Current deep visual local feature detectors do not model the spatial
uncertainty of detected features, producing suboptimal results in downstream
applications. In this work, we propose two post-hoc covariance estimates that
can be plugged into any pretrained deep feature detector: a simple, isotropic
covariance estimate that uses the predicted score at a given pixel location,
and a full covariance estimate via the local structure tensor of the learned
score maps. Both methods are easy to implement and can be applied to any deep
feature detector. We show that these covariances are directly related to errors
in feature matching, leading to improvements in downstream tasks, including
triangulation, solving the perspective-n-point problem and motion-only bundle
adjustment. Code is available at this https URL

该研究提出了两种后置协方差估计方法，可以用于任何经过预训练的深度特征检测器，这些协方差可以直接与特征匹配误差相关联，从而改善下游任务，包括三角化，透视 - N 点问题和只运动捆绑调整。

DAC: 深度局部特征的检测器不可知空间协方差

DAC: Detector-Agnostic Spatial Covariances for Deep Local Features

Mean-field Variational Bayes (MFVB) is an approximate Bayesian posterior
inference technique that is increasingly popular due to its fast runtimes on
large-scale datasets. However, even when MFVB provides accurate posterior means
for certain parameters, it often mis-estimates variances and covariances.
Furthermore, prior robustness measures have remained undeveloped for MFVB. By
deriving a simple formula for the effect of infinitesimal model perturbations
on MFVB posterior means, we provide both improved covariance estimates and
local robustness measures for MFVB, thus greatly expanding the practical
usefulness of MFVB posterior approximations. The estimates for MFVB posterior
covariances rely on a result from the classical Bayesian robustness literature
relating derivatives of posterior expectations to posterior covariances and
include the Laplace approximation as a special case. Our key condition is that
the MFVB approximation provides good estimates of a select subset of posterior
means---an assumption that has been shown to hold in many practical settings.
In our experiments, we demonstrate that our methods are simple, general, and
fast, providing accurate posterior uncertainty estimates and robustness
measures with runtimes that can be an order of magnitude faster than MCMC.

该论文提出了一种改进的 MFVB（Mean-field Variational Bayes）方法，通过推导无穷小模型扰动对 MFVB 后验均值的影响，提供了更精确的后验协方差估计和本地健壮性测量，扩展了 MFVB 的实用性，特别是适用于大规模数据集。实验表明，该方法简单、通用且速度快，可以提供准确的后验不确定性估计和健壮性测量，其运行时间比 MCMC 快一个数量级。