity.com/paper/2603.14765/) (2026)
- [A Dataset and Evaluation for Complex 4D Markerless Human Motion Capture](https://mlsanity.com/paper/2604.12765/) (2026)
- [Rethinking Dense Optical Flow without Test-Time Scaling](https://mlsanity.com/paper/2605.08000/) (2026)

## Abstract (arXiv)

This paper advocates the use of organic priors in classical non-rigid structure from motion (NRSfM). By organic priors, we mean invaluable intermediate prior information intrinsic to the NRSfM matrix factorization theory. It is shown that such priors reside in the factorized matrices, and quite surprisingly, existing methods generally disregard them. The paper's main contribution is to put forward a simple, methodical, and practical method that can effectively exploit such organic priors to solve NRSfM. The proposed method does not make assumptions other than the popular one on the low-rank shape and offers a reliable solution to NRSfM under orthographic projection. Our work reveals that the accessibility of organic priors is independent of the camera motion and shape deformation type. Besides that, the paper provides insights into the NRSfM factorization -- both in terms of shape and motion -- and is the first approach to show the benefit of single rotation averaging for NRSfM. Furthermore, we outline how to effectively recover motion and non-rigid 3D shape using the proposed organic prior based approach and demonstrate results that outperform prior-free NRSfM performance by a significant margin. Finally, we present the benefits of our method via extensive experiments and evaluations on several benchmark datasets.