# Dense Non-Rigid Structure from Motion: A Manifold Viewpoint

arXiv: https://arxiv.org/abs/2006.09197 · HTML: https://mlsanity.com/paper/2006.09197/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Jun 2020.

## Built on by (most cited first, 4 of 4)

- [Organic Priors in Non-Rigid Structure from Motion](https://mlsanity.com/paper/2207.06262/) (2022)
- [MBW: Multi-view Bootstrapping in the Wild](https://mlsanity.com/paper/2210.01721/) (2022)
- [Camera Movement Estimation and Path Correction using the Combination of Modified A-SIFT and Stereo System for 3D Modelling](https://mlsanity.com/paper/2503.17668/) (2025)
- [Next-Future: Sample-Efficient Policy Learning for Robotic-Arm Tasks](https://mlsanity.com/paper/2504.11247/) (2025)

## Abstract (arXiv)

Non-Rigid Structure-from-Motion (NRSfM) problem aims to recover 3D geometry of a deforming object from its 2D feature correspondences across multiple frames. Classical approaches to this problem assume a small number of feature points and, ignore the local non-linearities of the shape deformation, and therefore, struggles to reliably model non-linear deformations. Furthermore, available dense NRSfM algorithms are often hurdled by scalability, computations, noisy measurements and, restricted to model just global deformation. In this paper, we propose algorithms that can overcome these limitations with the previous methods and, at the same time, can recover a reliable dense 3D structure of a non-rigid object with higher accuracy. Assuming that a deforming shape is composed of a union of local linear subspace and, span a global low-rank space over multiple frames enables us to efficiently model complex non-rigid deformations. To that end, each local linear subspace is represented using Grassmannians and, the global 3D shape across multiple frames is represented using a low-rank representation. We show that our approach significantly improves accuracy, scalability, and robustness against noise. Also, our representation naturally allows for simultaneous reconstruction and clustering framework which in general is observed to be more suitable for NRSfM problems. Our method currently achieves leading performance on the standard benchmark datasets.