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.

中文翻译：

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来自运动的密集非刚性结构：一个流形的观点

Non-Rigid Structure-from-Motion (NRSfM) 问题旨在从跨多个帧的 2D 特征对应关系中恢复变形对象的 3D 几何形状。这个问题的经典方法假设少量特征点，并忽略形状变形的局部非线性，因此难以可靠地模拟非线性变形。此外，可用的密集 NRSfM 算法通常受到可扩展性、计算、噪声测量的阻碍，并且仅限于建模全局变形。在本文中，我们提出的算法可以克服以前方法的这些限制，同时可以以更高的精度恢复非刚性对象的可靠密集 3D 结构。假设变形形状由局部线性子空间的并集和，跨越多个帧的全局低秩空间使我们能够有效地对复杂的非刚性变形进行建模。为此，每个局部线性子空间都使用 Grassmannians 表示，并且跨多个帧的全局 3D 形状使用低秩表示表示。我们表明，我们的方法显着提高了准确性、可扩展性和对噪声的鲁棒性。此外，我们的表示自然允许同时重建和聚类框架，这通常被观察到更适合 NRSfM 问题。我们的方法目前在标准基准数据集上取得了领先的性能。跨多个帧的全局 3D 形状使用低秩表示表示。我们表明，我们的方法显着提高了准确性、可扩展性和对噪声的鲁棒性。此外，我们的表示自然允许同时重建和聚类框架，这通常被观察到更适合 NRSfM 问题。我们的方法目前在标准基准数据集上取得了领先的性能。跨多个帧的全局 3D 形状使用低秩表示表示。我们表明，我们的方法显着提高了准确性、可扩展性和对噪声的鲁棒性。此外，我们的表示自然允许同时重建和聚类框架，这通常被观察到更适合 NRSfM 问题。我们的方法目前在标准基准数据集上取得了领先的性能。