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Register a new userJumping Manifolds: Geometry Aware Dense Non-Rigid Structure from Motion
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Suryansh Kumar
Publication date
2019
fields
Informatics Engineering
and research's language is
English
Authors
Suryansh Kumar
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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 this task to set of local linear subspace reconstruction and clustering problem using Grassmann manifold representation cite{kumar2018scalable}. Unfortunately, their method missed on some of the critical issues associated with the modeling of surface deformations, for e.g., the dependence of a local surface deformation on its neighbors. Furthermore, their representation to group high dimensional data points inevitably introduce the drawbacks of categorizing samples on the high-dimensional Grassmann manifold cite{huang2015projection, harandi2014manifold}. Hence, to deal with such limitations with cite{kumar2018scalable}, we propose an algorithm that jointly exploits the benefit of high-dimensional Grassmann manifold to perform reconstruction, and its equivalent lower-dimensional representation to infer suitable clusters. To accomplish this, we project each Grassmannians onto a lower-dimensional Grassmann manifold which preserves and respects the deformation of the structure w.r.t its neighbors. These Grassmann points in the lower-dimension then act as a representative for the selection of high-dimensional Grassmann samples to perform each local reconstruction. In practice, our algorithm provides a geometrically efficient way to solve dense NRSfM by switching between manifolds based on its benefit and usage. Experimental results show that the proposed algorithm is very effective in handling noise with reconstruction accuracy as good as or better than the competing methods.
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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 local non-linearities of the shape deformation, and therefore, struggles to reliably model non-linear deformations. Furthermore, available dense NRSfM algorithms are often hurdled by scalability, computations, noisy measurements and, restricted to model just global deformation. In this paper, we propose algorithms that can overcome these limitations with the previous methods and, at the same time, can recover a reliable dense 3D structure of a non-rigid object with higher accuracy. Assuming that a deforming shape is composed of a union of local linear subspace and, span a global low-rank space over multiple frames enables us to efficiently model complex non-rigid deformations. To that end, each local linear subspace is represented using Grassmannians and, the global 3D shape across multiple frames is represented using a low-rank representation. We show that our approach significantly improves accuracy, scalability, and robustness against noise. Also, our representation naturally allows for simultaneous reconstruction and clustering framework which in general is observed to be more suitable for NRSfM problems. Our method currently achieves leading performance on the standard benchmark datasets.
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 within vision. In this paper we propose a novel deep neural network to recover camera poses and 3D points solely from an ensemble of 2D image coordinates. The proposed neural network is mathematically interpretable as a multi-layer block sparse dictionary learning problem, and can handle problems of unprecedented scale and shape complexity. Extensive experiments demonstrate the impressive performance of our approach where we exhibit superior precision and robustness against all available state-of-the-art works in the order of magnitude. We further propose a quality measure (based on the network weights) which circumvents the need for 3D ground-truth to ascertain the confidence we have in the reconstruction.
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 within vision. In this paper we propose a novel deep neural network to recover camera poses and 3D points solely from an ensemble of 2D image coordinates. The proposed neural network is mathematically interpretable as a multi-layer block sparse dictionary learning problem, and can handle problems of unprecedented scale and shape complexity. Extensive experiments demonstrate the impressive performance of our approach where we exhibit superior precision and robustness against all available state-of-the-art works. The considerable model capacity of our approach affords remarkable generalization to unseen data. We propose a quality measure (based on the network weights) which circumvents the need for 3D ground-truth to ascertain the confidence we have in the reconstruction. Once the networks weights are estimated (for a non-rigid object) we show how our approach can effectively recover 3D shape from a single image -- outperforming comparable methods that rely on direct 3D supervision.
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) the number of images, and (ii) the type of shape variability they can handle. These difficulties stem from the inherent conflict between the condition of the system and the degrees of freedom needing to be modeled -- which has hampered its practical utility for many applications within vision. In this paper we propose a novel hierarchical sparse coding model for NRSFM which can overcome (i) and (ii) to such an extent, that NRSFM can be applied to problems in vision previously thought too ill posed. Our approach is realized in practice as the training of an unsupervised deep neural network (DNN) auto-encoder with a unique architecture that is able to disentangle pose from 3D structure. Using modern deep learning computational platforms allows us to solve NRSfM problems at an unprecedented scale and shape complexity. Our approach has no 3D supervision, relying solely on 2D point correspondences. Further, our approach is also able to handle missing/occluded 2D points without the need for matrix completion. Extensive experiments demonstrate the impressive performance of our approach where we exhibit superior precision and robustness against all available state-of-the-art works in some instances by an order of magnitude. We further propose a new quality measure (based on the network weights) which circumvents the need for 3D ground-truth to ascertain the confidence we have in the reconstructability. We believe our work to be a significant advance over state-of-the-art in NRSFM.
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.
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