# FindMeIfYouCan: Bringing Open Set metrics to near, far and farther Out-of-Distribution Object detection

Daniel Montoya, Aymen Bouguerra, Alexandra Gomez-Villa, Fabio Arnez

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Daniel Montoya, Aymen Bouguerra, Alexandra Gomez-Villa, Fabio Arnez. FindMeIfYouCan: Bringing Open Set metrics to near, far and farther Out-of-Distribution Object detection. 2025. hal-05118736

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https://hal.science/hal-05118736v1

Preprint submitted on 18 Jun 2025

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<figure><img src="image_1.png" /></figure>
FindMeIfYouCan:
Bringing Open Set metrics to *near, far and farther*
Out-of-Distribution Object detection

**Daniel Montoya**

Université Paris-Saclay, CEA, List
F-91120, Palaiseau, France
daniel-alfonso.montoyavasquez@cea.fr

**Aymen Bouguerra**

Université Paris-Saclay, CEA, List
F-91120, Palaiseau, France
aymen.bouguerra@cea.fr

**Alexandra Gomez-Villa**

Computer Vision Center
Barcelona, Spain
agomezvi@cvc.uab.es

**Fabio Arnez**

Université Paris-Saclay, CEA, List
F-91120, Palaiseau, France
fabio.arnez@cea.fr

**Abstract**

State-of-the-art Object Detection (OD) methods predominantly operate under a closed-world assumption, where test-time categories match those encountered during training. However, detecting and localizing unknown objects is crucial for safety-critical applications in domains such as autonomous driving and medical imaging. Recently, Out-Of-Distribution (OOD) detection has emerged as a vital research direction for OD, focusing on identifying incorrect predictions typically associated with unknown objects. This paper shows that the current evaluation protocol for OOD-OD violates the assumption of non-overlapping objects with respect to the In-Distribution (ID) datasets, and obscures crucial situations such as ignoring unknown objects, potentially leading to overconfidence in deployment scenarios where truly novel objects might be encountered. To address these limitations, we manually curate, and enrich the existing benchmark by exploiting semantic similarity to create new evaluation splits categorized as *near, far, and farther* from ID distributions. Additionally, we incorporate established metrics from the Open Set community, providing deeper insights into how effectively methods detect unknowns, when they ignore them, and when they mistakenly classify OOD objects as ID. Our comprehensive evaluation demonstrates that semantically and visually close OOD objects are easier to localize than far ones, but are also more easily confounded with ID objects. *Far and farther objects are harder to localize but less prone to be taken for an ID object.*

# 1 Introduction

In the last decade, the rise of deep learning has introduced prominent breakthroughs and achievements in object detection (OD) Zou et al. [2023], where models are usually trained under a closed-world assumption: test-time categories are the same as the training ones. However, during deployment in the real world, OD models will encounter Out-of-Distribution (OOD) objects Nitsch et al. [2021], i.e., object categories different than those observed during training. While facing OOD objects, one of two safety-critical (high-risk) situations can arise: either the unknown objects are incorrectly classified as one of the In-Distribution (ID) classes, or the OOD objects will be ignored Dhamija et al. [2020].
<figure><img src="image_2.png" /><figcaption>Figure 1: Predictions of Faster-RCNN trained on two ID datasets on samples from each ID and the OOD datasets in blue rectangles. The first row contains predictions of the Faster-RCNN trained on Pascal-VOC. The second row contains the predictions by the model trained on BDD100k. Ground Truth (GT) labels are shown in clear green. The base model predictions are the inputs to OOD scoring functions; without predictions, objects in images will be ignored by OOD scoring functions too. The proposed FMIYC benchmark removes undesirable semantic overlaps and separates semantically *near*, *far*, and *farther* objects with respect to the ID dataset. FMIYC uses ground truth bounding boxes to leverage OSOD metrics that measure when unknown objects are ignored, when they are detected, and when they are confounded with ID objects.</figcaption></figure>

In response to these safety challenges, researchers have developed two primary approaches: Out-of-Distribution Object Detection (OOD-OD) Du et al. [2022b] and Open-Set Object Detection (OSOD) Dhamija et al. [2020]. OOD-OD focuses on identifying predictions that do not belong to the ID categories, while OSOD actively attempts to detect the unknown objects themselves. Though both approaches address the fundamental problem of encountering objects from a different semantic space than the training distribution, they employ significantly different methodologies, evaluation metrics, and benchmarks. This methodological divergence has led to isolated research communities and evaluation frameworks that fail to capture the complete picture of model performance when encountering unknown objects.

Currently, the evaluation of OOD-OD relies on a single benchmark, to the best of our knowledge: the VOS-benchmark Du et al. [2022b]. The fundamental assumption of this benchmark is that none of the images in the OOD datasets include any of the ID classes, implying non-overlapping semantic spaces. Consequently, any prediction made on the OOD datasets by a model trained on the ID classes is inherently incorrect, regardless of the accuracy of object localization. The benchmark employs the area under the ROC curve (AUROC) and the false positive rate at 95% true positive rate (FPR95) as metrics. However, these metrics can be misleading, as they might suggest that a higher AUROC or lower FPR95 indicates better localization of unknown objects, which is not necessarily true. The current benchmark metrics evaluate how well OOD-OD methods identify incorrect predictions, which may potentially correspond to unknown objects. Yet, they fall short of measuring the actual identification of unknown objects. This raises a critical question: *Are AUROC and FPR95 sufficient metrics for assessing the deployment of OOD-OD methods in real-world scenarios?*

In this study, we identify and address fundamental flaws in the existing OOD-OD benchmark and its metrics, while bridging the gap between OOD-OD and OSOD research communities. We demonstrate that the current evaluation violates the fundamental assumption of non-overlap, as the OOD datasets contain ID classes. The benchmark may give the misleading impression of evaluating the identification of unknown objects, fails to penalize ignored unknown objects, and lacks proper assessment of object localization precision—issues that cannot be overlooked for safety-critical applications. To address these challenges, we propose *FindMeIfYouCan* (FMIYC), a comprehensively curated benchmark that: (1) eliminates undesired semantic overlaps between ID and OOD datasets, (2) introduces
semantically stratified *near*, *far*, and *farther* OOD splits to evaluate detection robustness across varying levels of semantic similarity, and (3) properly evaluates the actual identification of unknown objects by integrating complementary metrics from the OSOD community, thus providing a robust OOD-OD evaluation framework. By combining strengths from both approaches, our benchmark enables fair comparison across multiple architectures (Faster R-CNN, YOLOv8, RT-DETR) and reveals insights previously obscured in the current standard benchmark. Additionally, we adapt OOD detection methods from image classification as strong baselines for both OOD-OD and OSOD tasks, establishing a solid foundation for future research that can benefit from both perspectives.

**Contributions.** In summary, the main contributions of this work are:

* We identify and address fundamental flaws in the existing OOD-OD evaluation methodology, demonstrating how the current approach fails to capture a complete picture of the model's performance when encountering unknown objects.

* We propose *FindMeIfYouCan*, a benchmark that removes the existing semantic overlaps and introduces stratified *near*, *far*, and *farther* OOD splits for OOD-OD evaluation across varying levels of semantic similarity.

* We reveal the limitations of legacy AUROC and FPR95 metrics and integrate complementary metrics from the OSOD community for a comprehensive OOD-OD evaluation that captures disregarded objects.

* We assess various methods and architectures for OOD-OD. In particular, we enhance OOD-OD detection techniques by incorporating post-hoc methods from image classification. Additionally, we expand the range of evaluated architectures, including the YOLOv8 and RT-DETR architectures alongside the commonly utilized Faster R-CNN, thereby establishing robust baselines for OOD-OD.

# 2 Background & Related Work

## 2.1 Object Detection

An object detector is a model $\mathcal{M}$ that takes as input an image $x$ and generates bounding boxes $b$ and classification scores $c$ for detected objects from a predefined set of categories $\mathcal{C}$ Girshick et al. [2014]. Such models are trained to localize the objects that belong to the ID classes $\mathcal{C}$ and, simultaneously, to ignore the rest of the objects and the background Dhamija et al. [2020]. Consequently, the object detector is usually set to function according to a given confidence threshold $t^*$ that corresponds to the one that maximizes the mAP with respect to the ID test dataset. All objects below such threshold $t^*$ are discarded. The model output is $\mathcal{M}(x, t^*) = \{b, c\}$. In the remainder of the paper, the terms “unknown” and “OOD” objects are used interchangeably, and refer to classes that do not belong to $\mathcal{C}$. Two problems can arise during real-world deployment when the model encounters an unknown object: it can be incorrectly detected as one of the ID classes with confidence above the confidence threshold $t^*$, or the unknown object may be ignored. Therefore, two approaches exist in the literature to address these problems: OOD-OD and OSOD.

## 2.2 OOD-OD & OSOD Benchmarks

Similar to OOD detection for image classification, OOD-OD is formulated as a binary classification task, that for each detected instance $b$ leverages a confidence scoring function $\mathcal{G}$ with its own threshold $\tau$ to calculate a per-object score $\mathcal{G}(b)$ that can distinguish between ID and OOD detections. Du et al. [2022b] introduced a benchmark that has been adopted by subsequent works Du et al. [2022a], Wilson et al. [2023], Wu and Deng [2023]. This benchmark utilizes BDD100k Yu et al. [2020] and Pascal-VOC Everingham et al. [2010] as ID datasets, along with subsets of COCO Lin et al. [2014] and Open Images Kuznetsova et al. [2020] as OOD datasets. Trained models on the ID datasets are then set to perform inference on the OOD datasets.

The proposed evaluation method is deemed consistent if it adheres to the critical condition that no ID class appears in any image within the OOD datasets. Consequently, any detection within these OOD datasets is automatically classified as “incorrect”, irrespective of whether the prediction corresponds to a ground truth OOD object. Conversely, all predictions on the test ID dataset are considered
"correct". By employing this approach, the binary classification metrics AUROC and the FPR95 are utilized to assess the efficacy of the OOD detection method. Specifically, these metrics evaluate how effectively $G(b)$ assigns different scores to predictions coming from the ID and the OOD datasets Du et al. [2022b].

On the other hand, OSOD directly adds an *unknown* class to the object detector, along with the ID classes for the training process. It was first formalized by Dhamija et al. [2020], and their goal was to tackle the fact that “unknown objects end up being incorrectly detected as known objects, often with very high confidence”. Moreover, the authors propose a benchmark and associated metrics, where the goal is to accurately detect known (ID) and unknown objects simultaneously, as measured by the metrics described in Section 4.2.

The benchmarking setup of OSOD is quite different from that of OOD-OD since, in this setting, the goal is to actively and correctly localize OOD and ID objects at the same time. Also, for OSOD, there is not one commonly accepted benchmark, but many benchmarks have appeared Ammar et al. [2024], Miller et al. [2018], Han et al. [2022], Dhamija et al. [2020]. The common rule is that there is one training dataset with a given set of labeled categories of objects (usually VOC, with 20 categories Everingham et al. [2010]), and there is one or several subsets of an evaluation dataset that contains the training categories and other labeled classes, semantically different from the ID ones (usually from COCO Lin et al. [2014]).

## 3 Pitfalls of the Current OOD-OD Benchmark

**Metrics.** The current benchmark uses the AUROC and the FPR95 metrics inherited from the image classification task. A misconception that may be conveyed by these metrics is that a higher AUROC or lower FPR95 means better localization of OOD objects, which is not necessarily the case. These metrics measure how well OOD-OD methods identify incorrect predictions, which may or may not correspond to ground-truth unknown objects. Therefore, these metrics do not evaluate the correct localization of OOD objects, and cannot measure when OOD objects are ignored. Figure 2 depicts an example of the current metrics issues described above. For more details on the metrics, see Appendix D.

<figure><img src="image_3.png" /><figcaption>Figure 2: AUROC and FPR95 do not assess whether the relevant unknown objects, such as camels, are overlooked. They only consider incorrect predictions, such as misidentifying a car.</figcaption></figure>

**Semantic overlaps.** The presence of semantic overlaps questions the validity of previously reported results since the key assumption of the OOD-OD benchmark is that no ID objects are present in any of the images of the OOD datasets. If the assumption is respected, all predictions made in the OOD datasets by the models trained on the ID classes can be safely considered incorrect. In contradiction with the core assumption of the benchmark, as illustrated in Figure 1, labeled and unlabeled people and parts of people are present in the OOD datasets. Another common overlap occurs with respect to the VOC ID class “dining table”. Several images in the OOD datasets contain pictures of dining tables, but the GT labels are at the level of spoons, knives, glasses, and food itself. For a complete list of overlapping categories in each OOD dataset, and additional examples of overlaps, see Appendix B. The OOD images containing ID classes need to be removed for consistency in the benchmark.

**Ignored objects.** As illustrated in Figure 1, not every image in each OOD dataset gets at least one prediction. The percentage of images with no predictions in the current benchmark can be seen in Table 1, which shows that up to 59% of images in one of the OOD splits have not a single prediction above the threshold $t^*$. This means that the metrics of AUROC and FPR95 reported in previous works Du et al. [2022b], Wilson et al. [2023], Du et al. [2022a], Wu and Deng [2023] are built using only ~40% of the images in that OOD split. By construction, the metrics of the benchmark cannot be
penalized by this, which obscures the omission of a non-negligible percentage of images and objects. To remedy this, we propose using the OSOD metrics presented in Section 4.2.

**Semantically similar categories.** We examined the semantic and perceptual similarity between ID and OOD datasets following Abbas et al. [2023], Mayilvahanan et al. [2023], who postulated that nearest neighbors in the image embedding space of CLIP Radford et al. [2021] share semantic and stylistic characteristics. We calculated the cosine similarity in the CLIP embedding space between ID and OOD datasets of the current benchmark. As seen in Figure 3a, BDD is farther away with respect to its OOD datasets than VOC. We propose to exploit the different degrees of similarity to create new splits, as detailed in Section 4.

<table><caption>Table 1: Percentage of images with no predictions in the current OOD-OD benchmark. OI=OpenImages</caption><thead><tr><th rowspan="2">Model</th><th>ID: VOC</th><th>ID: BDD</th></tr><tr><th>OI/COCO</th><th>OI/COCO</th></tr></thead><tbody><tr><td>F-RCNN</td><td>27.43/35.81</td><td>59.23/45.27</td></tr><tr><td>F-RCNN VOS</td><td>24.08/32.58</td><td>53.72/40.43</td></tr></tbody></table>

**Lack of use of ground truth labels.** The actual localization of ground truth (GT) unknown objects is crucial information that the current benchmark fails to utilize. A comprehensive evaluation of a system's behavior regarding unknown objects is incomplete if it only considers the detection of incorrect predictions. Identifying wrong predictions is indeed crucial, yet overlooking unknown objects can be as hazardous as misclassifying them, as presented in Figure 2. The OSOD community has developed a set of metrics that can evaluate the ability of methods to localize unknowns and quantify instances where unknowns are ignored or confused with in-distribution (ID) objects. In addition to current metrics, we propose leveraging GT labels to enable a more detailed evaluation by employing the OSOD metrics described in Section 4.2.

# 4 The FMIYC Benchmark

## 4.1 Creating the Evaluation Splits

The overlap removal process for the VOS benchmark datasets was conducted in two stages. Initially, an automatic stage was implemented to eliminate labeled instances of overlapping categories. Subsequently, a manual verification stage was carried out, during which the remaining images were individually inspected to ensure that no unlabeled instances of ID categories remained.

Afterward, the split into *near* and *far* subsets was performed with respect to Pascal-VOC as the ID dataset. Again, splitting into *near* and *far* subsets began with an automatic phase where images containing the predefined *near* categories were put into the *near* dataset, and the remaining images would go to the *far* dataset. Then, a manual check was performed where the remaining images in the *far* dataset were inspected to ensure no *near* category was present, and vice versa. This procedure was made for both COCO and OpenImages as OOD datasets. As a result, there are four OOD datasets with respect to Pascal-VOC: COCO-*near*, COCO-*far*, OpenImages-*near*, and OpenImages-*far*. For instance, when Pascal-VOC is ID, the following categories are present that have at least one corresponding OOD category that is semantically and visually close: television, dog, cat, horse, cow, and couch. Some of the similar OOD categories are: laptop, fox, bear, jaguar, leopard, cheetah, zebra, and bed. Appendix B presents a complete list and discussion of the *near* OOD categories.

