# Scalable Dense Non-rigid Structure-from-Motion: A Grassmannian Perspective

arXiv: https://arxiv.org/abs/1803.00233 · HTML: https://mlsanity.com/paper/1803.00233/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Mar 2018.

## Built on by (most cited first, 19 of 19)

- [Virtual Elastic Objects](https://mlsanity.com/paper/2201.04623/) (2022)
- [State of the Art in Dense Monocular Non-Rigid 3D Reconstruction](https://mlsanity.com/paper/2210.15664/) (2022)
- [Neural Radiance Fields Approach to Deep Multi-View Photometric Stereo](https://mlsanity.com/paper/2110.05594/) (2021)
- [Differentiable Event Stream Simulator for Non-Rigid 3D Tracking](https://mlsanity.com/paper/2104.15139/) (2021)
- [φ-SfT: Shape-from-Template with a Physics-Based Deformation Model](https://mlsanity.com/paper/2203.11938/) (2022)
- [Organic Priors in Non-Rigid Structure from Motion](https://mlsanity.com/paper/2207.06262/) (2022)
- [SceNeRFlow: Time-Consistent Reconstruction of General Dynamic Scenes](https://mlsanity.com/paper/2308.08258/) (2023)
- [PR-RRN: Pairwise-Regularized Residual-Recursive Networks for Non-rigid Structure-from-Motion](https://mlsanity.com/paper/2108.07506/) (2021)
- [Neural Architecture Search for Efficient Uncalibrated Deep Photometric Stereo](https://mlsanity.com/paper/2110.05621/) (2021)
- [Extracting Deformation-Aware Local Features by Learning to Deform](https://mlsanity.com/paper/2111.10617/) (2021)
- [MHR-Net: Multiple-Hypothesis Reconstruction of Non-Rigid Shapes from 2D Views](https://mlsanity.com/paper/2207.09086/) (2022)
- [DensePose 3D: Lifting Canonical Surface Maps of Articulated Objects to the Third Dimension](https://mlsanity.com/paper/2109.00033/) (2021)
- [Thin-Shell-SfT: Fine-Grained Monocular Non-rigid 3D Surface Tracking with Neural Deformation Fields](https://mlsanity.com/paper/2503.19976/) (2025)
- [Registration beyond Points: General Affine Subspace Alignment via Geodesic Distance on Grassmann Manifold](https://mlsanity.com/paper/2507.17998/) (2025)
- [Non-Rigid Structure-from-Motion via Differential Geometry with Recoverable Conformal Scale](https://mlsanity.com/paper/2510.01665/) (2025)
- [HeadRecon: High-Fidelity 3D Head Reconstruction from Monocular Video](https://mlsanity.com/paper/2312.08863/) (2023)
- [Non-rigid Structure-from-Motion: Temporally-smooth Procrustean Alignment and Spatially-variant Deformation Modeling](https://mlsanity.com/paper/2405.04309/) (2024)
- [SSR: A Training-Free Approach for Streaming 3D Reconstruction](https://mlsanity.com/paper/2603.14765/) (2026)
- [Rethinking Dense Optical Flow without Test-Time Scaling](https://mlsanity.com/paper/2605.08000/) (2026)

## Abstract (arXiv)

This paper addresses the task of dense non-rigid structure-from-motion (NRSfM) using multiple images. State-of-the-art methods to this problem are often hurdled by scalability, expensive computations, and noisy measurements. Further, recent methods to NRSfM usually either assume a small number of sparse feature points or ignore local non-linearities of shape deformations, and thus cannot reliably model complex non-rigid deformations. To address these issues, in this paper, we propose a new approach for dense NRSfM by modeling the problem on a Grassmann manifold. Specifically, we assume the complex non-rigid deformations lie on a union of local linear subspaces both spatially and temporally. This naturally allows for a compact representation of the complex non-rigid deformation over frames. We provide experimental results on several synthetic and real benchmark datasets. The procured results clearly demonstrate that our method, apart from being scalable and more accurate than state-of-the-art methods, is also more robust to noise and generalizes to highly non-linear deformations.