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A simple prior free factorization algorithm cite{dai2014simple} 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 cite{jensen2018benchmark,akhter2009nonrigid}. However, our subtle investigation provides some empirical statistics which made us think against such views. The statistical results we obtained supersedes Dai {it{et al.}}cite{dai2014simple} originally reported results on the benchmark datasets by a significant margin under some elementary changes in their core algorithmic idea cite{dai2014simple}. Now, these results not only exposes some unrevealed areas for research in NRSfM but also give rise to new mathematical challenges for NRSfM researchers. We argue that by textbf{properly} utilizing the well-established assumptions about a non-rigidly deforming shape i.e, it deforms smoothly over frames cite{rabaud2008re} 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 {it{et. al.}} work cite{dai2014simple} and how some elementary measures and modifications can enhance its performance, as high as approx. 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.
Current non-rigid structure from motion (NRSfM) algorithms are mainly limited with respect to: (i) the number of images, and (ii) the type of shape variability they can handle. This has hampered the practical utility of NRSfM for many applications wi
All current non-rigid structure from motion (NRSfM) algorithms are limited with respect to: (i) the number of images, and (ii) the type of shape variability they can handle. This has hampered the practical utility of NRSfM for many applications withi
Non-Rigid Structure from Motion (NRSfM) refers to the problem of reconstructing cameras and the 3D point cloud of a non-rigid object from an ensemble of images with 2D correspondences. Current NRSfM algorithms are limited from two perspectives: (i) t
Non-Rigid Structure-from-Motion (NRSfM) problem aims to recover 3D geometry of a deforming object from its 2D feature correspondences across multiple frames. Classical approaches to this problem assume a small number of feature points and, ignore the
Given dense image feature correspondences of a non-rigidly moving object across multiple frames, this paper proposes an algorithm to estimate its 3D shape for each frame. To solve this problem accurately, the recent state-of-the-art algorithm reduces