Formally Compensating Performance Limitations for Imprecise 2D Object Detection

In this paper, we consider the imperfection within machine learning-based 2D object detection and its impact on safety. We address a special sub-type of performance limitations related to the misalignment of bounding-box predictions to the ground truth: the prediction bounding box cannot be perfectly aligned with the ground truth. We formally prove the minimum required bounding box enlargement factor to cover the ground truth. We then demonstrate that this factor can be mathematically adjusted to a smaller value, provided that the motion planner uses a fixed-length buffer in making its decisions. Finally, observing the difference between an empirically measured enlargement factor and our formally derived worst-case enlargement factor offers an interesting connection between quantitative evidence (demonstrated by statistics) and qualitative evidence (demonstrated by worst-case analysis) when arguing safety-relevant properties of machine learning functions.