# Incremental Non-Rigid Structure-from-Motion with Unknown Focal Length

arXiv: https://arxiv.org/abs/1808.04181 · HTML: https://mlsanity.com/paper/1808.04181/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Aug 2018.

## Built on by (most cited first, 2 of 2)

- [MHR-Net: Multiple-Hypothesis Reconstruction of Non-Rigid Shapes from 2D Views](https://mlsanity.com/paper/2207.09086/) (2022)
- [Convex Relaxations for Isometric and Equiareal NRSfM](https://mlsanity.com/paper/2211.16005/) (2022)

## Abstract (arXiv)

The perspective camera and the isometric surface prior have recently gathered increased attention for Non-Rigid Structure-from-Motion (NRSfM). Despite the recent progress, several challenges remain, particularly the computational complexity and the unknown camera focal length. In this paper we present a method for incremental Non-Rigid Structure-from-Motion (NRSfM) with the perspective camera model and the isometric surface prior with unknown focal length. In the template-based case, we provide a method to estimate four parameters of the camera intrinsics. For the template-less scenario of NRSfM, we propose a method to upgrade reconstructions obtained for one focal length to another based on local rigidity and the so-called Maximum Depth Heuristics (MDH). On its basis we propose a method to simultaneously recover the focal length and the non-rigid shapes. We further solve the problem of incorporating a large number of points and adding more views in MDH-based NRSfM and efficiently solve them with Second-Order Cone Programming (SOCP). This does not require any shape initialization and produces results orders of times faster than many methods. We provide evaluations on standard sequences with ground-truth and qualitative reconstructions on challenging YouTube videos. These evaluations show that our method performs better in both speed and accuracy than the state of the art.