# Convex Relaxations for Isometric and Equiareal NRSfM

arXiv: https://arxiv.org/abs/2211.16005 · HTML: https://mlsanity.com/paper/2211.16005/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 34 references that are in the map.
- First posted on arXiv 29 Nov 2022.

## Builds on (most cited first, 7 of 7)

- [EndoMapper dataset of complete calibrated endoscopy procedures](https://mlsanity.com/paper/2204.14240/) (2022)
- [Non-Rigid Structure from Motion: Prior-Free Factorization Method Revisited](https://mlsanity.com/paper/1902.10274/) (2019)
- [Organic Priors in Non-Rigid Structure from Motion](https://mlsanity.com/paper/2207.06262/) (2022)
- [Convex Relaxations for Consensus and Non-Minimal Problems in 3D Vision](https://mlsanity.com/paper/1909.12034/) (2019)
- ["Maximizing rigidity" revisited: a convex programming approach for generic 3D shape reconstruction from multiple perspective views](https://mlsanity.com/paper/1707.05009/) (2017)
- [Incremental Non-Rigid Structure-from-Motion with Unknown Focal Length](https://mlsanity.com/paper/1808.04181/) (2018)
- [Angle-Based Sensor Network Localization](https://mlsanity.com/paper/1912.01665/) (2019)

## Abstract (arXiv)

Extensible objects form a challenging case for NRSfM, owing to the lack of a sufficiently constrained extensible model of the point-cloud. We tackle the challenge by proposing 1) convex relaxations of the isometric model up to quasi-isometry, and 2) convex relaxations involving the equiareal deformation model, which preserves local area and has not been used in NRSfM. The equiareal model is appealing because it is physically plausible and widely applicable. However, it has two main difficulties: first, when used on its own, it is ambiguous, and second, it involves quartic, hence highly nonconvex, constraints. Our approach handles the first difficulty by mixing the equiareal with the isometric model and the second difficulty by new convex relaxations. We validate our methods on multiple real and synthetic data, including well-known benchmarks.