Overcoming the Limitations of Localization Uncertainty: Efficient &
  Exact Non-Linear Post-Processing and Calibration
Moussa Kassem Sbeyti Michelle Karg Christian Wirth Azarm Nowzad Sahin Albayrak
Robustly and accurately localizing objects in real-world environments can be
challenging due to noisy data, hardware limitations, and the inherent
randomness of physical systems. To account for these factors, existing works
estimate the aleatoric uncertainty of object detectors by modeling their
localization output as a Gaussian distribution
$\mathcal{N}(\mu,\,\sigma^{2})\,$, and training with loss attenuation. We
identify three aspects that are unaddressed in the state of the art, but
warrant further exploration: (1) the efficient and mathematically sound
propagation of $\mathcal{N}(\mu,\,\sigma^{2})\,$ through non-linear
post-processing, (2) the calibration of the predicted uncertainty, and (3) its
interpretation. We overcome these limitations by: (1) implementing loss
attenuation in EfficientDet, and proposing two deterministic methods for the
exact and fast propagation of the output distribution, (2) demonstrating on the
KITTI and BDD100K datasets that the predicted uncertainty is miscalibrated, and
adapting two calibration methods to the localization task, and (3)
investigating the correlation between aleatoric uncertainty and task-relevant
error sources. Our contributions are: (1) up to five times faster propagation
while increasing localization performance by up to 1\%, (2) up to fifteen times
smaller expected calibration error, and (3) the predicted uncertainty is found
to correlate with occlusion, object distance, detection accuracy, and image
quality.