To enhance the newly created *near* and *far* splits, additional images from each of the original datasets were incorporated into each split. The process involved pre-selecting a set of candidates for each new dataset by excluding categories that overlapped with the ID ones and utilizing the existing categories within each dataset. Each candidate image was then manually reviewed to ensure there was no overlap and to confirm its correct assignment to either the *far* or *near* subsets. The entire process was carried out by manually recording image IDs in configuration files for each subset, ensuring that the construction is fully reproducible from beginning to end. The code that creates the new splits is available in the repository: *FMIYC OOD-OD Benchmark Repository*. The dataset is hosted in *huggingface - FindMeIfYouCan*.

Following the observations in Figure 3a and the manual inspection of images, for BDD100k as ID dataset, only the removal of overlapping images with labeled or unlabeled ID classes was done without the creation of separate *far* or *near* subsets, nor the addition of new images. This is because, as can be seen in Figure 3a, BDD100k is already farther away from its respective OOD datasets than Pascal-VOC. The visualization of images that illustrate the semantic and vi-
<figure><img src="image_4.png" /><figcaption>(a) Current benchmark: VOC is semantically and visually more similar to OOD datasets than BDD.</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>(b) The FMIYC benchmark distinction of *near*, *far* and *farther* splits can be appreciated</figcaption></figure>

<caption>Figure 3: Perceptual and semantic (cosine) similarity Mayilvahanan et al. [2023] between ID and OOD datasets using CLIP image encoder embeddings.</caption>

sual similarity among all ID and OOD datasets can be found in the Appendix B. This situation allows for the distinction of three degrees of similarity between ID and OOD datasets: we have *near* and *far* for the OOD datasets with respect to Pascal-VOC, and we argue (after considering Figure 3b and the results) that the OOD datasets with respect to BDD can be called *farther* OOD. This distinction will prove insightful after considering the results in Section 5. The number of images in each of the subsets of the new benchmark can be found in Table 2. In addition, Figure 3b shows CLIP vision embeddings similarity for each new split.

<table><caption>Table 2: Number of images in each subset of the newly proposed benchmark</caption><thead><tr><th>ID</th><th>OOD</th><th>No. Images</th></tr></thead><tbody><tr><td rowspan="4">VOC</td><td>COCO-Near</td><td>1174</td></tr><tr><td>COCO-Far</td><td>938</td></tr><tr><td>OpenImages-Near</td><td>908</td></tr><tr><td>OpenImages-Far</td><td>1179</td></tr><tr><td rowspan="2">BDD</td><td>COCO-Farther</td><td>1873</td></tr><tr><td>OpenImages-Farther</td><td>1695</td></tr></tbody></table>

## 4.2 Proposed Metrics

**OSOD Metrics.** The OSOD community uses as metrics the absolute open-set error (AOSE), the wilderness impact (WI), the unknown precision ($P_U$), unknown recall ($R_U$), and the average precision of the unknowns $AP_U$ Gupta et al. [2022], Miller et al. [2018], Maaz et al. [2022]. The AOSE reports the absolute number of unknown objects incorrectly classified as one of the ID classes. WI evaluates the proportion of AOSE among all the known detections. Unknown recall $R_U$ is the ratio of unknown detected objects by the number of unknown ones, and the unknown precision $P_U$ is the ratio of true positive detections divided by all the detections Ammar et al. [2024]. The OSOD metrics are fine-grained in the sense that they assess how well the methods can localize and correctly classify known and unknown objects in images where both types of objects appear.

In addition to the widely used metrics of AUROC and FPR95, we propose using the following OSOD metrics: $AP_U$, $P_U$, and $R_U$. We omit the WI since our benchmark does not allow both ID and OOD classes in the OOD datasets. In addition, we propose a new metric that we call *normalized open set error* (nOSE), which is the AOSE divided by the total number of (labeled) unknowns. We propose this metric since the absolute number of unknowns depends on the dataset, and therefore, the AOSE is not comparable across datasets, whereas the nOSE is. The nOSE assesses the proportion of unknown objects detected as one of the ID classes. A summary of the overall metrics used in the FMIYC benchmark can be found in Appendix D.

# 5 Experiments and Results

## 5.1 Object Detection Architectures

We used the Faster-RCNN Girshick et al. [2014] in its *vanilla* and VOS (regularized) versions, YOLOv8 Jocher et al. [2023], Sohan et al. [2024], and RT-DETR Zhao et al. [2024]. For YOLOv8 and RT-DETR, the models were trained on the same ID datasets (Pascal-VOC and BDD100k). The training details can be found in Appendix G. For the Faster-RCNN models, we used the pre-trained checkpoints provided by Du et al. [2022b]. Table 3 shows the architectures mAP for each ID dataset.
## 5.2 Out-of-Distribution Object Detection Methods

We implemented prominent methods from OOD detection literature on image classification. Specifically, we selected *post-hoc* methods, as they do not require retraining of the base model. Consequently, we adapted the common families of methods from image classification to operate at the object level, as detailed below.

**Output-based post-hoc methods** take the logits, or the softmax activations, as inputs to their scoring functions. Here we can find MSP Hendrycks and Gimpel [2016], energy score Liu et al. [2020], and GEN Liu et al. [2023].

**Feature-space post-hoc methods** use the previous-to-last activations as the input to the scoring functions. To this category belong kNN Sun et al. [2022], DDU Mukhoti et al. [2023] and Mahalanobis Lee et al. [2018].

**Mixed output-feature-space post-hoc methods** rely on the previous-to-last activations and the outputs as the input to the scoring functions. Here we find ViM Wang et al. [2022], ASH Djurisic et al. [2022], DICE Sun and Li [2022], and ReAct Sun et al. [2021].

**Latent-space post-hoc methods.** We take inspiration from recent works Yang et al. [2023], Mukhoti et al. [2023], Arnez et al. [2024] and implement an adapted confidence score, called LaRD, that uses latent activations of a given intermediate or hidden layer.

The adaptation of *post-hoc* methods for object detection is quite straightforward, as it is based on the filtering mechanisms used by each architecture. All object detectors deliver many predictions (usually ~ 1000). Then, a first filtering is done based on the threshold $t^*$ (see Section 2). The predictions with a score above $t^*$ go through non-maximum suppression (NMS) for Faster-RCNN and YOLOv8. Next, for each retained prediction, it is possible to access the full logits, and (except for YOLOv8) it is also possible to access the previous-to-last layer features associated uniquely with each predicted object. For YOLOv8, only MSP, GEN, and energy could be tested, as this network does not have a final fully connected layer or a set of latent features that can be directly linked with a predicted object.

In addition to the adapted *post-hoc* OOD detection methods, we evaluated the VOS method Du et al. [2022b], i.e., the regularized Faster-RCNN with the energy score. For both versions of Faster-RCNN, all *post-hoc* methods were tested. The confidence score threshold for each OOD detection method was calculated in an automatic way such that for each score, 95% of the ID samples would be above the threshold.

<table><caption>Table 3: mAP across architectures and VOC & BDD ID datasets</caption><thead><tr><th>Model</th><th>VOC</th><th>BDD</th></tr></thead><tbody><tr><td>Faster-RCNN</td><td>48.7</td><td>31.20</td></tr><tr><td>Faster-RCNN VOS</td><td>48.9</td><td>31.30</td></tr><tr><td>Yolov8</td><td>54.73</td><td>32.15</td></tr><tr><td>RT-DETR</td><td>70.4</td><td>33.30</td></tr></tbody></table>

## 5.3 Results

In Figure 4, we present a summarized plot of the AUROC and FPR95 metrics from the new FMIYC benchmark, averaged across different architectures for each family of methods and each OOD dataset. Feature-based methods and those utilizing latent representations tend to identify incorrect predictions more effectively in the *farther* split compared to other splits. Conversely, mixed methods exhibit a decline in performance as semantic distance increases. Overall, there is no distinct trend among baseline families indicating whether incorrect detections are more easily identified for *near*, *far*, or *farther* objects. This observation may be surprising; however, the differences among splits will become more apparent when considering the OSOD metrics discussed subsequently.

Figure 5 illustrates the results for the incorporated OSOD metrics, averaged across architectures for each family of methods and each OOD dataset split. For the nOSE, there is a clear decreasing trend across method families when transitioning from *near* to *farther* splits. The *near* datasets exhibit the highest nOSE, indicating that more objects are mistakenly predicted as one of the in-distribution (ID) classes among the correctly localized objects. Conversely, objects in the *farther* split are less confounded with ID objects. Regarding the $AP_U$, it is generally observed to be low across OOD datasets, with a trend of decreasing further in the *farther* datasets. This suggests that objects that are semantically *near* are localized more accurately. Feature-based methods and those utilizing latent space representations appear to perform better than other methods for the *farther* objects.
<figure><img src="image_6.png" /><figcaption>Figure 4: Average OOD-OD performance across baseline families and classic metrics (architectures are averaged).</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Figure 5: Average OSOD performance comparison across baseline families and metrics (architectures are averaged).</figcaption></figure>

The $P_U$ exhibits the highest variability across methods and also the highest values among the OSOD metrics. It is particularly elevated for the near splits. However, drops drastically for the farther objects, indicating that in such splits, more OOD predictions do not correspond to ground truth objects, as illustrated in Figure 2. Finally, the $R_U$ is generally quite low across OOD datasets and methods, with a similar trend showing that objects in *far* and *farther* OOD datasets are harder to detect. The metrics reveal that, on average, most unknown objects are ignored (not found), and this challenge is even more pronounced for *far* and *farther* OOD objects. For the *near* splits, ~14% of unknown objects are correctly identified. This figure drops to approximately 3% in the *farther* splits for output-based and mixed methods. However, feature-based and latent representation methods seem to perform slightly better, identifying ~9% of the unknown objects in the *farther* splits. For a comprehensive presentation of the results for each architecture, method, and metric, please refer to Appendix E.
It is important to note how unrelated the previous OOD-OD benchmark metrics may seem with
respect to the OSOD metrics. The AUROC and FPR95 cannot actually tell much difference between
*far* and *near* datasets. This difference becomes clear in light of the OSOD metrics, which show that,
contrary to the case of image classification, for object detection, the semantically and visually closer
objects are easier to identify and localize. But when the unknown objects are too different from the
ID ones, they will most likely be ignored by the methods and architectures evaluated. These insights
are impossible to obtain using only the AUROC and FPR95.

# 6 Discussion

**The value of OSOD metrics.** It is crucial to note that the OSOD metrics are necessary to quantify the effectiveness of OOD-OD methods in detecting actual OOD objects (*AP*<sub>U</sub> and *P*<sub>U</sub>) and accounting for instances when OOD objects are overlooked (*R*<sub>U</sub>) or misclassified (nOSE). Unlike AUROC and FPR95, the OSOD metrics provide a more nuanced understanding by addressing confounding unknowns for ID objects, the oversight of OOD objects, and the localization of unknowns. The added value of the OSOD metrics is clearer when considering the semantic stratified splits.

*Near, far and farther splits.* The partition of the benchmark into *near*, *far*, and *farther* proved insightful and meaningful since it details that semantic similarity plays an important role in the detection ability of different methods and architectures. It is especially insightful how the *near* OOD objects are more easily detectable than *far* and *farther* ones in the case of Object Detection. This is the opposite of the case of image classification, where *near* classes are considered harder than *far* ones. We may hypothesize that since OD deals with multiple objects per image and also with the task of localization, it might be, in fact, the localization part that facilitates finding *near* unknowns. However, the *near* objects are also more easily confounded with ID objects, in agreement with image classification observations. Moreover, the observation that *far* and *farther* objects are more usually ignored, and therefore are hardly localizable, is demonstrated by the OSOD metrics, as only around 5% of the unknown objects are localized, as opposed to about 20% for some methods in the *near* datasets.

**Why not only use OSOD?** The main limitation of OSOD metrics is their dependence on correct and exhaustive GT labels, since unlabeled unknown objects are present in the OOD datasets. The OSOD metrics cannot correctly handle the situation when an unlabeled unknown object is detected as such. For this case, the OOD-OD metrics are relevant. We argue that both sets of metrics give a deeper understanding of OD models and methods when facing unknown objects. This work quantifies and confirms that OOD-OD methods can find unknown objects, even if it is not the explicit goal. It is to be noted that the results are dependent on the OD threshold *t*\*. Therefore, it can be tuned to match certain requirements. For instance, if lowered, more low-confidence predictions could appear, with the consequence that OOD-OD methods would have more candidates and could find more unknown objects if present. For a more in-depth discussion of the nuances and relations between OOD-OD and OSOD, refer to Appendix H.

**Future work.** Inspired by the BRAVO Benchmark for semantic segmentation Vu et al. [2024], one interesting possible avenue for this work is to enrich the benchmark by generating a split that includes synthetically generated objects along the real ones. Another direction that could be explored is how vision-language models (VLMs) Zhang et al. [2024] perform in the benchmark in comparison with the already tested architectures. To the best of our knowledge, no work has yet proposed any specific method for OOD-OD using VLMs Miyai et al. [2024], Zhang et al. [2025].

# 7 Conclusion

We introduce the *FindMeIfYouCan* benchmark, which refines the existing evaluation framework for out-of-distribution object detection and incorporates open-set object detection metrics to comprehensively assess OOD-OD methods on their ability to identify unknown objects. This benchmark facilitates a holistic evaluation, measuring the detection of semantically *near*, *far*, and *farther* objects, instances where they are overlooked, and cases where they are misclassified as in-distribution (ID) objects. We hope our work lays a solid foundation for the deployment of OOD-OD methods in real-world scenarios.
Acknowledgments and Disclosure of Funding

This publication was made possible by the use of FactoryIA supercomputer, financially supported by the Ile-de-France Regional Council.

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# Appendix

## A Datasheet for Datasets

Here we provide complete answers to the datasheet in Gebru et al. [2021].

### A.1 Motivation

* **For what purpose was the dataset created? Was there a specific task in mind? Was there a specific gap that needed to be filled? Please provide a description.** Yes. FMIYC was created for robust evaluation of Out-Of-Distribution Object Detection (OOD-OD). Its primary task is to assess a model's ability to accurately detect unknown (Out-of-Distribution, OOD) objects as novel, rather than misclassifying them. It addresses the gap left by previous benchmarks by providing a structured framework to evaluate performance against varying OOD novelty levels ("near", "far", "farther") based on semantic similarity to ID data. This dataset, with its associated OOD-OD and open set metrics, forms the benchmark.

* **Who created the dataset (e.g., which team, research group) and on behalf of which entity (e.g., company, institution, organization)?** This dataset, a curated subset of COCO and OpenImages, was developed by Daniel Montoya et al. at CEA (The French Alternative Energies and Atomic Energy Commission), as detailed in "FindMeIfYouCan: Bringing Open Set metrics to *near, far* and *farther* Out-of-Distribution Object detection. It is hosted on Hugging Face under 'CEAAi'.

* **Who funded the creation of the dataset?** This work was funded by CEA.

* **Any other comments?** FMIYC's creation is driven by the essential need for realistic OOD-OD benchmarks, crucial for safety and reliability in real-world AI applications like autonomous systems, where correctly identifying novel objects is paramount.

### A.2 Composition

* **What do the instances that comprise the dataset represent?** Instances are images containing objects, curated to present scenarios with "unknown" (OOD) objects to models trained on specific ID classes. Annotations detail these objects.

* **How many instances are there in total?** The dataset contains 7,767 image instances, organized into configurations (e.g., coco_far_voc) designed to test OOD-OD performance using varying semantic distances from ID sets.

