Paper: Bounding Box Stability against Feature Dropout Reflects Detector Generalization across Environments (ICLR-2024)

Reviewer comment (Evaluation):
My main concern on the proposed method is how it can be applied in the real world object detection and what it benefits. The proposed method has requirements on the detector's performance (mAP>15%) on target data. However, in real-world scenarios, we cannot be certain if the detector performs well enough to meet this requirement. We don't know how reliable is the BoS score. Can BoS be used to improve the detection results?

Author response:
**A1.** Thanks. As mentioned in the fifth paragraph of Sec. 5.5, our method works very well when mAP is greater than 0.15. We believe this could cover sufficiently many scenarios. As for extreme cases, we recognized the potential failure of our system: we cannot even compute BoS score if there are too many missed detections. That said, existing methods also face the same problem. As we make an early attempt at accuracy prediction in object detection, we believe future endeavors can be made to address this problem. In the revised version, we also discuss another two limitations on the working scope of BoS score in the fifth paragraph of Sec. 5.5. Please refer to our reply to Q2 of Reviewer h1Z9.

**A2.** Great question. We have discussed this question in the third paragraph of Sec. 5.5 of our paper. Our answer is no. There are two reasons. (1) The BoS-mAP correlation might not hold when a model just starts training, whose performance on a test set is extremely poor. (2) BoS score is not differentiable, since its calculation involves the perturbed detection results which are constantly changing during training. However, we might improve detector performance from the insights of our paper. For example, we can apply a resistance module (like MC-DropBlock [1]) to improve detector generalization ability.

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[1] Deepshikha, Kumari, et al. "Monte Carlo dropblock for modelling uncertainty in object detection." arXiv preprint arXiv:2108.03614 (2021).
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Many thanks for the further question. Application wise, BoS can be used to assess detection performance, where no test ground truths are given. By focusing on this 'last-mile' problem in model deployment, our system has the potential to identify scenarios where the detector deviates from its optimal states (in-distribution performance), and how much the deviation is. This will allow users to have a quick understanding of their system performance in the wild, which informs their decision making.

Admittedly, as an early attempt, our system is still not perfect: low-end accuracy (mAP < 15%) and multi-class detectors are non-trivial to estimate, due to difficulty in estimating recall and finding class-shared datasets (Sec. 5.5). But, through the opportunity of sharing our findings, we believe joint efforts in the community will allow this problem to be solved in the end.

Reviewer comment (Experiments):
Another issue is that the evaluation of BoS is primarily focused on single-class scenarios, and it does not perform as well in multi-class settings. In real-world applications, we often encounter multiple bounding boxes detected across different classes. Consequently, the accuracy of matching between the original prediction and the prediction after feature perturbation may be compromised. It remains uncertain whether the performance of BoS will degrade when dealing with multi-class data.

Author response:
**A3.** As described in Sec. 5.2, BoS score can be easily extended to multi-class detectors theoretically because of its class-wise nature. To verify this, we should collect *a large scale* object detection datasets that have *diverse appearances* and the *same label space*. To answer this question, we implemented BoS on the 5 datasets we can find that contain pedestrians and vehicles simultaneously. The results in Table 3, where BoS is shown to be overall competitive compared with existing methods. In another aspect, we would like to emphasize there are very few real-world object detection datasets that satisfy the requirements of the *same label space*, so we primarily focused on single-class scenarios. We clarify this reason in Sec. 5.5 of our revised paper.

Many thanks for the further question. Application wise, BoS can be used to assess detection performance, where no test ground truths are given. By focusing on this 'last-mile' problem in model deployment, our system has the potential to identify scenarios where the detector deviates from its optimal states (in-distribution performance), and how much the deviation is. This will allow users to have a quick understanding of their system performance in the wild, which informs their decision making.

Admittedly, as an early attempt, our system is still not perfect: low-end accuracy (mAP < 15%) and multi-class detectors are non-trivial to estimate, due to difficulty in estimating recall and finding class-shared datasets (Sec. 5.5). But, through the opportunity of sharing our findings, we believe joint efforts in the community will allow this problem to be solved in the end.

