We consider the problem of learning uncertainty regions for parameter
estimation problems. The regions are ellipsoids that minimize the average
volumes subject to a prescribed coverage probability. As expected, under the
assumption of jointly Gaussian data, we prove that the optimal ellipsoid is
centered around the conditional mean and shaped as the conditional covariance
matrix. In more practical cases, we propose a differentiable optimization
approach for approximately computing the optimal ellipsoids using a neural
network with proper calibration. Compared to existing methods, our network
requires less storage and less computations in inference time, leading to
accurate yet smaller ellipsoids. We demonstrate these advantages on four
real-world localization datasets.

学习参数估计问题的不确定性区域，通过最小化平均体积以满足给定覆盖概率，我们证明在联合高斯数据假设下，最优椭圆以条件均值为中心，条件协方差矩阵为形状；在实践中，我们提出了一种可微分优化方法，通过使用适当标定的神经网络近似计算最优椭圆，与现有方法相比，我们的网络在推断时间内需要更少的存储和计算，从而导致准确但更小的椭圆。我们在四个真实的定位数据集上证明了这些优势。

学习最小体积不确定性椭球

Learning minimal volume uncertainty ellipsoids

We address the visual relocalization problem of predicting the location and
camera orientation or pose (6DOF) of the given input scene. We propose a method
based on how humans determine their location using the visible landmarks. We
define anchor points uniformly across the route map and propose a deep learning
architecture which predicts the most relevant anchor point present in the scene
as well as the relative offsets with respect to it. The relevant anchor point
need not be the nearest anchor point to the ground truth location, as it might
not be visible due to the pose. Hence we propose a multi task loss function,
which discovers the relevant anchor point, without needing the ground truth for
it. We validate the effectiveness of our approach by experimenting on
CambridgeLandmarks (large scale outdoor scenes) as well as 7 Scenes (indoor
scenes) using variousCNN feature extractors. Our method improves the median
error in indoor as well as outdoor localization datasets compared to the
previous best deep learning model known as PoseNet (with geometric
re-projection loss) using the same feature extractor. We improve the median
error in localization in the specific case of Street scene, by over 8m.

本文提出了一种基于深度学习的方法，通过视觉定位，使用锚点来预测场景的位置和摄像机方向或姿态（6 自由度），该方法使用统一定义的锚点并提出了一个深度学习架构，该架构预测场景中存在的最相关的锚点以及相对偏移量，并为该任务提出了一个多任务损失函数，无需基于真实位置信息评定，并在 CambridgeLandmarks 和 7 Scenes 上进行了实验以验证效果。与使用相同的特征提取器的先前最佳深度学习模型 Posenet（具有几何重投影损失）相比，我们的方法提升了室内和室外定位数据集中的中位误差，并在特定情况下，如街景中，将中位误差降低了 8m 以上。