# Non-Rigid Structure from Motion: Prior-Free Factorization Method Revisited

arXiv: https://arxiv.org/abs/1902.10274 · HTML: https://mlsanity.com/paper/1902.10274/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Feb 2019.

## Built on by (most cited first, 18 of 18)

- [BANMo: Building Animatable 3D Neural Models from Many Casual Videos](https://mlsanity.com/paper/2112.12761/) (2021)
- [State of the Art in Dense Monocular Non-Rigid 3D Reconstruction](https://mlsanity.com/paper/2210.15664/) (2022)
- [Organic Priors in Non-Rigid Structure from Motion](https://mlsanity.com/paper/2207.06262/) (2022)
- [BAGS: Building Animatable Gaussian Splatting from a Monocular Video with Diffusion Priors](https://mlsanity.com/paper/2403.11427/) (2024)
- [DreaMo: Articulated 3D Reconstruction From A Single Casual Video](https://mlsanity.com/paper/2312.02617/) (2023)
- [CAMM: Building Category-Agnostic and Animatable 3D Models from Monocular Videos](https://mlsanity.com/paper/2304.06937/) (2023)
- [PAUL: Procrustean Autoencoder for Unsupervised Lifting](https://mlsanity.com/paper/2103.16773/) (2021)
- [Neural Architecture Search for Efficient Uncalibrated Deep Photometric Stereo](https://mlsanity.com/paper/2110.05621/) (2021)
- [DynamicSurf: Dynamic Neural RGB-D Surface Reconstruction with an Optimizable Feature Grid](https://mlsanity.com/paper/2311.08159/) (2023)
- [High Fidelity 3D Reconstructions with Limited Physical Views](https://mlsanity.com/paper/2110.11599/) (2021)
- [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)
- [Unsupervised 2D-3D lifting of non-rigid objects using local constraints](https://mlsanity.com/paper/2504.19227/) (2025)
- [Generalizing Shape-from-Template to Topological Changes](https://mlsanity.com/paper/2511.03459/) (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)
- [Prosthesis-Aware 3D Human Pose Estimation: A Dataset and Benchmark for RSP Users](https://mlsanity.com/paper/2609.18406/) (2026)

## Abstract (arXiv)

A simple prior free factorization algorithm citedai2014simple is quite often cited work in the field of Non-Rigid Structure from Motion (NRSfM). The benefit of this work lies in its simplicity of implementation, strong theoretical justification to the motion and structure estimation, and its invincible originality. Despite this, the prevailing view is, that it performs exceedingly inferior to other methods on several benchmark datasets citejensen2018benchmark,akhter2009nonrigid. However, our subtle investigation provides some empirical statistics which made us think against such views. The statistical results we obtained supersedes Dai itet al.citedai2014simple originally reported results on the benchmark datasets by a significant margin under some elementary changes in their core algorithmic idea citedai2014simple. Now, these results not only exposes some unrevealed areas for research in NRSfM but also give rise to new mathematical challenges for NRSfM researchers. We argue that by properly utilizing the well-established assumptions about a non-rigidly deforming shape i.e, it deforms smoothly over frames citerabaud2008re and it spans a low-rank space, the simple prior-free idea can provide results which is comparable to the best available algorithms. In this paper, we explore some of the hidden intricacies missed by Dai itet. al. work citedai2014simple and how some elementary measures and modifications can enhance its performance, as high as approx. 18% on the benchmark dataset. The improved performance is justified and empirically verified by extensive experiments on several datasets. We believe our work has both practical and theoretical importance for the development of better NRSfM algorithms.