Reviewer comment (Evaluation):
In Table 3, under the multi-class detection setting on Cityscapes and Self-driving datasets, the BoS performs much worse than other methods on car. While under single class setting, the RMSE of BoS of car on Cityscapes is 0.89, which is much better than others. There is no explaination on this point. Does the proposed method unstable in multi-class setting?

Author response:
**A5.** When confronted with multi-category mAP predictions, the features between different categories may interfere with each other. Thus, it is expected that the performance on single-category datasets is better than multi-category for the proposed approach. Existing methods also face the same problem. For example, In Table 3, under the multi-class detection setting on the Kitti dataset, the method of prediction score (0.99% -> 2.26%), entropy score (2.23% -> 4.71%), average confidence (1.69% -> 3.2%) and Fr´echet distance (2.98% -> 3.35%) all perform much worse than their performance on single-class pedestrian detection setting in Table 2. We appreciate the reviewer’s comment and have added an explanation on this point to the paper.

Reviewer comment (Evaluation):
In each table, does the number besides the dataset or class name reports the real mAP? For example, COCO (34.2) in Table 1. If so, in Table 2, on Kitti and CityPersons datasets, the mAP is 13.3 and 11.8 respectively, which are lower than the requirement (mAP > 15%).

Author response:
**A6.** Yes, the number beside the dataset or class name reports the real mAP. The condition of mAP  > 15% is not a strict mandatory condition for mAP estimation. But when mAP < 15%, the performance of BoS including other existing metrics might be worse than when mAP > 15%. To compare the mAP estimation performance for pedestrian detection in Table 2, we train a detector on a CrowdHuman training set (mAP = 33.5%) and report its ground truth mAP (%) on different unseen test sets in the header (besides the dataset). Since the domain shift, the detector performance on Kitti and CityPersons datasets drops to 13.3% and 11.8%, respectively.

Reviewer comment (Presentation):
I find it hard to understand the experiments. In Table 1, the authors say "we report its ground truth mAP (%) on different unseen test sets in the header, the estimated mAP (%) in the main table". However, the numbers for estimated mAP reported in the main table are very low. So what do the numbers in Table 1 represent for? Same for Table 2, Table 3 and Table 4. What are the best numbers in each column?

Author response:
**A1**. Thanks for the reviewer's careful review. We will clarify it in the revised paper. In Table 1, we report ground truth mAP (%) on different unseen test sets in the header and the RMSE (%) in the main table. The lower the numbers reported in the main table are,  the worse the mAP estimation performance is. The best number in each column is the lowest one. The same for Table 2, Table 3, and Table 4.

Reviewer comment (Evaluation):
Why there is a big gap between dropout rate=0.1 and 0.15 in Figure 3 (b)?

Author response:
**A2.**  Hyperparameters of BoS Score like dropout rate are selected during training (see Sec. 4.1 for training meta-set details). The results of Figure 3 (b) are actually based on empirical experiments. On further analysis, we find that the gap between the dropout rate=0.1 and 0.15 in Figure 3 (b) might be caused by the Roboflow dataset. If we remove sample sets generated by the Roboflow dataset in the training meta set (See M8 in the table below), the big gap disappears and the trend curve has smoothed out. In Table 1, we also find that the Roboflow dataset is the most difficult dataset for BoS to predict mAP. 

|              | M1      | M2       | M3        | M4             | M5         | M6         | M7               | M8           | M9          | M10         |
| ------------ | ------- | -------- | --------- | -------------- | ---------- | ---------- | ---------------- | ------------ | ----------- | ----------- |
| Dropout Rate | w/o BDD | w/o COCO | w/o Kitti | w/o Cityscapes | w/o DETRAC | w/o Exdark | w/o Self-driving | w/o Roboflow | w/o Udacity | w/o Traffic |
| 0.05         | 0.944   | 0.907    | 0.893     | 0.892          | 0.904      | 0.939      | 0.924            | 0.92         | 0.928       | 0.897       |
| 0.1          | 0.921   | 0.877    | 0.844     | 0.843          | 0.85       | 0.894      | 0.896            | 0.935        | 0.897       | 0.851       |
| 0.15         | 0.96    | 0.936    | 0.921     | 0.918          | 0.924      | 0.947      | 0.942            | 0.939        | 0.947       | 0.924       |
| 0.2          | 0.951   | 0.938    | 0.916     | 0.911          | 0.918      | 0.935      | 0.94             | 0.936        | 0.944       | 0.918       |
| 0.25         | 0.936   | 0.932    | 0.911     | 0.898          | 0.909      | 0.92       | 0.93             | 0.929        | 0.933       | 0.905       |
| 0.3          | 0.911   | 0.924    | 0.891     | 0.871          | 0.886      | 0.894      | 0.916            | 0.911        | 0.916       | 0.885       |

