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.

本文提出了一种基于深度神经网络的非刚性运动结构恢复方法，该方法在订单级别上表现出比所有现有技术更出色的精度和鲁棒性，能够处理规模和形状复杂度前所未有的问题，并提出了一种基于网络权重的质量度量来评估重建可信度。

深度非刚性结构运动

Deep Non-Rigid Structure from Motion

We study in this paper the consequences of using the Mean Absolute Percentage
Error (MAPE) as a measure of quality for regression models. We prove the
existence of an optimal MAPE model and we show the universal consistency of
Empirical Risk Minimization based on the MAPE. We also show that finding the
best model under the MAPE is equivalent to doing weighted Mean Absolute Error
(MAE) regression, and we apply this weighting strategy to kernel regression.
The behavior of the MAPE kernel regression is illustrated on simulated data.

本文研究了使用平均绝对百分比误差（MAPE）作为回归模型质量度量的后果。我们证明了最佳 MAPE 模型的存在，并展示了基于 MAPE 的经验风险最小化的普适一致性。我们还表明，在 MAPE 下找到最佳模型等价于进行加权平均绝对误差（MAE）回归，并将此加权策略应用于核回归。作者还展示了 MAPE 核回归在模拟数据上的行为。