* **Does the dataset contain all possible instances or is it a sample from a larger set? If a sample, what is the larger set and is the sample representative?** FMIYC is a combination of curated subsets from the COCO and OpenImages datasets. The selection was methodology-driven, with a small element of randomness (e.g. what images were presented to be curated), to construct specific OOD evaluation sets categorized by semantic distance ("near," "far," "farther") from ID reference datasets (e.g., VOC, BDD), crucial for systematic OOD-OD evaluation.

* **What data does each instance consist of?** Each instance includes "raw" image data and OSOD-relevant metadata:

- image, file_name, image_id, height, width.

- dataset_origin: ("COCO" or "OpenImages").

- distance_category: ("near", "far", "farther") - key for this benchmark, indicating semantic distance.

- objects: List of object annotations (ID, area, bbox coordinates, category_id of the potentially unknown object).

- categories: Definitions of category names and supercategories.

* **Is there a label or target associated with each instance?** Yes, The category_id serves as ground truth for evaluating this. As well as "near", "Far" and "Farther" to group by semantic similarity with the ID.

* **Is any information missing from individual instances?** No.
* **Are relationships between individual instances made explicit?** No explicit relationships, other than grouping by *distance_category* for OOD-OD evaluation.
* **Are there recommended data splits and their rationale?** No. This dataset is test/evaluation only, "train" split was automatically enforced by the Huggingface's parquet converter.
* **Are there any errors, sources of noise, or redundancies?** Potential errors/biases from source datasets (COCO, OpenImages) may be present. FMIYC curation focused on semantic categorization for OOD-OD.
* **Is the dataset self-contained or does it rely on external resources? (Guarantees, archival versions, restrictions?)** Hosted on Hugging Face Hub. Relies on COCO/OpenImages for original image licenses (various Flickr, CC BY 2.0, etc.), which users must respect. FMIYC annotations/scripts are CC BY 4.0.
* **Does the dataset contain confidential or offensive data?** Unlikely to contain widespread confidential data as it's from public sources. Offensive content is possible due to the diverse nature of source datasets; FMIYC's curation focused on semantic distance with visual verification, and it is very unlikely to contain offensive material.

## A.3 Collection Process

* **How was data associated with each instance acquired and validated?** Base images/annotations from COCO/OpenImages. And semantic distance (*distance_category*) was added.

## A.4 Preprocessing/Cleaning/Labeling

* **Was any preprocessing/cleaning/labeling done?** Yes. The key OOD-OD specific labeling was assigning each instance to a *distance_category* ("near", "far", "farther") via semantic similarity relative to defined ID reference datasets (e.g., VOC, BDD). This is FMIYC's core preprocessing contribution.

* **Was "raw" data saved? Link?** Yes, "raw" refers to original COCO (https://cocodataset.org/) and OpenImages (https://storage.googleapis.com/openimages/web/index.html) datasets. FMIYC provides a curated subset with annotation labels.

* **Is the software used for preprocessing available? Link?** The code for making this dataset is available at the FMIYC OOD-OD Benchmark Repository

## A.5 Uses

* **Has the dataset been used for any tasks already?** Yes, for benchmarking and evaluation of OOD-OD performance of models, assessing distinction between ID objects and performance against varying OOD similarity levels.

* **Is there a repository linking to papers/systems using the dataset?** The following hubs include all the information related to the benchmark: FindMeIfYouCan - On huggingface and the FMIYC OOD-OD Benchmark Repository.

* **What (other) tasks could the dataset be used for?** Research into semantic similarity, model calibration/uncertainty for OOD, and few/zero-shot learning of novel classes, open-set Object Detection, and Domain Generalization.

* **Anything about composition/collection/preprocessing impacting future uses (e.g., unfair treatment, risks)? How to mitigate?** Yes:
  - **Inherited Biases:** Biases from COCO/OpenImages can propagate. .
  - **Evaluation Focus:** This dataset is not intended for training.
  - **OSOD Metrics Importance:** Crucial for meaningful evaluation in OOD-OD or OSOD tasks.

* **Are there tasks for which the dataset should not be used?** This dataset is not for training. Training should be previously done on each of the respective ID datasets: BDD100k and Pascal-VOC, as presented in Du et al. [2022b].
## Essentiality of this Benchmark

FMIYC is essential for testing model reliability before deployment in real-life scenarios:

- **Metrics proposed:** AOSE (Absolute Open-Set Error), WI (Wilderness Impact - omitted for FMIYC's setup), $R_U$ (Unknown Recall), $P_U$ (Unknown Precision), $AP_U$ (Average Precision of Unknowns). $n$OSE (normalized Open Set Error) = $AOSE / \text{Total Labeled Unknowns}$.

- Previously existent discrimination metrics (AUROC, FPR95) are also calculated, as in Du et al. [2022b].

## A.6 Distribution

- **Will it be distributed to third parties?** Yes, publicly available on Hugging Face Hub for the OOD-OD research community.

- **How distributed? DOI?** Via Hugging Face Hub *FindMeIfYouCan*, accessible via 'datasets' library or direct download, we recommend using the croissant file and mlcroissant for data-preparation. Hugging Face ID: *CEAai/FindMeIfYouCan*. Alternatively, you can make the same dataset using the code available in *FMIYC OOD-OD Benchmark Repository*.

- **When distributed?** Currently available.

- **Copyright/license/ToU? Fees?** FMIYC annotations/scripts: CC BY 4.0. Images: Subject to original COCO/OpenImages licenses. No fees for Hugging Face access mentioned.

- **Third-party IP restrictions?** Yes, original image licenses from COCO/OpenImages.

- **Export controls or regulatory restrictions?** No, please check CC BY 2.0/4.0 license permissions for more information

## A.7 Maintenance

- **Who will support/host/maintain?** Hosted by 'CEAai' on Hugging Face. Original authors (Daniel Montoya et al.) for scientific maintenance.

- **How can owner/curator be contacted?** Via Hugging Face "Community" tab or author contacts from research paper.

- **Is there an erratum?** Not explicitly provided. Updates via new versions on Hugging Face Hub.

- **Will dataset be updated? How?** Depends on the popularity of the benchmark and if adopted by the community

- **Retention limits for data relating to people?** N/A for FMIYC directly; governed by source dataset policies.

- **Older versions supported/hosted?** Hugging Face versioning typically keeps older versions accessible for reproducibility.

- **Mechanism for others to contribute/extend? Validation?** Through Hugging Face community features or direct contact with maintainers for relevant extensions. Validation at maintainers' discretion.
## B Semantic overlap and similarities in previous benchmark

As stated in Section 3, the main assumption of the current OOD-OD benchmark is that no ID category can be present in the OOD datasets. This is what we call the no-overlap condition. If this condition is met, it is ensured that all predictions done by a model trained on the ID datasets can be considered “incorrect” predictions. The non-overlap condition can mainly be enforced by manual inspection of OOD datasets, due to the existence of unlabeled instances of several objects.

A close inspection of the dataset showed that, in fact, the core assumption of no overlap is not met, since there are labeled and unlabeled instances of ID categories in the OOD datasets. The amount of images in the OOD datasets that contain ID categories is shown in Table 4.

<table><caption>Table 4: Semantic overlap: Number of OOD images containing ID classes</caption><thead><tr><td>ID class</td><td>No. Images</td></tr></thead><tbody><tr><td>Person (or part)</td><td>106</td></tr><tr><td>Dining table</td><td>142</td></tr><tr><td>Other</td><td>4</td></tr></tbody></table>

<figure><img src="image_8.png" /><figcaption>Figure 6: Examples of images in the OOD datasets that contain humans or parts of humans. There exists a semantic overlap between ID and OOD datasets. The images must be removed for the benchmark to have consistency.</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>Figure 7: Examples of images in the OOD datasets that contain dining tables. Some of these contain also humans. There exists a semantic overlap between ID and OOD datasets. The images must be removed for the benchmark to have consistency.</figcaption></figure>

Some examples of images in the OOD datasets that contain humans or parts of humans are shown in Figure 6. Similarly, examples of images containing “dining tables” in the OOD datasets w.r.t. VOC are shown in Figure 7. Table 5 shows the overlapping categories in each OOD dataset.

<table><caption>Table 5: Overlapping categories in each OOD dataset w.r.t. VOC</caption><thead><tr><th>ID: VOC</th><th>COCO</th><th>OpenImages</th></tr></thead><tbody><tr><td>Person</td><td>Person</td><td>Person, human face, human arm, woman, human head, human hand, human hair, human nose, human ear, human mouth, human nose, human eye, human beard, body part</td></tr><tr><td>Dining table</td><td>Spoon, fork, pizza, sandwich, cake, hot dog, wine glass, spoon</td><td>Salad, plate, broccoli, tableware, fork, baked goods, spoon</td></tr><tr><td>Boat</td><td>-</td><td>Boat</td></tr><tr><td>Potted plant</td><td>-</td><td>Houseplant, flowerpot</td></tr><tr><td>Cat</td><td>-</td><td>Cat</td></tr></tbody></table>

All images containing overlapping classes with the ID ones must be removed for the benchmark to comply with the non-overlap condition. Table 5 presents the detailed list of OOD categories that overlap with the corresponding ID category in each OOD dataset with respect to VOC categories. For BDD100k as ID, only the images containing instances of people or parts of people were removed.

Furthermore, we present a list of OOD categories and their corresponding ID category that are considered semantically or visually *near* w.r.t. VOC in Table 6. All the other categories in the OOD datasets that are not in the *near* list are considered *far* categories when VOC is the ID dataset. It is important to note, as explained in Section 4, that the images were manually checked to ensure the correct assignment into each new split, or removal.
<table><caption>Table 6: Semantically and visually *near* categories in each OOD dataset w.r.t. VOC</caption><thead><tr><th>VOC category</th><th>COCO</th><th>OpenImages</th></tr></thead><tbody><tr><td>Horse</td><td>Zebra</td><td>-</td></tr><tr><td>Cat</td><td>-</td><td>Jaguar, leopard, cheetah</td></tr><tr><td>Chair</td><td>Bench</td><td>-</td></tr><tr><td>Person</td><td>-</td><td>Clothing</td></tr><tr><td>Dining table</td><td>Spoon, fork, carrot, orange, apple, cup, bowl</td><td>Zucchini, food, knife</td></tr><tr><td>Television</td><td>Laptop</td><td>Tablet computer, laptop</td></tr><tr><td>Couch</td><td>Bed</td><td>-</td></tr><tr><td>Dog</td><td>Bear</td><td>Fox</td></tr><tr><td>Potted plant</td><td>Vase</td><td>-</td></tr><tr><td>Various</td><td>-</td><td>Raccoon, harbor seal, hedgehog, otter, sea lion</td></tr></tbody></table>

## C Details on the construction of the FMIYC benchmark

Here we provide more details into how the new benchmark was created, in addition to what is already presented in Section 4. Following the observations made in Appendix B with respect to the semantic overlaps existing in the current OOD-OD benchmark Du et al. [2022b], the first step was to remove the images where semantic overlap exists with the ID categories.

The second step consisted of splitting into *near* and *far* subsets with respect to Pascal-VOC. The images containing semantically and visually similar categories from Table 6 were put into the *near* split. The rest were put into the *far* split. The images were manually inspected to ensure no unlabeled instances of ID categories were present, in which case the image was removed from the benchmark. The manual inspection also ensured the correct assignment of images to each split.

Next, new images were added to each split. Candidate images from the training sets of COCO and OpenImages were first selected for manual inspection. The candidate images didn't have labeled ID categories, and needed to contain labeled instances of either the *near* or the *far* categories. Candidate images for each split were then manually inspected to ensure also that no ID category was present, and the correct assignment to each split.

For BDD100k as ID, the only modification done to the existing OOD datasets was the removal of images with people, because of overlap with the ID category “pedestrian”.

Later, the semantic and visual similarity was assessed using CLIP Radford et al. [2021] embedding space. The embeddings for both ID datasets, and for OOD samples in each split were extracted. Then, following the procedure in Mayilvahanan et al. [2023], we calculated the cosine similarity between ID and their respective OOD datasets. The obtained results before and after creating the splits can be seen in Figure 3. It can be observed that three groups are present. This allowed us to propose the distinction into *near*, *far* and *farther* datasets. *Near* and *far*, are splits that are OOD w.r.t. VOC. Farther are the subsets w.r.t. BDD100k. Each of these subsets exists for COCO and OpenImages, which means that in total, there are six subsets of OOD datasets: COCO-near, COCO-far, OpenImages-near, OpenImages-far w.r.t. VOC; along with COCO-farther and OpenImages-farther w.r.t. BDD100k. The amount of images in each subset is shown in Table 2. In total, there are 7767 images across all splits.
<figure><img src="image_10.png" /><figcaption>Figure 8: Top 20 category count for OOD datasets w.r.t. Pascal-VOC</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Figure 9: Top 20 category count for OOD datasets w.r.t. BDD100k</figcaption></figure>

Finally, Figure 8 and Figure 9 show the top-20 category count for the images in each split of the new benchmark.

## D Details on the metrics used

This section provides more details about the previous and the newly incorporated metrics.

**Previous OOD-OD metrics** AUROC and FPR metrics come from binary classification problems. The receiver-operating-characteristic (ROC) curve evaluates the performance of a classifier at varying threshold values. It consists of the plot of the true positive rate (TPR) against the false positive rate (FPR) at each threshold setting. TPR and FPR are defined as follows:

$$FPR = \frac{FP}{FP + TN} \qquad (1)$$
<figure><img src="image_12.png" /><figcaption>Figure 10: Incorrect predictions of Faster-RCNN trained on BDD100k on images from the OOD datasets in the current benchmark. AUROC and FPR95 cannot measure that the main OOD objects are ignored. They can only take into account the incorrect predictions. OSOD metrics can quantify the dismissal of unknown objects</figcaption></figure>

$$TPR = \frac{TP}{TP + FN} \qquad (2)$$

where *FP* is the number of false positives, *TP* is the number of true positives, *TN* is the number of true negatives, and *FN* is the number of false negatives.

The AUROC is the area under the ROC curve. Since both TPR and FPR are bounded to the interval [0, 1], the AUROC is bounded to the same interval. A perfect classifier would have an AUROC of 1, whereas a random classifier would have an AUROC of 0.5. The value of 0 would mean that the classifier is a perfect misclassifier (predicts negatives as positives and vice-versa). The FPR95 is the false positive rate at 95% true positive rate. The lower the FPR95, the fewer false positives the classifier predicts Lasko et al. [2005].

For the previous OOD-OD benchmark, the main limitation of these two metrics lies in the fact that they have no relation with ground truth (GT) bounding boxes, and rely exclusively on the compliance with the non-overlap assumption, as described in Section 2.2 and Appendix B. Therefore, AUROC and FPR95 are unable to measure the actual localization of OOD objects. For an illustration of this, see Figure 10.

Moreover, a non-negligible amount of images does not have a single prediction at all, as can be seen in Table 1. AUROC and FPR95 cannot measure that the main objects in Figure 2, Figure 10 and Figure 11 are ignored. They can only take into account the incorrect predictions as in Figure 10. Even if the unknown objects are correctly localized, AUROC and FPR95 are not measuring this since
<figure><img src="image_13.png" /><figcaption>Figure 11: Absence of predictions of Faster-RCNN trained on BDD100k on images from the OOD datasets in the current benchmark. AUROC and FPR95 cannot measure that all OOD objects in these images are ignored. Dismissing OOD objects is not measurable using the current metrics. OSOD metrics can quantify the dismissal of unknown objects</figcaption></figure>

they are unrelated to the GT bounding boxes. For these reasons, we raise the critical question: *are AUROC and FPR95 sufficient metrics to assess the deployment of OOD-OD methods in safety-critical real-world scenarios?*

**OSOD metrics** The newly proposed metrics for the benchmark exist in the Open Set for object detection (OSOD) community. The metrics were already introduced in Section 4.2. here we give a more detailed definition for each one of them. It is important to note that all of the metrics were calculated using an intersection over union (IoU) threshold of 0.5. This means that one detection is considered as a true positive (*TP*<sub>U</sub>) if the unknown is classified correctly (as unknown or OOD), and its predicted bounding box has an IoU≥ 0.5 with a ground truth (GT) unknown object.