(The coefficients of determination $R^2$ between BoS and mAP are reported on different training meta-sets. M means "training meta-set" and the leave-one-out evaluation procedure is employed.)

Reviewer comment (Evaluation):
Why there is a peak at around 5 in Figure 4 (a)?

Author response:
**A3.** As described in Sec. 4.2, from the strong correlation of BoS and mAP, we train a linear regression model as the mAP estimator on the constructed training meta-set to fit this relationship. As shown in the table below, the performance of the mAP estimator (measured by RMSE) can suffer from some fluctuations due to higher prediction variance when the meta set size is small. The peak at around 5 also means the performance of the mAP estimator fluctuates when the meta set size is too small. Nevertheless, we observe that as the meta set size is increased, both the RMSE and the variance in RMSE are reduced which leads to improved system robustness.

| Meta Set Size             | 1     | 2     | 4     | 6     | 8     | 10    | 15    | 20    | 25    |
| :------------------------ | ----- | ----- | ----- | ----- | ----- | ----- | ----- | ----- | ----- |
| Avg. RMSE (%)             | 2.276 | 2.261 | 2.298 | 2.271 | 2.239 | 2.232 | 2.234 | 2.248 | 2.24  |
| Variance of Avg. RMSE (%) | 1.110 | 0.930 | 0.050 | 0.110 | 0.040 | 0.020 | 0.160 | 0.002 | 0.002 |

Reviewer comment (Evaluation):
The BoS is correlated with the accuracy on the dataset level but failed on the individual level. It does not make sense. This part needs more explanation and provides more evidence.

Author response:
**A1.** Thanks for the question. For individual bounding boxes, as shown in Fig. 8 of our supplementary material, we tried to correlate box stability score with ground truth IoU (GT IoU) on individual bounding boxes. Compared to confidence score (coefficients of determination $R^2>0.49$ ), BoS achieves a stronger correlation (coefficients of determination $R^2>0.72$) with GT IoU. The result of "coefficients of determination $R^2>0.72$" indicates *BoS could predict detector performance on individual bounding boxes to a certain extent.* However, it is weaker when compared to the correlation on the dataset level (coefficients of determination $R^2>0.93$). This is because, at the dataset level, the impact of the randomness of BoS score is averaged out over many bbox samples, leading to a more stable and statistically significant measure of box stability. In contrast, for the level of individual bounding boxes, the box stability is measured on a single bbox sample and is thus more susceptible to the inherent randomness.

Reviewer comment (Evaluation):
A limitation section is needed for a comprehensive analysis.

Author response:
**A2.** We agree with the reviewer that a limitation section is needed. In the original 'discussions' section, we have mentioned some limitations of BoS score about its performance on the individual level, indifferentiable character, and working scope. In the revised version, we renamed the 'discussions' section to the 'discussions and limitations' section for better understanding. Besides, we add two other limitations on the working scope of BoS score. (1) We might encounter images from unseen classes in the open world. To improve the mAP estimation performance under this scenario, a feasible solution is using out-of-distribution detection techniques to detect and reject such novel images. (2) The effectiveness of the BoS score in predicting the mAP for multi-class detectors requires further investigation. This requires *a large scale collection* of object detection datasets across *diverse appearances* and the *same label space*. However, real-world datasets meeting these criteria are scarce, which limits us from exploring more findings. Part of our future work is to collect such datasets to share with the community.