Overcoming the Limitations of Localization Uncertainty: Efficient & Exact Non-Linear Post-Processing and Calibration

Abstract: 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.