Abstract
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.
T. Schuster and E. Seferis—Equal contribution.
This work is funded by the Bavarian Ministry for Economic Affairs, Regional Development and Energy as part of a project to support the thematic development of the Fraunhofer Institute for Cognitive Systems.
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Notes
- 1.
Precisely, when the DNN has not-so-good performance where within the collected dataset the observed intersection-over-union \(\alpha \) is small, one needs to enlarge the bounding box more conservatively to ensure box coverage.
- 2.
Due to space limits, we refer readers to the extended version [16] for further details.
- 3.
Based on the analysis, for low IoU values, the required expansion factors can be very large. For example, for \(\alpha = 0.4\), Eq. 9 would give an enlargement factor of \(k_{math} = 4\), thus a vehicle with a bounding box of length \(w = 5\,\mathrm {m}\) would be enlarged to \(w' = 20\,\mathrm {m}\), which is forbiddingly large in practice. Hence, for meaningful practical applications, the implication of our result is the need of high IoUs within the collected dataset.
- 4.
- 5.
- 6.
If we assume that the occurrence of bounding box non-alignment is a random variable, and the measured mean and variance match the real ones, then from Chebyshev’s inequality we know that the probability of exceeding \(6\sigma _{W,data}\) is below 2.78%.
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Schuster, T., Seferis, E., Burton, S., Cheng, CH. (2022). Formally Compensating Performance Limitations for Imprecise 2D Object Detection. In: Trapp, M., Saglietti, F., Spisländer, M., Bitsch, F. (eds) Computer Safety, Reliability, and Security. SAFECOMP 2022. Lecture Notes in Computer Science, vol 13414. Springer, Cham. https://doi.org/10.1007/978-3-031-14835-4_18
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