Also, for this case it is important to distinguish two types of false negatives: dismissed or ignored ones, denoted *FN*^D, and misclassified ones, denoted *FN*^M. One prediction is considered as *FN*^D if no predicted bounding box has IoU≥ 0.5 with the GT label. A detection is considered *FN*^M if a bounding box has IoU≥ 0.5 with a GT unknown but the predicted class is one of the ID categories. The total false negatives for the unknowns are then:
$$FN_U = FN_U^D + FN_U^M \qquad (3)$$

The precision of the unknowns $P_U$ is defined in a similar way as the binary classification metric:

$$P_U = \frac{TP_U}{TP_U + FP_U} \qquad (4)$$

where all quantities refer to unknowns: $TP_U$ are the true positive predictions, and $FP_U$ are the false positive predictions. Also, let us note that $TP_U + FP_U$ are the total number of predictions for the unknown class. Therefore, what $P_U$ is measuring is the ratio of true positives divided by all unknown predictions. In other words, $P_U$ tells the proportion of predictions for unknowns that were actually ground-truth unknowns Powers [2011].

The recall of the unknowns $R_U$ is defined as:

$$R_U = \frac{TP_U}{TP_U + FN_U} \qquad (5)$$

where $FN_U$ are the false negatives. Let us note that $TP_U + FN_U$ are the total number of ground-truth unknowns. In other words, $R_U$ tells us the proportion of ground-truth unknowns that were found by the detector.

For the average precision of the unknowns $AP_U$, it is defined as the area under the precision-recall curve:

$$AP = \int_{0}^{1} p(r)dr \qquad (6)$$

which is usually calculated by the interpolation of rectangles of the sampled values:

$$AP = \sum_{m}^{M} (r_{n+1} - r_{n})p_{in}(r_{n+1}), \qquad (7)$$

$$p_{in}(r_{n+1}) = \max_{\tilde{r} \ge r_{n+1}} p(\tilde{r}) \qquad (8)$$

where $p_{in}$ represents the interpolated precision at each detection point, which is obtained by taking the maximum precision whose recall value is greater or equal than ($r_{n+1}$) Padilla et al. [2020].

Next, usually OSOD works report the absolute open set error (AOSE), that is defined as the total number of unknown objects that are predicted as one of the ID classes (which would correspond to $FN_U^M$). Since the absolute number of these is not comparable across datasets (because each dataset has a different number of unknown objects), we propose using a metric that we call normalized open set error (nOSE) that is defined as:

$$nOSE = \frac{FN_U^M}{TP_U + FN_U} \qquad (9)$$

where indeed $TP_U + FN_U$ is once more the total number of ground-truth unknown objects. The nOSE is comparable across datasets, and estimates the proportion of OOD objects that are confounded with ID objects.

A summary of the purpose, limitations, and advantages of the used metrics can be found in Table 7.
<table><caption>Table 7: Overall metrics summary</caption><thead><tr><th>Metric</th><th>Purpose</th><th>Limitations</th><th>Advantages</th></tr></thead><tbody><tr><td>AUROC, FPR95</td><td>Measures the ability of a scoring function to detect incorrect predictions</td><td>Cannot take into account ignored objects</td><td>Does not depend on GT labels, can detect incorrect predictions that do not overlap with labeled objects</td></tr><tr><td>Precision</td><td>Measures the percent of correct predictions over the total of predictions</td><td rowspan="3">Need good GT labels. Cannot measure unlabeled unknowns.</td><td rowspan="3">Measure localization of GT objects</td></tr><tr><td>Recall</td><td>Measures the percent of found objects divided by the total number of labeled objects</td></tr><tr><td>nOSE</td><td>Measures the percent of unknown objects confounded with an ID object</td></tr></tbody></table>

## E Detailed results per method and architecture

This section provides detailed results per architecture and per method on all metrics. First, the results for previous metrics are presented. Afterward, the results for the new metrics are detailed. Finally, a study of the correlations among previous and new metrics is presented.

### E.1 Detailed results on the previous OOD-OD metrics

<table><caption>Table 8: OOD detection performance for FasterRCNN (Vanilla) on various OOD splits (ID: PascalVOC). Metrics are AUC↑ (%) and FPR95↓ (%). LaRD represents best of (Mahalanobis PCA, KNN PCA, GMM PCA). Best result per metric column is in **bold**. <sup>B</sup>Indicates the primary scoring method of the VOS (Virtual Outlier Synthesis).</caption><thead><tr><th rowspan="3">Method</th><th colspan="8">FasterRCNN (Vanilla) — PascalVOC</th></tr><tr><th colspan="2">COCO-Near (OOD)</th><th colspan="2">COCO-Far (OOD)</th><th colspan="2">OpImg-Near (OOD)</th><th colspan="2">OpImg-Far (OOD)</th></tr><tr><th>AUC↑</th><th>FPR95↓</th><th>AUC↑</th><th>FPR95↓</th><th>AUC↑</th><th>FPR95↓</th><th>AUC↑</th><th>FPR95↓</th></tr></thead><tbody><tr><td>ViM</td><td>75.7</td><td>85.5</td><td>77.8</td><td>87.4</td><td>73.0</td><td>87.1</td><td>74.9</td><td>91.6</td></tr><tr><td>Mahalanobis</td><td>59.8</td><td>95.9</td><td>64.9</td><td>95.5</td><td>59.7</td><td>94.6</td><td>60.3</td><td>95.9</td></tr><tr><td>MSP</td><td>73.8</td><td>88.3</td><td>77.3</td><td>88.0</td><td>70.5</td><td>90.4</td><td>75.4</td><td>87.9</td></tr><tr><td>Energy</td><td>86.5</td><td>45.5</td><td>82.3</td><td>56.2</td><td>81.5</td><td>57.9</td><td>81.8</td><td>52.6</td></tr><tr><td>ASH</td><td>82.9</td><td>49.9</td><td>74.5</td><td>66.6</td><td>78.7</td><td>59.9</td><td>74.8</td><td>60.8</td></tr><tr><td>DICE</td><td>82.7</td><td>62.0</td><td>78.2</td><td>76.7</td><td>79.1</td><td>67.3</td><td>76.7</td><td>71.6</td></tr><tr><td>ReAct</td><td>85.1</td><td>58.1</td><td>75.2</td><td>82.5</td><td>83.1</td><td>66.0</td><td>73.4</td><td>83.0</td></tr><tr><td>GEN</td><td>87.4</td><td>44.8</td><td>84.5</td><td>55.0</td><td>82.8</td><td><strong>56.2</strong></td><td>83.7</td><td>52.1</td></tr><tr><td>DICE+ReAct</td><td>66.3</td><td>89.8</td><td>56.0</td><td>94.8</td><td>71.4</td><td>88.9</td><td>48.3</td><td>99.0</td></tr><tr><td>DDU</td><td>64.0</td><td>97.6</td><td>68.3</td><td>97.0</td><td>70.4</td><td>97.2</td><td>66.3</td><td>98.3</td></tr><tr><td>VOS<sup>B</sup>(Energy)</td><td><strong>90.0</strong></td><td><strong>44.6</strong></td><td><strong>89.1</strong></td><td><strong>44.9</strong></td><td><strong>84.4</strong></td><td>60.0</td><td><strong>86.0</strong></td><td><strong>49.1</strong></td></tr><tr><td>LaRD</td><td>73.8</td><td>81.7</td><td>68.6</td><td>88.0</td><td>70.0</td><td>88.4</td><td>70.0</td><td>89.2</td></tr></tbody></table>
<table><caption>Table 9: OOD detection performance for FasterRCNN enhanced with VOS (Virtual Outlier Synthesis) on various OOD splits (ID: PascalVOC). Metrics are AUC↑ (%) and FPR95↓ (%). LaRD represents best of (Mahalanobis PCA, KNN PCA, GMM PCA). Best result per metric column is in **bold**. <sup>B</sup>Indicates the primary scoring method of the VOS (Virtual Outlier Synthesis).</caption><thead><tr><th rowspan="3">Method</th><th colspan="8">FasterRCNN (VOS) — PascalVOC</th></tr><tr><th colspan="2">COCO-Near (OOD)</th><th colspan="2">COCO-Far (OOD)</th><th colspan="2">OpImg-Near (OOD)</th><th colspan="2">OpImg-Far (OOD)</th></tr><tr><th>AUC↑</th><th>FPR95↓</th><th>AUC↑</th><th>FPR95↓</th><th>AUC↑</th><th>FPR95↓</th><th>AUC↑</th><th>FPR95↓</th></tr></thead><tbody><tr><td>ViM</td><td>77.4</td><td>87.7</td><td>80.3</td><td>85.9</td><td>73.4</td><td>89.8</td><td>77.2</td><td>92.2</td></tr><tr><td>Mahalanobis</td><td>60.9</td><td>95.9</td><td>65.5</td><td>94.9</td><td>60.3</td><td>95.5</td><td>64.8</td><td>95.5</td></tr><tr><td>MSP</td><td>69.1</td><td>91.5</td><td>75.1</td><td>89.2</td><td>65.6</td><td>91.1</td><td>72.6</td><td>88.2</td></tr><tr><td>ASH</td><td><strong>90.2</strong></td><td>44.1</td><td>87.4</td><td>51.4</td><td>84.8</td><td>59.8</td><td>82.5</td><td>56.2</td></tr><tr><td>DICE</td><td>88.0</td><td>56.5</td><td>88.3</td><td>53.4</td><td>82.7</td><td>67.8</td><td>80.8</td><td>59.0</td></tr><tr><td>ReAct</td><td>87.1</td><td>57.1</td><td>79.9</td><td>72.2</td><td><strong>85.6</strong></td><td>64.5</td><td>77.1</td><td>76.3</td></tr><tr><td>GEN</td><td>89.7</td><td><strong>42.9</strong></td><td><strong>89.3</strong></td><td>45.7</td><td>85.3</td><td><strong>58.2</strong></td><td><strong>86.0</strong></td><td>50.7</td></tr><tr><td>DICE+ReAct</td><td>74.9</td><td>84.8</td><td>67.3</td><td>88.1</td><td>74.8</td><td>88.5</td><td>58.6</td><td>98.9</td></tr><tr><td>DDU</td><td>67.5</td><td>99.2</td><td>70.0</td><td>96.9</td><td>72.5</td><td>99.3</td><td>72.7</td><td>98.3</td></tr><tr><td>VOS<sup>B</sup>(Energy)</td><td>90.0</td><td>44.6</td><td>89.1</td><td><strong>44.9</strong></td><td>84.4</td><td>60.0</td><td>86.0</td><td><strong>49.1</strong></td></tr><tr><td>LaRD</td><td>75.1</td><td>77.5</td><td>68.1</td><td>87.8</td><td>67.8</td><td>87.2</td><td>67.8</td><td>89.2</td></tr></tbody></table>

<table><caption>Table 10: OOD detection performance for FasterRCNN variants on Farther OOD splits (ID: BDD). LaRD represents best of (Mahalanobis PCA, KNN PCA, GMM PCA). Higher AUC is better (↑), lower FPR95 is better (↓). Best result per metric column is in **bold**. <sup>B</sup>For the FasterRCNN (VOS) architecture, this indicates the primary scoring method of the VOS (Virtual Outlier Synthesis).</caption><thead><tr><th rowspan="3">Method</th><th colspan="4">FasterRCNN (Vanilla) — ID: BDD</th><th colspan="4">FasterRCNN (VOS) — ID: BDD</th></tr><tr><th colspan="2">COCO-Farther (OOD)</th><th colspan="2">OpImg-Farther (OOD)</th><th colspan="2">COCO-Farther (OOD)</th><th colspan="2">OpImg-Farther (OOD)</th></tr><tr><th>AUC↑ (%)</th><th>FPR95↓ (%)</th><th>AUC↑ (%)</th><th>FPR95↓ (%)</th><th>AUC↑ (%)</th><th>FPR95↓ (%)</th><th>AUC↑ (%)</th><th>FPR95↓ (%)</th></tr></thead><tbody><tr><td>ViM</td><td>91.4</td><td>39.3</td><td>91.6</td><td>39.3</td><td>92.9</td><td>32.3</td><td>93.1</td><td>31.5</td></tr><tr><td>Mahalanobis</td><td>89.5</td><td>48.8</td><td>89.0</td><td>51.5</td><td>91.1</td><td>43.3</td><td>90.6</td><td>46.7</td></tr><tr><td>MSP</td><td>80.0</td><td>77.7</td><td>81.2</td><td>76.8</td><td>79.1</td><td>79.4</td><td>80.0</td><td>76.6</td></tr><tr><td>Energy</td><td>72.4</td><td>64.4</td><td>73.3</td><td>60.3</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>ASH</td><td>48.9</td><td>81.0</td><td>49.0</td><td>77.3</td><td>67.6</td><td>70.6</td><td>71.7</td><td>61.4</td></tr><tr><td>DICE</td><td>68.3</td><td>69.2</td><td>69.3</td><td>65.0</td><td>77.7</td><td>57.9</td><td>71.6</td><td>49.0</td></tr><tr><td>ReAct</td><td>65.7</td><td>95.1</td><td>58.8</td><td>97.4</td><td>79.6</td><td>71.2</td><td>77.0</td><td>76.4</td></tr><tr><td>GEN</td><td>78.8</td><td>62.7</td><td>79.6</td><td>58.9</td><td>86.6</td><td>52.7</td><td>89.5</td><td>47.8</td></tr><tr><td>DICE+ReAct</td><td>57.9</td><td>97.7</td><td>48.5</td><td>98.9</td><td>66.8</td><td>90.5</td><td>59.4</td><td>95.5</td></tr><tr><td>DDU</td><td>90.8</td><td>41.6</td><td>91.5</td><td>42.6</td><td>92.2</td><td>37.2</td><td>92.9</td><td>40.1</td></tr><tr><td>VOS<sup>B</sup>(Energy)</td><td>84.8</td><td>49.1</td><td>88.1</td><td>38.5</td><td>84.8</td><td>49.1</td><td>88.1</td><td>38.5</td></tr><tr><td>LaRD</td><td><strong>96.6</strong></td><td><strong>15.8</strong></td><td><strong>97.7</strong></td><td><strong>8.6</strong></td><td><strong>96.6</strong></td><td><strong>15.8</strong></td><td><strong>97.4</strong></td><td><strong>10.9</strong></td></tr></tbody></table>

