Abstract
A simple prior free factorization algorithm 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. However, our subtle investigation provides some empirical statistics which made us think against such views. The statistical results we obtained supersedes Dai et al. originally reported results on the benchmark datasets by a significant margin under some elementary changes in their core algorithmic idea. Now, these results not only exposes some unrevealed areas for research in NRSfM but also give rise to new mathematical challengesfor 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 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 et. al. work and how some elementary measures and modifications can enhance its performance, as high as approximately 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.

Non-rigid Structure from Motion: Prior-Free Factorization Method Revisited Suryansh Kumar IEEE/CVF WACV 2020, Colorado, USA.

The work is supported by ETH Zurich Foundation and Google project as part of bringing together the best of academics and industrial research (2019-HE-323). The author thank Prof. Carl Olsson for the datasets and useful discussion related to this work. The author thank ETH CVL Lab Head Prof. Dr. Luc van Gool for the opportunity and the extraordinary research-lab facility.