Reliable spatial uncertainty evaluation of object detection models is of special interest and has been subject of recent work. In this work, we review the existing definitions for uncertainty calibration of probabilistic regression tasks. We inspect the calibration properties of common detection networks and extend state-of-the-art recalibration methods. Our methods use a Gaussian process (GP) recalibration scheme that yields parametric distributions as output (e.g. Gaussian or Cauchy). The usage of GP recalibration allows for a local (conditional) uncertainty calibration by capturing dependencies between neighboring samples. The use of parametric distributions such as as Gaussian allows for a simplified adaption of calibration in subsequent processes, e.g., for Kalman filtering in the scope of object tracking. In addition, we use the GP recalibration scheme to perform covariance estimation which allows for post-hoc introduction of local correlations between the output quantities, e.g., position, width, or height in object detection. To measure the joint calibration of multivariate and possibly correlated data, we introduce the quantile calibration error which is based on the Mahalanobis distance between the predicted distribution and the ground truth to determine whether the ground truth is within a predicted quantile. Our experiments show that common detection models overestimate the spatial uncertainty in comparison to the observed error. We show that the simple Isotonic Regression recalibration method is sufficient to achieve a good uncertainty quantification in terms of calibrated quantiles. In contrast, if normal distributions are required for subsequent processes, our GP-Normal recalibration method yields the best results. Finally, we show that our covariance estimation method is able to achieve best calibration results for joint multivariate calibration.

本文研究目标检测模型的可靠空间不确定性评估，并介绍了常见检测网络的校准属性，并扩展了最新的校准方法。我们使用高斯过程（GP）重新校准方案，通过捕捉相邻样本之间的依赖关系，获得参数分布输出。此外，我们使用GP重新校准方案进行协方差估计，实现联合多元校准，并引入基于马氏距离的量化校准误差进行测量。在实验中，我们发现普通检测模型在空间不确定性方面存在高估问题，而简单的Isotonic回归校准方法足以实现校准分位数。

回归和目标检测的参数化和多元不确定性校准