<table><caption>Table 11: OOD detection performance for YOLOv8 (ID: PascalVOC). LaRD represents results from available PCA methods (KNN PCA 32 only in provided data). Higher AUC is better (↑), lower FPR95 is better (↓). Best result per metric column is in **bold**.</caption><thead><tr><th rowspan="3">Method</th><th colspan="8">YOLOv8 — PascalVOC</th></tr><tr><th colspan="2">COCO-Near (OOD)</th><th colspan="2">COCO-Far (OOD)</th><th colspan="2">OpImg-Near (OOD)</th><th colspan="2">OpImg-Far (OOD)</th></tr><tr><th>AUC↑ (%)</th><th>FPR95↓ (%)</th><th>AUC↑ (%)</th><th>FPR95↓ (%)</th><th>AUC↑ (%)</th><th>FPR95↓ (%)</th><th>AUC↑ (%)</th><th>FPR95↓ (%)</th></tr></thead><tbody><tr><td>MSP</td><td><strong>85.2</strong></td><td><strong>64.0</strong></td><td>81.4</td><td>73.7</td><td><strong>85.1</strong></td><td><strong>67.4</strong></td><td>82.0</td><td>74.4</td></tr><tr><td>Energy</td><td>57.0</td><td>95.2</td><td>66.1</td><td>91.3</td><td>51.6</td><td>96.1</td><td>65.6</td><td>92.4</td></tr><tr><td>GEN</td><td>81.3</td><td>65.0</td><td>79.5</td><td><strong>67.2</strong></td><td>81.0</td><td>68.9</td><td><strong>82.3</strong></td><td><strong>59.1</strong></td></tr><tr><td>LaRD</td><td>78.6</td><td>76.4</td><td><strong>82.0</strong></td><td>68.8</td><td>71.4</td><td>85.7</td><td>80.9</td><td>75.7</td></tr></tbody></table>
<table><caption>Table 12: OOD detection performance on Farther OOD splits (ID: BDD). LaRD for RT-DETR represents best of (Mahalanobis PCA, KNN PCA, GMM PCA). Higher AUC is better (↑), lower FPR95 is better (↓). Best result for each metric column is in **bold**. ‘—’ indicates data not available.</caption><thead><tr><th rowspan="3">Method</th><th colspan="4">YOLOv8 — ID: BDD</th><th colspan="4">RT-DETR — ID: BDD</th></tr><tr><th colspan="2">COCO-Farther (OOD)</th><th colspan="2">OI-Farther (OOD)</th><th colspan="2">COCO-Farther (OOD)</th><th colspan="2">OI-Farther (OOD)</th></tr><tr><th>AUC↑ (%)</th><th>FPR95↓ (%)</th><th>AUC↑ (%)</th><th>FPR95↓ (%)</th><th>AUC↑ (%)</th><th>FPR95↓ (%)</th><th>AUC↑ (%)</th><th>FPR95↓ (%)</th></tr></thead><tbody><tr><td>ViM</td><td>—</td><td>—</td><td>—</td><td>—</td><td>89.5</td><td>30.7</td><td>95.2</td><td>15.2</td></tr><tr><td>Mahalanobis</td><td><strong>98.2</strong></td><td><strong>7.8</strong></td><td><strong>99.6</strong></td><td><strong>1.3</strong></td><td><strong>99.1</strong></td><td>5.0</td><td><strong>99.7</strong></td><td>1.1</td></tr><tr><td>MSP</td><td>69.4</td><td>77.1</td><td>69.4</td><td>75.4</td><td>79.4</td><td>60.9</td><td>85.1</td><td>57.2</td></tr><tr><td>Energy</td><td>64.8</td><td>91.1</td><td>62.8</td><td>91.5</td><td>57.9</td><td>97.4</td><td>64.4</td><td>96.2</td></tr><tr><td>ASH</td><td>—</td><td>—</td><td>—</td><td>—</td><td>33.1</td><td>98.6</td><td>35.4</td><td>99.2</td></tr><tr><td>DICE</td><td>—</td><td>—</td><td>—</td><td>—</td><td>60.7</td><td>90.8</td><td>58.1</td><td>96.4</td></tr><tr><td>ReAct</td><td>—</td><td>—</td><td>—</td><td>—</td><td>56.5</td><td>96.8</td><td>63.2</td><td>95.0</td></tr><tr><td>GEN</td><td>63.8</td><td>71.9</td><td>66.8</td><td>68.8</td><td>77.1</td><td>67.9</td><td>83.8</td><td>63.3</td></tr><tr><td>DICE+ReAct</td><td>—</td><td>—</td><td>—</td><td>—</td><td>59.3</td><td>92.7</td><td>57.0</td><td>97.3</td></tr><tr><td>DDU</td><td>—</td><td>—</td><td>—</td><td>—</td><td>99.1</td><td><strong>3.5</strong></td><td>99.6</td><td><strong>0.6</strong></td></tr><tr><td>LaRD</td><td>—</td><td>—</td><td>—</td><td>—</td><td>98.8</td><td>5.3</td><td>99.4</td><td>1.4</td></tr></tbody></table>

<table><caption>Table 13: OOD detection performance for RT-DETR (ID: PascalVOC). LaRD represents best of (Mahalanobis PCA, KNN PCA, GMM PCA). Higher AUC is better (↑), lower FPR95 is better (↓). Best result per metric column is in **bold**.</caption><caption>RT-DETR — PascalVOC</caption><thead><tr><th rowspan="2">Method</th><th colspan="2">COCO-Near (OOD)</th><th colspan="2">COCO-Far (OOD)</th><th colspan="2">OpenImages-Near (OOD)</th><th colspan="2">OpenImages-Far (OOD)</th></tr><tr><th>AUC↑ (%)</th><th>FPR95↓ (%)</th><th>AUC↑ (%)</th><th>FPR95↓ (%)</th><th>AUC↑ (%)</th><th>FPR95↓ (%)</th><th>AUC↑ (%)</th><th>FPR95↓ (%)</th></tr></thead><tbody><tr><td>ViM</td><td><strong>96.8</strong></td><td>10.9</td><td><strong>90.0</strong></td><td><strong>35.7</strong></td><td>74.1</td><td>59.7</td><td>87.7</td><td>39.7</td></tr><tr><td>Mahalanobis</td><td>96.6</td><td><strong>10.8</strong></td><td>87.2</td><td>42.4</td><td><strong>91.7</strong></td><td>32.6</td><td><strong>92.0</strong></td><td><strong>29.9</strong></td></tr><tr><td>MSP</td><td>94.2</td><td>21.7</td><td>84.5</td><td>58.3</td><td>62.7</td><td>79.0</td><td>76.7</td><td>67.3</td></tr><tr><td>Energy</td><td>68.1</td><td>97.7</td><td>70.8</td><td>92.6</td><td>50.1</td><td>96.3</td><td>62.8</td><td>96.7</td></tr><tr><td>ASH</td><td>64.7</td><td>86.2</td><td>57.5</td><td>92.9</td><td>46.8</td><td>96.6</td><td>49.3</td><td>94.3</td></tr><tr><td>DICE</td><td>63.4</td><td>89.7</td><td>70.7</td><td>83.0</td><td>81.9</td><td>73.7</td><td>81.3</td><td>78.2</td></tr><tr><td>ReAct</td><td>66.3</td><td>96.0</td><td>71.5</td><td>90.8</td><td>50.9</td><td>97.5</td><td>61.9</td><td>98.1</td></tr><tr><td>GEN</td><td>74.9</td><td>97.7</td><td>75.6</td><td>94.7</td><td>53.2</td><td>96.0</td><td>69.9</td><td>90.1</td></tr><tr><td>DICE+ReAct</td><td>68.0</td><td>90.0</td><td>70.1</td><td>84.1</td><td>81.5</td><td>75.4</td><td>79.0</td><td>83.0</td></tr><tr><td>DDU</td><td>96.4</td><td>11.9</td><td>86.7</td><td>45.2</td><td>91.2</td><td><strong>32.2</strong></td><td>91.4</td><td>31.5</td></tr><tr><td>LaRD</td><td>91.8</td><td>26.6</td><td>83.3</td><td>48.8</td><td>77.8</td><td>76.2</td><td>81.2</td><td>76.0</td></tr></tbody></table>

The evaluation using traditional OOD metrics (AUC/FPR95) reveals a significant method-architecture interaction effect on OOD discrimination performance. While certain methods like GEN demonstrate robust OOD separation on specific architectures (e.g., FasterRCNN), their efficacy is not universally transferable. Conversely, density-based methods like Mahalanobis show high sensitivity to the feature space, achieving exceptional discrimination in some contexts (e.g., YOLOv8/RT-DETR on BDD) but underperforming in others. This variability underscores that current OOD scoring functions often exploit specific architectural properties or data distributions rather than embodying a generalizable principle of OOD detection.

Across the presented experiments, traditional OOD detection metrics like AUC and FPR95 generally indicated that distinguishing out-of-distribution objects becomes less challenging as their semantic distance from the in-distribution data increases. This broad trend falsely suggests that greater dissimilarity simplifies the OOD object detection task. However, these metrics, while useful for gauging overall separability, offer limited insight into if these unknown objects are actually found, or the precision of their identification within an object detection framework.
## E.2 Detailed results on the newly incorporated OSOD metrics

<table><caption>Table 14: OOD detection performance comparison on COCO splits (ID: PascalVOC). Lower nOSE is better (↓), higher AP<sub>U</sub>/P<sub>U</sub>/R<sub>U</sub> is better (↑). Best result per metric column is in **bold**.</caption><thead><tr><th rowspan="3">Method</th><th colspan="8">YOLOv8 — PascalVOC</th></tr><tr><th colspan="4">COCO-Near (OOD)</th><th colspan="4">COCO-Far (OOD)</th></tr><tr><th>nOSE↓</th><th>APU↑</th><th>PU↑</th><th>RU↑</th><th>nOSE↓</th><th>APU↑</th><th>PU↑</th><th>RU↑</th></tr></thead><tbody><tr><td>MSP</td><td>32.3</td><td>8.5</td><td>62.0</td><td>11.0</td><td>18.7</td><td>4.5</td><td><strong>61.1</strong></td><td>5.7</td></tr><tr><td>Energy</td><td>43.6</td><td>1.3</td><td>44.3</td><td>3.0</td><td>23.2</td><td>1.0</td><td>34.8</td><td>2.7</td></tr><tr><td>GEN</td><td>27.2</td><td>11.7</td><td>64.7</td><td>16.5</td><td>14.2</td><td>6.3</td><td>59.3</td><td>10.1</td></tr><tr><td>LaRD</td><td><strong>24.9</strong></td><td><strong>13.7</strong></td><td><strong>67.8</strong></td><td><strong>18.8</strong></td><td><strong>11.4</strong></td><td><strong>7.0</strong></td><td>52.5</td><td><strong>12.7</strong></td></tr></tbody></table>

<table><caption>Table 15: OOD detection performance comparison on OpenImages splits (ID: PascalVOC). Lower nOSE is better (↓), higher AP<sub>U</sub>/P<sub>U</sub>/R<sub>U</sub> is better (↑). Best result per metric column is in **bold**.</caption><thead><tr><th rowspan="3">Method</th><th colspan="8">YOLOv8 — PascalVOC</th></tr><tr><th colspan="4">OpenImages-Near (OOD)</th><th colspan="4">OpenImages-Far (OOD)</th></tr><tr><th>nOSE↓</th><th>APU↑</th><th>PU↑</th><th>RU↑</th><th>nOSE↓</th><th>APU↑</th><th>PU↑</th><th>RU↑</th></tr></thead><tbody><tr><td>MSP</td><td>26.2</td><td>6.2</td><td><strong>62.6</strong></td><td>7.6</td><td>13.8</td><td>2.1</td><td>52.3</td><td>3.1</td></tr><tr><td>Energy</td><td>34.3</td><td>0.9</td><td>41.2</td><td>2.0</td><td>15.9</td><td>0.8</td><td>42.0</td><td>1.8</td></tr><tr><td>GEN</td><td><strong>23.4</strong></td><td><strong>7.5</strong></td><td>62.2</td><td><strong>11.0</strong></td><td><strong>9.5</strong></td><td>4.0</td><td>52.1</td><td>6.9</td></tr><tr><td>LaRD</td><td>26.9</td><td>5.5</td><td>60.1</td><td>8.2</td><td>9.8</td><td><strong>4.1</strong></td><td><strong>52.8</strong></td><td><strong>7.0</strong></td></tr></tbody></table>

<table><caption>Table 16: OOD detection performance comparison on Far OOD sets (ID: BDD). Lower nOSE is better (↓), higher AP<sub>U</sub>/P<sub>U</sub>/R<sub>U</sub> is better (↑). Best result per metric column is in **bold**.</caption><thead><tr><th rowspan="3">Method</th><th colspan="8">YOLOv8 — BDD</th></tr><tr><th colspan="4">COCO-Farther (OOD)</th><th colspan="4">OpenImages-Farther (OOD)</th></tr><tr><th>nOSE↓</th><th>APU↑</th><th>PU↑</th><th>RU↑</th><th>nOSE↓</th><th>APU↑</th><th>PU↑</th><th>RU↑</th></tr></thead><tbody><tr><td>MSP</td><td>4.6</td><td>0.3</td><td>31.4</td><td>1.0</td><td>4.0</td><td>0.6</td><td><strong>36.5</strong></td><td>1.2</td></tr><tr><td>Energy</td><td>5.3</td><td>0.1</td><td>26.0</td><td>0.4</td><td>5.0</td><td>0.1</td><td>22.6</td><td>0.3</td></tr><tr><td>GEN</td><td>3.9</td><td>0.6</td><td><strong>34.3</strong></td><td>1.7</td><td>3.2</td><td>0.8</td><td>36.0</td><td>2.0</td></tr><tr><td>LaRD</td><td><strong>0.1</strong></td><td><strong>1.6</strong></td><td>31.1</td><td><strong>4.8</strong></td><td><strong>0.0</strong></td><td><strong>1.4</strong></td><td>28.3</td><td><strong>4.7</strong></td></tr></tbody></table>

<table><caption>Table 17: OOD detection performance for FasterRCNN (Vanilla) on COCO splits (ID: PascalVOC). Lower nOSE is better (↓), higher AP<sub>U</sub>/P<sub>U</sub>/R<sub>U</sub> is better (↑). Best result per metric column is in **bold**.

