# Robust Isometric Non-Rigid Structure-from-Motion

arXiv: https://arxiv.org/abs/2010.04690 · HTML: https://mlsanity.com/paper/2010.04690/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Oct 2020.

## Built on by (most cited first, 7 of 7)

- [Recent Trends in 3D Reconstruction of General Non-Rigid Scenes](https://mlsanity.com/paper/2403.15064/) (2024)
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- [GAPS: Geometry-Aware, Physics-Based, Self-Supervised Neural Garment Draping](https://mlsanity.com/paper/2312.01490/) (2023)
- [IntrinsicNGP: Intrinsic Coordinate based Hash Encoding for Human NeRF](https://mlsanity.com/paper/2302.14683/) (2023)
- [The Drunkard's Odometry: Estimating Camera Motion in Deforming Scenes](https://mlsanity.com/paper/2306.16917/) (2023)
- [Non-Rigid Structure-from-Motion via Differential Geometry with Recoverable Conformal Scale](https://mlsanity.com/paper/2510.01665/) (2025)
- [Non-rigid Structure-from-Motion: Temporally-smooth Procrustean Alignment and Spatially-variant Deformation Modeling](https://mlsanity.com/paper/2405.04309/) (2024)

## Abstract (arXiv)

Non-Rigid Structure-from-Motion (NRSfM) reconstructs a deformable 3D object from the correspondences established between monocular 2D images. Current NRSfM methods lack statistical robustness, which is the ability to cope with correspondence errors.This prevents one to use automatically established correspondences, which are prone to errors, thereby strongly limiting the scope of NRSfM. We propose a three-step automatic pipeline to solve NRSfM robustly by exploiting isometry. Step 1 computes the optical flow from correspondences, step 2 reconstructs each 3D point's normal vector using multiple reference images and integrates them to form surfaces with the best reference and step 3 rejects the 3D points that break isometry in their local neighborhood. Importantly, each step is designed to discard or flag erroneous correspondences. Our contributions include the robustification of optical flow by warp estimation, new fast analytic solutions to local normal reconstruction and their robustification, and a new scale-independent measure of 3D local isometric coherence. Experimental results show that our robust NRSfM method consistently outperforms existing methods on both synthetic and real datasets.