<sup>B</sup>Indicates the primary scoring method of the VOS (Virtual Outlier Synthesis).</caption><thead><tr><th rowspan="3">Method</th><th colspan="8">FasterRCNN (Vanilla) — PascalVOC</th></tr><tr><th colspan="4">COCO-Near (OOD)</th><th colspan="4">COCO-Far (OOD)</th></tr><tr><th>nOSE↓</th><th>APU↑</th><th>PU↑</th><th>RU↑</th><th>nOSE↓</th><th>APU↑</th><th>PU↑</th><th>RU↑</th></tr></thead><tbody><tr><td>ViM</td><td>38.3</td><td>5.0</td><td>69.0</td><td>6.3</td><td>17.9</td><td>1.9</td><td>56.5</td><td>2.6</td></tr><tr><td>Mahalanobis</td><td>44.6</td><td>0.2</td><td>85.7</td><td>0.2</td><td>20.6</td><td>0.1</td><td><strong>100.0</strong></td><td>0.1</td></tr><tr><td>MSP</td><td>33.5</td><td>7.4</td><td>65.4</td><td>10.2</td><td>15.2</td><td>2.8</td><td>49.5</td><td>5.2</td></tr><tr><td>KNN</td><td>39.6</td><td>4.2</td><td>77.0</td><td>5.0</td><td>18.9</td><td>1.0</td><td>53.2</td><td>1.7</td></tr><tr><td>Energy</td><td>16.0</td><td>22.3</td><td>75.9</td><td>24.8</td><td>9.8</td><td>8.0</td><td>66.3</td><td>9.9</td></tr><tr><td>ASH</td><td>21.0</td><td>18.1</td><td>76.4</td><td>20.5</td><td>13.5</td><td>5.6</td><td>71.2</td><td>6.6</td></tr><tr><td>DICE</td><td>26.7</td><td>14.2</td><td>77.4</td><td>16.2</td><td>15.3</td><td>3.9</td><td>66.2</td><td>4.9</td></tr><tr><td>ReAct</td><td>33.3</td><td>10.0</td><td><strong>86.5</strong></td><td>10.8</td><td>19.0</td><td>1.3</td><td>83.3</td><td>1.5</td></tr><tr><td>GEN</td><td><strong>14.3</strong></td><td><strong>23.2</strong></td><td>73.8</td><td><strong>26.1</strong></td><td><strong>8.7</strong></td><td>8.6</td><td>65.2</td><td>11.0</td></tr><tr><td>DICE+ReAct</td><td>43.0</td><td>1.3</td><td>69.6</td><td>1.8</td><td>20.2</td><td>0.3</td><td>72.7</td><td>0.4</td></tr><tr><td>DDU</td><td>44.3</td><td>0.3</td><td>40.5</td><td>0.5</td><td>20.2</td><td>0.3</td><td>40.0</td><td>0.4</td></tr><tr><td>VOS<sup>B</sup>(Energy)</td><td>20.5</td><td>21.5</td><td>72.1</td><td>24.6</td><td>9.6</td><td><strong>8.3</strong></td><td>55.6</td><td><strong>11.3</strong></td></tr><tr><td>LaRD</td><td>39.9</td><td>3.3</td><td>65.5</td><td>4.3</td><td>17.5</td><td>2.6</td><td>71.8</td><td>3.1</td></tr></tbody></table>
<table><caption>Table 18: OOD detection performance for FasterRCNN (Vanilla) on OpenImages splits (ID: PascalVOC). Lower nOSE is better (↓), higher AP<sub>U</sub>/P<sub>U</sub>/R<sub>U</sub> is better (↑). Best result per metric column is in **bold**. <sup>B</sup>Indicates the primary scoring method of the VOS (Virtual Outlier Synthesis).</caption><thead><tr><th rowspan="3">Method</th><th colspan="10">FasterRCNN (Vanilla) — PascalVOC</th></tr><tr><th colspan="4">OpenImages-Near (OOD)</th><th colspan="4">OpenImages-Far (OOD)</th></tr><tr><th>nOSE↓</th><th>AP<sub>U</sub>↑</th><th>P<sub>U</sub>↑</th><th>R<sub>U</sub>↑</th><th>nOSE↓</th><th>AP<sub>U</sub>↑</th><th>P<sub>U</sub>↑</th><th>R<sub>U</sub>↑</th></tr></thead><tbody><tr><td>ViM</td><td>30.6</td><td>3.1</td><td>66.0</td><td>4.1</td><td>11.7</td><td>0.8</td><td>59.7</td><td>1.1</td></tr><tr><td>Mahalanobis</td><td>35.0</td><td>0.2</td><td><strong>100.0</strong></td><td>0.2</td><td>12.7</td><td>0.0</td><td>0.0</td><td>0.0</td></tr><tr><td>MSP</td><td>28.4</td><td>4.1</td><td>59.9</td><td>6.1</td><td>9.7</td><td>1.7</td><td>53.0</td><td>2.9</td></tr><tr><td>KNN</td><td>33.5</td><td>1.0</td><td>57.5</td><td>1.7</td><td>11.7</td><td>0.9</td><td>62.0</td><td>1.1</td></tr><tr><td>Energy</td><td>18.1</td><td>12.9</td><td>73.6</td><td>15.2</td><td>5.8</td><td>5.3</td><td>70.1</td><td>6.6</td></tr><tr><td>ASH</td><td>21.1</td><td>10.7</td><td>75.3</td><td>12.5</td><td>7.8</td><td>3.8</td><td>69.9</td><td>4.6</td></tr><tr><td>DICE</td><td>23.0</td><td>9.7</td><td>75.8</td><td>11.0</td><td>9.0</td><td>2.9</td><td>70.0</td><td>3.5</td></tr><tr><td>ReAct</td><td>28.4</td><td>5.7</td><td>86.4</td><td>6.1</td><td>11.8</td><td>0.8</td><td><strong>78.7</strong></td><td>0.9</td></tr><tr><td>GEN</td><td><strong>15.9</strong></td><td><strong>14.1</strong></td><td>72.0</td><td><strong>16.9</strong></td><td><strong>5.4</strong></td><td>5.4</td><td>68.0</td><td>6.9</td></tr><tr><td>DICE+ReAct</td><td>33.4</td><td>1.5</td><td>82.4</td><td>1.7</td><td>12.7</td><td>0.0</td><td>50.0</td><td>0.0</td></tr><tr><td>DDU</td><td>34.5</td><td>0.5</td><td>51.6</td><td>0.6</td><td>12.6</td><td>0.1</td><td>46.2</td><td>0.1</td></tr><tr><td>VOS<sup>B</sup>(Energy)</td><td>22.3</td><td>10.3</td><td>64.1</td><td>12.8</td><td>6.3</td><td><strong>5.5</strong></td><td>67.3</td><td><strong>7.1</strong></td></tr><tr><td>LaRD</td><td>31.1</td><td>3.4</td><td>74.6</td><td>3.7</td><td>10.0</td><td>2.2</td><td>68.8</td><td>2.6</td></tr></tbody></table>

<table><caption>Table 19: OOD detection performance for FasterRCNN (Vanilla) on Far OOD sets (ID: BDD). Lower nOSE is better (↓), higher AP<sub>U</sub>/P<sub>U</sub>/R<sub>U</sub> is better (↑). Best result per metric column is in **bold**. <sup>B</sup>Indicates the primary scoring method of the VOS (Virtual Outlier Synthesis).</caption><thead><tr><th rowspan="3">Method</th><th colspan="10">FasterRCNN (Vanilla) — BDD</th></tr><tr><th colspan="4">COCO-Farther (OOD)</th><th colspan="4">OpenImages-Farther (OOD)</th></tr><tr><th>nOSE↓</th><th>AP<sub>U</sub>↑</th><th>P<sub>U</sub>↑</th><th>R<sub>U</sub>↑</th><th>nOSE↓</th><th>AP<sub>U</sub>↑</th><th>P<sub>U</sub>↑</th><th>R<sub>U</sub>↑</th></tr></thead><tbody><tr><td>ViM</td><td>1.1</td><td>1.2</td><td>22.9</td><td>3.9</td><td>0.7</td><td>0.9</td><td>18.3</td><td>3.3</td></tr><tr><td>Mahalanobis</td><td>2.0</td><td>1.0</td><td>21.4</td><td>3.1</td><td>2.4</td><td>0.4</td><td>11.8</td><td>1.8</td></tr><tr><td>MSP</td><td>3.3</td><td>0.3</td><td>17.8</td><td>1.9</td><td>2.4</td><td>0.3</td><td>14.9</td><td>1.7</td></tr><tr><td>KNN</td><td>1.9</td><td>1.0</td><td>23.3</td><td>3.2</td><td>0.7</td><td>1.1</td><td>20.5</td><td>3.3</td></tr><tr><td>Energy</td><td>2.0</td><td>0.9</td><td>22.9</td><td>3.0</td><td>0.6</td><td>1.2</td><td>22.1</td><td>3.4</td></tr><tr><td>ASH</td><td>3.3</td><td>0.5</td><td>20.5</td><td>1.8</td><td>2.1</td><td>0.6</td><td>19.0</td><td>2.1</td></tr><tr><td>DICE</td><td>2.3</td><td>0.8</td><td>22.7</td><td>2.8</td><td>1.0</td><td>1.0</td><td>21.4</td><td>3.0</td></tr><tr><td>ReAct</td><td>4.0</td><td>0.4</td><td>17.9</td><td>1.2</td><td>3.6</td><td>0.1</td><td>7.7</td><td>0.6</td></tr><tr><td>GEN</td><td>2.0</td><td>1.0</td><td>22.9</td><td>3.0</td><td>0.7</td><td>1.2</td><td>21.8</td><td>3.3</td></tr><tr><td>DICE+ReAct</td><td>4.3</td><td>0.1</td><td>14.4</td><td>0.9</td><td>3.7</td><td>0.0</td><td>7.3</td><td>0.5</td></tr><tr><td>DDU</td><td>3.2</td><td>0.6</td><td>19.7</td><td>2.0</td><td>3.2</td><td>0.1</td><td>9.4</td><td>1.0</td></tr><tr><td>VOS<sup>B</sup>(Energy)</td><td>1.8</td><td><strong>1.8</strong></td><td><strong>26.7</strong></td><td><strong>4.7</strong></td><td><strong>0.6</strong></td><td><strong>2.2</strong></td><td><strong>26.2</strong></td><td><strong>5.6</strong></td></tr><tr><td>LaRD</td><td><strong>0.7</strong></td><td>1.3</td><td>21.0</td><td>4.2</td><td><strong>0.6</strong></td><td>0.8</td><td>16.5</td><td>3.4</td></tr></tbody></table>

<table><caption>Table 20: OOD detection performance for FasterRCNN (VOS) on COCO splits (ID: PascalVOC). Lower nOSE is better (↓), higher AP<sub>U</sub>/P<sub>U</sub>/R<sub>U</sub> is better (↑). Best result per metric column is in **bold**. <sup>B</sup>Indicates the primary scoring method of the VOS (Virtual Outlier Synthesis).</caption><thead><tr><th rowspan="3">Method</th><th colspan="10">FasterRCNN (VOS) — PascalVOC</th></tr><tr><th colspan="4">COCO-Near (OOD)</th><th colspan="4">COCO-Far (OOD)</th></tr><tr><th>nOSE↓</th><th>AP<sub>U</sub>↑</th><th>P<sub>U</sub>↑</th><th>R<sub>U</sub>↑</th><th>nOSE↓</th><th>AP<sub>U</sub>↑</th><th>P<sub>U</sub>↑</th><th>R<sub>U</sub>↑</th></tr></thead><tbody><tr><td>ViM</td><td>45.5</td><td>3.1</td><td>64.0</td><td>4.3</td><td>20.3</td><td>1.3</td><td>48.9</td><td>2.2</td></tr><tr><td>Mahalanobis</td><td>50.0</td><td>0.0</td><td>0.0</td><td>0.0</td><td>22.6</td><td>0.0</td><td>0.0</td><td>0.0</td></tr><tr><td>MSP</td><td>39.6</td><td>7.0</td><td>66.6</td><td>9.6</td><td>17.6</td><td>2.6</td><td>44.5</td><td>4.7</td></tr><tr><td>KNN</td><td>36.3</td><td>10.3</td><td>73.9</td><td>12.2</td><td>14.9</td><td>4.7</td><td>55.7</td><td>6.9</td></tr><tr><td>ASH</td><td>17.6</td><td>23.3</td><td>71.3</td><td>26.5</td><td>9.5</td><td>8.7</td><td>60.4</td><td>11.4</td></tr><tr><td>DICE</td><td>33.0</td><td>12.4</td><td>73.6</td><td>15.2</td><td>14.1</td><td>5.1</td><td>56.6</td><td>7.4</td></tr><tr><td>ReAct</td><td>42.4</td><td>6.6</td><td><strong>83.6</strong></td><td>6.8</td><td>20.7</td><td>1.3</td><td><strong>66.0</strong></td><td>1.7</td></tr><tr><td>GEN</td><td><strong>15.9</strong></td><td><strong>24.1</strong></td><td>69.4</td><td><strong>27.8</strong></td><td><strong>8.0</strong></td><td><strong>9.1</strong></td><td>54.9</td><td><strong>12.7</strong></td></tr><tr><td>DICE+ReAct</td><td>50.0</td><td>0.0</td><td>0.0</td><td>0.0</td><td>22.6</td><td>0.0</td><td>0.0</td><td>0.0</td></tr><tr><td>DDU</td><td>49.8</td><td>0.2</td><td>46.7</td><td>0.2</td><td>22.3</td><td>0.2</td><td>25.0</td><td>0.3</td></tr><tr><td>VOS<sup>B</sup>(Energy)</td><td>20.5</td><td>21.5</td><td>72.1</td><td>24.6</td><td>9.6</td><td>8.3</td><td>55.6</td><td>11.3</td></tr><tr><td>LaRD</td><td>42.1</td><td>6.0</td><td>70.7</td><td>7.1</td><td>19.9</td><td>2.1</td><td>64.5</td><td>2.5</td></tr></tbody></table>
<table><caption>Table 21: OOD detection performance for FasterRCNN (VOS) on OpenImages splits (ID: PascalVOC). Lower nOSE is better (↓), higher AP<sub>U</sub>/P<sub>U</sub>/R<sub>U</sub> is better (↑). Best result per metric column is in **bold**. <sup>B</sup>Indicates the primary scoring method of the VOS (Virtual Outlier Synthesis).</caption><thead><tr><th rowspan="3">Method</th><th colspan="8">FasterRCNN (VOS) — PascalVOC</th></tr><tr><th colspan="4">OpenImages-Near (OOD)</th><th colspan="4">OpenImages-Far (OOD)</th></tr><tr><th>nOSE↓</th><th>AP<sub>U</sub>↑</th><th>P<sub>U</sub>↑</th><th>R<sub>U</sub>↑</th><th>nOSE↓</th><th>AP<sub>U</sub>↑</th><th>P<sub>U</sub>↑</th><th>R<sub>U</sub>↑</th></tr></thead><tbody><tr><td>ViM</td><td>34.9</td><td>1.5</td><td>49.1</td><td>2.2</td><td>13.2</td><td>0.4</td><td>46.3</td><td>0.6</td></tr><tr><td>Mahalanobis</td><td>37.3</td><td>0.0</td><td>0.0</td><td>0.0</td><td>13.8</td><td>0.0</td><td>0.0</td><td>0.0</td></tr><tr><td>MSP</td><td>31.7</td><td>3.0</td><td>53.2</td><td>5.4</td><td>10.9</td><td>1.4</td><td>49.1</td><td>2.7</td></tr><tr><td>KNN</td><td>31.6</td><td>3.7</td><td>58.7</td><td>5.3</td><td>8.9</td><td>3.5</td><td>63.5</td><td>4.6</td></tr><tr><td>ASH</td><td>20.7</td><td>11.9</td><td>65.5</td><td>14.1</td><td>7.1</td><td>4.8</td><td>65.5</td><td>6.3</td></tr><tr><td>DICE</td><td>28.9</td><td>6.0</td><td>62.9</td><td>7.6</td><td>9.4</td><td>3.1</td><td>63.3</td><td>4.2</td></tr><tr><td>ReAct</td><td>32.2</td><td>4.4</td><td><strong>84.2</strong></td><td>4.7</td><td>12.7</td><td>0.9</td><td><strong>72.1</strong></td><td>1.1</td></tr><tr><td>GEN</td><td><strong>18.4</strong></td><td><strong>12.9</strong></td><td>63.3</td><td><strong>15.9</strong></td><td><strong>5.9</strong></td><td><strong>5.7</strong></td><td>66.1</td><td><strong>7.5</strong></td></tr><tr><td>DICE+ReAct</td><td>37.3</td><td>0.0</td><td>0.0</td><td>0.0</td><td>13.8</td><td>0.0</td><td>0.0</td><td>0.0</td></tr><tr><td>DDU</td><td>37.3</td><td>0.0</td><td>0.0</td><td>0.0</td><td>13.7</td><td>0.0</td><td>21.4</td><td>0.1</td></tr><tr><td>VOS<sup>B</sup>(Energy)</td><td>22.3</td><td>10.3</td><td>64.1</td><td>12.8</td><td>6.3</td><td>5.5</td><td>67.3</td><td>7.1</td></tr><tr><td>LaRD</td><td>32.8</td><td>3.7</td><td>75.0</td><td>4.1</td><td>11.3</td><td>1.9</td><td>73.1</td><td>2.3</td></tr></tbody></table>

<table><caption>Table 22: OOD detection performance for FasterRCNN (VOS) on Far OOD sets (ID: BDD). Lower nOSE is better (↓), higher AP<sub>U</sub>/P<sub>U</sub>/R<sub>U</sub> is better (↑). Best result per metric column is in **bold**. <sup>B</sup>Indicates the primary scoring method of the VOS (Virtual Outlier Synthesis).</caption><thead><tr><th rowspan="3">Method</th><th colspan="8">FasterRCNN (VOS) — BDD</th></tr><tr><th colspan="4">COCO-Farther (OOD)</th><th colspan="4">OpenImages-Farther (OOD)</th></tr><tr><th>nOSE↓</th><th>AP<sub>U</sub>↑</th><th>P<sub>U</sub>↑</th><th>R<sub>U</sub>↑</th><th>nOSE↓</th><th>AP<sub>U</sub>↑</th><th>P<sub>U</sub>↑</th><th>R<sub>U</sub>↑</th></tr></thead><tbody><tr><td>ViM</td><td>1.1</td><td>1.7</td><td>24.1</td><td>5.3</td><td>0.8</td><td>1.7</td><td>23.1</td><td>5.5</td></tr><tr><td>Mahalanobis</td><td>2.3</td><td>1.3</td><td>22.1</td><td>4.3</td><td>3.3</td><td>0.8</td><td>17.8</td><td>3.4</td></tr><tr><td>MSP</td><td>4.4</td><td>0.5</td><td>19.9</td><td>2.4</td><td>3.9</td><td>0.6</td><td>21.9</td><td>2.9</td></tr><tr><td>KNN</td><td>2.3</td><td>1.5</td><td>24.8</td><td>4.2</td><td>0.8</td><td>2.0</td><td>26.6</td><td>5.5</td></tr><tr><td>ASH</td><td>3.6</td><td>1.0</td><td>23.7</td><td>3.0</td><td>2.4</td><td>1.6</td><td>26.7</td><td>4.1</td></tr><tr><td>DICE</td><td>2.8</td><td>1.4</td><td>25.9</td><td>3.8</td><td>1.1</td><td><strong>2.3</strong></td><td><strong>29.1</strong></td><td>5.2</td></tr><tr><td>ReAct</td><td>3.6</td><td>1.1</td><td>24.0</td><td>3.1</td><td>4.7</td><td>0.5</td><td>17.6</td><td>2.1</td></tr><tr><td>GEN</td><td>1.6</td><td>1.8</td><td>26.3</td><td>4.8</td><td>0.6</td><td>2.1</td><td>25.5</td><td>5.6</td></tr><tr><td>DICE+ReAct</td><td>5.4</td><td>0.3</td><td>16.7</td><td>1.4</td><td>5.9</td><td>0.1</td><td>13.4</td><td>1.0</td></tr><tr><td>DDU</td><td>3.8</td><td>0.7</td><td>20.6</td><td>2.9</td><td>4.8</td><td>0.3</td><td>14.9</td><td>2.1</td></tr><tr><td>VOS<sup>B</sup>(Energy)</td><td>1.8</td><td>1.8</td><td><strong>26.7</strong></td><td>4.7</td><td>0.6</td><td>2.2</td><td>26.2</td><td>5.6</td></tr><tr><td>LaRD</td><td><strong>0.4</strong></td><td><strong>2.0</strong></td><td>23.5</td><td><strong>6.0</strong></td><td><strong>0.0</strong></td><td>1.8</td><td>21.8</td><td><strong>6.3</strong></td></tr></tbody></table>

<table><caption>Table 23: OOD detection performance for RT-DETR on COCO splits (ID: PascalVOC). Lower nOSE is better (↓), higher AP<sub>U</sub>/P<sub>U</sub>/R<sub>U</sub> is better (↑). Best result per metric column is in **bold**.</caption><thead><tr><th rowspan="3">Method</th><th colspan="8">RT-DETR — PascalVOC</th></tr><tr><th colspan="4">COCO-Near (OOD)</th><th colspan="4">COCO-Far (OOD)</th></tr><tr><th>nOSE↓</th><th>AP<sub>U</sub>↑</th><th>P<sub>U</sub>↑</th><th>R<sub>U</sub>↑</th><th>nOSE↓</th><th>AP<sub>U</sub>↑</th><th>P<sub>U</sub>↑</th><th>R<sub>U</sub>↑</th></tr></thead><tbody><tr><td>MSP</td><td>2.9</td><td>20.0</td><td>96.4</td><td>20.8</td><td>2.3</td><td>4.4</td><td>87.7</td><td>5.1</td></tr><tr><td>ViM</td><td>4.2</td><td>18.9</td><td>96.4</td><td>19.6</td><td>1.5</td><td>5.5</td><td>92.1</td><td>5.9</td></tr><tr><td>Mahalanobis</td><td>0.9</td><td>21.3</td><td>93.6</td><td>22.8</td><td>0.7</td><td>5.5</td><td>83.9</td><td>6.6</td></tr><tr><td>KNN</td><td><strong>0.8</strong></td><td><strong>21.4</strong></td><td>93.0</td><td><strong>23.0</strong></td><td><strong>0.4</strong></td><td><strong>5.6</strong></td><td>80.8</td><td><strong>6.8</strong></td></tr><tr><td>Energy</td><td>23.8</td><td>0.0</td><td>0.0</td><td>0.0</td><td>7.5</td><td>0.0</td><td>0.0</td><td>0.0</td></tr><tr><td>ASH</td><td>22.2</td><td>1.5</td><td>89.5</td><td>1.6</td><td>7.4</td><td>0.0</td><td>16.7</td><td>0.1</td></tr><tr><td>DICE</td><td>23.7</td><td>0.1</td><td><strong>100.0</strong></td><td>0.1</td><td>7.2</td><td>0.3</td><td><strong>100.0</strong></td><td>0.3</td></tr><tr><td>ReAct</td><td>23.8</td><td>0.0</td><td>0.0</td><td>0.0</td><td>7.4</td><td>0.1</td><td><strong>100.0</strong></td><td>0.1</td></tr><tr><td>GEN</td><td>23.8</td><td>0.0</td><td>0.0</td><td>0.0</td><td>7.5</td><td>0.0</td><td>0.0</td><td>0.0</td></tr><tr><td>DICE+ReAct</td><td>23.6</td><td>0.2</td><td><strong>100.0</strong></td><td>0.2</td><td>6.9</td><td>0.5</td><td>90.9</td><td>0.5</td></tr><tr><td>DDU</td><td>1.2</td><td>21.2</td><td>94.1</td><td>22.5</td><td>1.0</td><td>5.5</td><td>86.3</td><td>6.4</td></tr><tr><td>LaRD</td><td>5.7</td><td>17.1</td><td>95.4</td><td>17.9</td><td>3.2</td><td>3.2</td><td>75.7</td><td>4.2</td></tr></tbody></table>
<table><caption>Table 24: OOD detection performance for RT-DETR on OpenImages splits (ID: PascalVOC). Lower nOSE is better (↓), higher AP<sub>U</sub>/P<sub>U</sub>/R<sub>U</sub> is better (↑). Best result per metric column is in **bold**.</caption><thead><tr><th rowspan="3">Method</th><th colspan="12">RT-DETR — PascalVOC</th></tr><tr><th colspan="4">OpenImages-Near (OOD)</th><th colspan="4">OpenImages-Far (OOD)</th></tr><tr><th>nOSE↓</th><th>AP<sub>U</sub>↑</th><th>P<sub>U</sub>↑</th><th>R<sub>U</sub>↑</th><th>nOSE↓</th><th>AP<sub>U</sub>↑</th><th>P<sub>U</sub>↑</th><th>R<sub>U</sub>↑</th></tr></thead><tbody><tr><td>MSP</td><td>24.6</td><td>4.8</td><td>69.6</td><td>6.9</td><td>10.8</td><td>3.1</td><td>58.0</td><td>5.3</td></tr><tr><td>ViM</td><td>23.1</td><td>6.7</td><td>77.9</td><td>8.5</td><td>8.8</td><td>5.7</td><td>72.0</td><td>7.3</td></tr><tr><td>Mahalanobis</td><td><b>6.0</b></td><td><b>21.8</b></td><td>78.5</td><td><b>24.8</b></td><td><b>2.9</b></td><td><b>9.6</b></td><td>66.3</td><td><b>12.6</b></td></tr><tr><td>KNN</td><td>7.8</td><td>19.7</td><td>76.7</td><td>23.0</td><td>3.3</td><td>9.0</td><td>62.9</td><td>12.2</td></tr><tr><td>Energy</td><td>31.7</td><td>0.0</td><td>0.0</td><td>0.0</td><td>16.4</td><td>0.0</td><td>0.0</td><td>0.0</td></tr><tr><td>ASH</td><td>31.6</td><td>0.0</td><td>8.7</td><td>0.1</td><td>16.1</td><td>0.1</td><td>31.6</td><td>0.3</td></tr><tr><td>DICE</td><td>29.5</td><td>2.1</td><td><b>91.5</b></td><td>2.2</td><td>15.1</td><td>1.1</td><td><b>81.0</b></td><td>1.3</td></tr><tr><td>ReAct</td><td>31.7</td><td>0.0</td><td>0.0</td><td>0.0</td><td>16.4</td><td>0.0</td><td>0.0</td><td>0.0</td></tr><tr><td>GEN</td><td>31.7</td><td>0.0</td><td>0.0</td><td>0.0</td><td>16.4</td><td>0.0</td><td>0.0</td><td>0.0</td></tr><tr><td>DICE+ReAct</td><td>28.5</td><td>3.1</td><td>90.9</td><td>3.2</td><td>15.1</td><td>1.0</td><td>76.9</td><td>1.2</td></tr><tr><td>DDU</td><td>7.3</td><td>20.3</td><td>77.2</td><td>23.5</td><td>3.9</td><td>9.0</td><td>66.2</td><td>11.7</td></tr><tr><td>LaRD</td><td>27.3</td><td>3.0</td><td>66.5</td><td>4.2</td><td>13.2</td><td>1.6</td><td>47.9</td><td>3.0</td></tr></tbody></table>

<table><caption>Table 25: OOD detection performance for RT-DETR on Far OOD sets (ID: BDD). Lower nOSE is better (↓), higher AP<sub>U</sub>/P<sub>U</sub>/R<sub>U</sub> is better (↑). Best result per metric column is in **bold**.</caption><thead><tr><th rowspan="3">Method</th><th colspan="12">RT-DETR — BDD</th></tr><tr><th colspan="4">COCO-Farther (OOD)</th><th colspan="4">OpenImages-Farther (OOD)</th></tr><tr><th>nOSE↓</th><th>AP<sub>U</sub>↑</th><th>P<sub>U</sub>↑</th><th>R<sub>U</sub>↑</th><th>nOSE↓</th><th>AP<sub>U</sub>↑</th><th>P<sub>U</sub>↑</th><th>R<sub>U</sub>↑</th></tr></thead><tbody><tr><td>MSP</td><td>15.4</td><td>4.2</td><td>35.6</td><td>11.8</td><td>7.2</td><td>1.9</td><td>18.3</td><td>10.1</td></tr><tr><td>ViM</td><td>14.1</td><td>4.8</td><td>34.5</td><td>12.8</td><td>5.4</td><td>1.7</td><td>14.4</td><td>11.6</td></tr><tr><td>Mahalanobis</td><td><b>0.2</b></td><td>11.2</td><td>33.0</td><td><b>25.0</b></td><td><b>0.0</b></td><td>2.3</td><td>12.4</td><td><b>14.9</b></td></tr><tr><td>KNN</td><td>0.4</td><td>11.4</td><td>33.0</td><td>24.8</td><td><b>0.0</b></td><td>2.4</td><td>12.5</td><td><b>14.9</b></td></tr><tr><td>Energy</td><td>28.6</td><td>0.0</td><td>0.0</td><td>0.0</td><td>20.6</td><td>0.0</td><td>0.0</td><td>0.0</td></tr><tr><td>ASH</td><td>28.5</td><td>0.0</td><td>19.1</td><td>0.1</td><td>20.6</td><td>0.0</td><td>10.5</td><td>0.0</td></tr><tr><td>DICE</td><td>27.9</td><td>0.5</td><td><b>77.5</b></td><td>0.7</td><td>20.5</td><td>0.0</td><td><b>36.4</b></td><td>0.1</td></tr><tr><td>ReAct</td><td>28.6</td><td>0.0</td><td>7.1</td><td>0.0</td><td>20.6</td><td>0.0</td><td>25.0</td><td>0.0</td></tr><tr><td>GEN</td><td>27.9</td><td>0.4</td><td>54.2</td><td>0.7</td><td>20.0</td><td>0.2</td><td>33.9</td><td>0.4</td></tr><tr><td>DICE+ReAct</td><td>27.7</td><td>0.7</td><td>70.9</td><td>0.9</td><td>20.6</td><td>0.0</td><td>25.0</td><td>0.1</td></tr><tr><td>DDU</td><td>0.6</td><td><b>11.5</b></td><td>34.1</td><td>24.7</td><td><b>0.0</b></td><td><b>2.4</b></td><td>12.6</td><td><b>14.9</b></td></tr><tr><td>LaRD</td><td>0.8</td><td>10.7</td><td>32.3</td><td>24.4</td><td><b>0.0</b></td><td>2.3</td><td>12.4</td><td><b>14.9</b></td></tr></tbody></table>

Looking at the results, we don't find a universally best method, neither across architecture nor across semantic distance, e.g: GEN frequently demonstrates strong performance on FasterRCNN (Vanilla and VOS) and YOLOv8 when PascalVOC is the ID, often achieving leading nOSE, AP<sub>U</sub>, and R<sub>U</sub> values. However, its efficacy sharply declines on the RT-DETR architecture with PascalVOC as the ID. Energy, particularly its VOS variant on FasterRCNN and for Far OOD scenarios on BDD, shows competitive results but generally struggles on YOLOv8 and RT-DETR (ID: PascalVOC), characterized by high nOSE and poor recall of unknowns (R<sub>U</sub>). LaRD's performance is more varied; it excels on YOLOv8 (especially for Far OOD BDD splits) and demonstrates strength on FasterRCNN for BDD Far OOD detection tasks, often leading in nOSE, AP<sub>U</sub>, and R<sub>U</sub>. Conversely, its effectiveness is less prominent on FasterRCNN and RT-DETR architectures when trained on PascalVOC. This work also highlights the performance volatility of OOD-OD methods and offers a comprehensive comparative analysis across architectures and semantic similarity.

The introduction of OSOD metrics (nOSE, AP<sub>U</sub>, P<sub>U</sub>, R<sub>U</sub>) provides a much more nuanced understanding of performance related to semantic distance. These metrics reveal that even if general OOD discrimination (AUC/FPR95) seems satisfactory, the actual ability to comprehensively find OOD objects remains unknown. This challenges the intuition that greater dissimilarity inherently makes all aspects of OOD object detection easier.
<figure><img src="image_14.png" /><figcaption>Figure 12: Empirical correlations among old and new metrics.</figcaption></figure>

### E.3 Correlations among metrics

Additionally, in Figure 12 it is possible to find the empirical matrix of correlations among all (old and new) metrics. This matrix is calculated from the overall results previously presented. It shows correlations among metrics across all methods, architectures, and OOD datasets. The figure indicates in general significant but moderate correlations between old metrics and new ones, meaning that the AUROC and FPR95 can be indicative of the performance of OOD-OD methods for finding unknown objects. However the correlations don't have a high absolute value (minimum 0.56 an maximum 0.70), which means that new information is added by the new metrics.

Moreover the results indicate that there is no correlation found between old metrics (AUC & FPR95) and $P_U$. This means the $P_U$ is orthogonal to the previous metrics, and therefore the information measured by $P_U$ is invisible to the old metrics. This reinforces the utility of adding OSOD metrics to the benchmark.
# F Details On Evaluated OOD Detection Methods

We present further details on the OOD detection methods used in the paper. All of the methods come from the Image classification literature Yang et al. [2024], except for VOS Du et al. [2022b].

## F.1 Preliminaries.

Using the notation from Section 2.1, let us recall that a trained object detector $\mathcal{M}$ takes as input an image $x$, along with a confidence threshold $t^*$, to output a set of bounding boxes $b \in \mathbb{R}^4$ and a vector of logits $c \in \mathbb{R}^{|c|}$, with dimension equal to the number of ID classes $\mathcal{C}$. The model output is the set:

$$ \mathcal{M}(x, t^*) = \{(b_i, c_i)\}_{i=1}^D \qquad (10) $$

where $D$ is the number of detections in each image. Each tuple $(b_i, c_i)$ corresponds to one detected object. Note that $D = 0$ is possible, and in such case the output is empty. Furthermore, the so-called softmax activation is given by:

$$ \sigma(c_j) = \frac{e^{c_j}}{\sum_m^{|c|} e^{c_m}} \qquad (11) $$

which transforms the logits vector into a vector of probabilities for each ID class, such that $\sum_j^{|c|} \sigma(c_j) = 1$. An alternative output is then given by the vector of probabilities after softmax: $\mathcal{M}(x, t^*) = \{(b_i, p_i)\}_{i=1}^D$, where $p_i = \sigma(c_i)$. In any case, to have $D > 0$, there must be at least one prediction such that $p_i \ge t^*$.

**The OOD detection problem.** Is formulated as a binary classification task leveraging a (confidence) scoring function $\mathcal{G}$ for each detected instance $(b_i, c_i)$, so that:

$$ \mathcal{G}(x, b_i, c_i) = g_i \in \mathbb{R} \qquad (12) $$

The scoring function aims to distinguish between ID and OOD objects, using a thresholding function $\Omega$ with threshold $\tau$ as presented in eq. (13).

$$ \Omega(g_i, \tau) = \begin{cases} 1 & \text{ID} \quad \text{if } g_i \ge \tau \\ 0 & \text{OOD} \quad \text{if } g_i < \tau \end{cases} \qquad (13) $$

For the OOD-OD problem, only those detected objects above the threshold $t^*$ are considered. Therefore, if no object is detected in a given image, there is no input for the scoring function $\mathcal{G}$ for such an image. In a general sense, each of the OOD detection methods is a realization of the scoring functions $\mathcal{G}$. Figure 13 presents a depiction of the workflow of OOD-OD scoring functions.

It is important to avoid possible confusion and it can be useful to reiterate here that $t^*$ and $\tau$ are two different thresholds. The object detection model $\mathcal{M}$ uses a confidence threshold $t^* \in \mathbb{R}^{[0,1]}$ that is usually the one that maximizes the mAP in the ID test set. This threshold filters the output of the model so that all detected objects satisfy $p_i \ge t^*$. On the other hand, the OOD scoring functions $\mathcal{G}$ use each one its own threshold $\tau \in \mathbb{R}$, which corresponds to the one that makes that 95% of the $g_i$ of detected ID objects are above the threshold.

## F.2 Evaluated methods

For the adaptation of each method from image classification to object detection, in each case, the score is calculated per each detected object above the threshold $t^*$. Therefore, there can be zero or several detections per image. Each of the equations in the following section has been adapted to match our notation, and all of them explain the adaptation done to work at the object level.

### F.2.1 Output-based methods

Output based methods take either the $c_i$ or the $p_i$ as input to the scoring functions. This family of methods is applicable to all of the architectures tested: Faster-RCNN, Yolov8 and RT-DETR.
<figure><img src="image_15.png" /><figcaption>Figure 13: General workflow of OOD-OD scoring functions. The outputs of the base model $\mathcal{M}$ are the inputs to scoring functions $\mathcal{G}$. If the object detector ignores a given object, scoring functions will ignore it, too. The model predictions not marked as OOD, remain with the predicted class.</figcaption></figure>

**Maximum softmax probability (MSP).** This is perhaps the most classical baseline in OOD detection for image classification Hendrycks and Gimpel [2016]. It consists of directly choosing the maximum softmax value:

$$ \max_j p_j = \max_j \frac{e^{c_j}}{\sum_m^{|c|} e^{c_m}} \qquad (14) $$

where $e$ is the Euler number.

**Energy score.** Proposed by Liu et al. [2020], it calculates the energy score using the activation logs $c_i$ as:

$$ E(c_i, T) = -T \log \sum_j^{|c|} e^{c_j/T} \qquad (15) $$

where $T$ is the temperature (usually set to $T = 1$).

**Generalized entropy score (GEN).** Presented by Liu et al. [2023], the authors propose using the family of generalized entropies:

$$ G_{\lambda}(p_i) = \sum_j p_j^{\lambda} (1 - p_j)^{\lambda} \qquad (16) $$

when $\lambda = 1/2$:
$$G_{1/2}(p_i) = \sum_j \sqrt{p_j(1-p_j)} \qquad (17)$$

## F.2.2 Feature-based methods

If the model $\mathcal{M}$ has $L$ total layers, and its last layer $L$ is a linear one (also called fully connected), then the activations of the $L-1$ (penultimate) layer are considered the extracted features $z_{L-1} \in \mathbb{R}^d$, where $d$ is the dimension of the feature. Then, for a given input image $x$, and a detection $(b_i, c_i)$, then the features of each detected object are defined as:

$$z_{L-1}^i = \mathcal{M}_{L-1}(x, t^*) \qquad (18)$$

where $\mathcal{M}_l$ denotes the latent activation of $\mathcal{M}$ at layer $l$. To simplify notation, let us denote the per-object feature $z_{L-1}^i$ by $z_i$. In all cases, $z_i^*$ denotes the features of a detected object $(b_i^*, c_i^*)$ from a test image $x^*$. Feature-based methods considered here need a training phase, and for this phase they take as input the $z_i$ of the training set. At test time, their input is the $z_i^*$ of test samples.

This family of methods is not applicable to Yolov8, since this architecture has no final linear layer: it is fully convolutional. Therefore, it is not possible to associate a set of features to a specific detected object. This family of methods can be used with Faster-RCNN and RT-DETR.

**k-Nearest neighbors (kNN).** Introduced by Sun et al. [2022], first normalizes the feature for each detected object: $\mathbf{z}_i = z_i/\|z_i\|_2$, where $\| \cdot \|_2$ denotes the L2 norm. Then, the normalized embeddings of the training data are stored: $\bar{\mathbb{Z}}_N = (\mathbf{z}_1, ..., \mathbf{z}_N)$, where $N$ are the number of objects detected in the training set.

During testing, the normalized features $\mathbf{z}_i^*$ are derived, and the euclidean distances $\|\mathbf{z}_i^* - \mathbf{z}_j\|_2$ are calculated with respect to the train embeddings $\mathbf{z}_j \in \mathbb{Z}_N$. Afterward, the embeddings are reordered according to the increasing distance $\|\mathbf{z}_i^* - \mathbf{z}_j\|_2$. The reordered embedding sequence is $\bar{\mathbb{Z}}'_N = (\mathbf{z}_{(1)}, \mathbf{z}_{(2)}, ..., \mathbf{z}_{(N)})$. The scoring function is defined as:

$$r_k(\mathbf{z}_i^*) = \|\mathbf{z}_i^* - \mathbf{z}_{(k)}\|_2 \qquad (19)$$

which corresponds to the distance to the k-th nearest neighbor in the normalized feature space Sun et al. [2022].

**Mahalanobis distance.** Proposed by Lee et al. [2018], the Mahalanobis score calculates the distance to the centroids of a class-conditional Gaussian distribution. The predicted class per detected object is denoted $y_c^i$ and corresponds to the index of the max value of either the $c_i$ or the $p_i$. Then the empirical class mean and covariance matrix of training samples are estimated:

$$\hat{\mu}_c = \frac{1}{N_c} \sum_{j:y_c} z_j, \quad \hat{\Sigma} = \frac{1}{N} \sum_c^C \sum_{j:y_c} (z_j - \hat{\mu}_c)(z_j - \hat{\mu}_c)^{\top} \qquad (20)$$

where $N_c$ denotes the total number of objects of class $y_c$ detected in the training set, $N$ is the total number of detected objects in the training set in all classes, and $j$ are de indexes of detected objects of class $y_c$. Then the Mahalanobis confidence score is defined as the Mahalanobis distance between the features $z_i^*$, and the closest class-conditional Gaussian distribution:

$$M(z_i^*) = \max_c - (z_i^* - \hat{\mu}_c) \hat{\Sigma}^{-1} (z_i^* - \hat{\mu}_c)^{\top} \qquad (21)$$

which corresponds to the log of the probability of the test sample Lee et al. [2018].
**Deep deterministic uncertainty (DDU).** A work by Mukhoti et al. [2023], fits a Gaussian mixture model (GMM) on the feature space, then computes the density under the GMM. Similar to Equation (20), the mean per class $\hat{\mu}_c$ and the covariance matrix $\hat{\Sigma}$ are computed for the features $z_i$ of each detected object $(b_i^*, c_i^*)$. Then the weights of the GMM are computed as:

$$ \pi_c = \frac{1}{N} \sum y_c \qquad (22) $$

which denotes the proportion of detected objects for each class $y_c$ over the total $N$ detected objects in the training dataset. During inference time, the density under the GMM is computed for the features $z_i^*$ of a detected object $(b_i^*, c_i^*)$ from a test image $x^*$:

$$ q(z_i^*) = \sum_{y_c} q(z_i^*|y_c)\pi_c, \quad \text{where} \quad q(z_i^*|y_c) \sim \mathcal{N}(\mu_c; \sigma_{y_c}) \qquad (23) $$

### F.2.3 Output-feature (mixed) based methods

This family of methods takes both the outputs (either the $c_i$ or the $p_i$) and the features $z_i$ for each detected object $(b_i, c_i)$ as inputs to the scoring functions. This family of methods was not applicable to Yolov8 for the same reasons as for the previous family of methods.

**Activation shaping (ASH).** Showcased by Djurisic et al. [2022], involves a reshaping of the feature $z_i$, and subsequent use of the energy score from Equation (15). The reshaping is done by first calculating a threshold $t$ that corresponds to the $p$-th percentile of the entire set of the detected objects representations of the training set:

$$ \mathbb{Z}_N = (z_1, \dots, z_N) \qquad (24) $$

Afterward, we calculate $s_1 = \sum_j z_j$. Then all values below $t$ are set to 0 to obtain a pruned version of the features $\mathbb{Z}_N^p = (z_1^p, \dots, z_N^p)$. Using the $\mathbb{Z}_N^p$, we calculate $s_2 = \sum_j z_j^p$. Finally, all non-zero values in $\mathbb{Z}_N^p$ are multiplied with $\exp(s_1/s_2)$, to obtain the pruned and reshaped features:

$$ \begin{aligned} \mathbb{Z}_N^r &= \mathbb{Z}_N^p \exp(s_1/s_2) \\ &= (z_1^p \exp(s_1/s_2), \dots, z_N^p \exp(s_1/s_2)) \\ &= (z_1^r, \dots, z_N^r) \end{aligned} \qquad (25) $$

Finally, the pruned and reshaped features are passed through the final fully connected layer $L$ to obtain the logit activations $c_i$, which are passed to the energy score calculation as in Equation (15). The authors found that the method works best when using a pruning percentile of about 90% Djurisic et al. [2022].

**Directed sparsification (DICE).** Introduced by Sun and Li [2022], the authors consider the weight matrix of the final fully connected layer $\mathbf{W} \in \mathbb{R}^{d \times |C|}$, where $d$ is the dimension of the feature $z_i$, and $|C|$ is the number of ID categories. This matrix is then subject to sparsification, to preserve the most important weights in it. The contribution is measured by a matrix $\mathbf{V} \in \mathbb{R}^{d \times |C|}$, where each column $\mathbf{v}_c \in \mathbb{R}^d$ is given by:

$$ \mathbf{v}_c = \mathbb{E}_{z_j \in \mathbb{Z}_N} [\mathbf{w}_c \odot z_j] \qquad (26) $$

where $\odot$ represents the element-wise multiplication, $\mathbf{v}_c$ indicates the weight vector for class $y_c$, and $\mathbb{Z}_N$ is as defined in Equation (24). Then the top-k weights are selected from the largest values of $\mathbf{V}$, to obtain a sparsified matrix $\mathbf{W}'$. This matrix is now used as the final layer weights instead of the $\mathbf{W}$. Finally, the obtained $c_i$ are passed to the energy scoring function from Equation (15) Sun and Li [2022].
**Rectified activations (ReAct).** Proposed by Sun et al. [2021], it performs a clipping operation on the features $z_i$, and the calculation of the energy score. The rectification (or clipping) is performed as:

$$ \bar{z}_i = \min(z_i, t) \qquad (27) $$

where each element of $z_i$ is truncated to be at most equal to the threshold $t$. This threshold is calculated so that a given percentile of the activations are less than the threshold. For instance, at percentile $p = 90, 90\%$ of ID train activations are below the threshold $t$. The authors found that a percentile of 90 works best. Then, the $\bar{z}_i$ are passed as inputs to the final layer to obtain the outputs $c_i$, which are then used to calculate the energy score as in Equation (15) Sun et al. [2021].

**Virtual logit matching (ViM).** A method inspired by a thorough geometrical analysis of the space of the matrix $Z$, whose rows are the $z_i$ for all detected objects in the training set. Let $X$ denote a centered version of $Z$, obtained by offsetting the $z_i$ by a vector $\mathbf{o} = -(\mathbf{W}^\top)^+\mathbf{b}$, where $(\cdot)^+\mathbf{b}$ denotes the Moore-Penrose inverse, $\mathbf{W}$ is the final layer weight matrix and $\mathbf{b}$ is the final layer bias. The eigendecomposition of the matrix $\mathbf{X}^\top\mathbf{X}$ is:

$$ \mathbf{X}^\top\mathbf{X} = \mathbf{Q}\mathbf{\Lambda}\mathbf{Q}^{-1} \qquad (28) $$

where eigenvalues $\mathbf{\Lambda}$ are ordered decreasingly. The first $D$ columns of $\mathbf{Q}$ are called the $D$-dimensional principal subspace $\mathbf{P}$. The residual subspace $\mathbf{P}^\perp$ is spanned by the remaining $D+1$ to the last columns of $\mathbf{Q}$, and is represented by the matrix $\mathbf{R} \in \mathbb{R}^{N \times (N-D)}$, where $N$ is the number of detected objects in the train set. Then $z_i^{P^\perp}$ denotes the projection of $z_i$ onto $\mathbf{R}$: $z_i^{P^\perp} = \mathbf{R}\mathbf{R}^\top z_i$. The virtual logit $c_0$ is calculated as:

$$ c_0 = \alpha \|z_i^{P^\perp}\| = \alpha \sqrt{z_i^\top \mathbf{R}\mathbf{R}^\top z_i} \qquad (29) $$

which corresponds to the norm of the residual $z_i^{P^\perp}$ rescaled by a constant $\alpha$. This constant is calculated as:

$$ \alpha = \frac{\sum_{j=1}^{K} \max_{m=1,...,|C|} |c_m^j|}{\sum_{j=1}^{K} \|z_i^{P^\perp}\|} \qquad (30) $$

where $z_1, z_2, ..., z_K$ are uniformly sampled $K$ training examples, and $c_m^j$ is the $m$-th logit of $c_j$. This constant scales the virtual logit to the average maximum of the original logits. Finally, the ViM score is calculated as:

$$ \text{ViM}(z_i) = \alpha \|z_i^{P^\perp}\| - \ln \sum_{j=1}^{|C|} e^{c_j} \qquad (31) $$

which, in summary, is the virtual logit minus the energy score of the rest of the logits. For the hyperparameter $D$, the authors recommend using $D = 1000$ if the dimension of the feature $d > 1000$, or use $D = 512$ otherwise Wang et al. [2022].

### F.2.4 Latent space methods

In this family we find methods that take as input other latent activations inside the network. We took inspiration from Arnez et al. [2024], Wilson et al. [2023] and built a method based on the latent space convolutional activations. In our case, we used directly the latent activations without doing Monte Carlo dropout sampling of entropy estimation as in Arnez et al. [2024], nor using a surrogate model or the generation of adversarial examples as in Wilson et al. [2023].
**Latent representation density (LaRD).** We start by considering a convolutional feature map $z_{i,l} \in \mathbb{R}^{N_c \times W \times H}$, where $N_c$ is the number of channels, $W$ is the width and $H$ is the height of the latent activation, extracted at layer $l$. Then it is possible to use the predicted bounding boxes $b_i$ and the feature maps as inputs for the ROIAliign (RA) algorithm He et al. [2017], which can extract the corresponding portion of the feature maps per each predicted object:

$$o_{i,l} = \mathrm{RA}(z_{i,l}, b_i), \text{ where } o_{i,l} \in \mathbb{R}^{N_c \times R \times R} \qquad (32)$$

Where $R$ is the parameter that fixes the size of the output of the RA algorithm, that outputs crops of the feature map $z_{i,l}$ with a given fixed-sized for all objects, independently of their aspect ratio or actual size in the image. Then an average per channel is taken to reduce the dimensionality of these representations:

$$\bar{o}_{i,l} = \frac{1}{HW} \sum_{h=1}^{H} \sum_{w=1}^{W} o_{i,l}(c, h, w), \text{ where } \bar{o}_{i,l} \in \mathbb{R}^{N_c} \qquad (33)$$

The set $O_l = \{\bar{o}_{i,l}, y_i\}_{d=1}^D$ consists of all the averaged latent representations at layer $l$ of each object found by the object detector in one image, along with the predicted class $y_i$. Then, we also want to build a density estimator, by making a forward pass through the training set to obtain the set of all the ID objects latent representations: $O_{train,l} = \{O_l\}_{x=1}^{N_t}$, where $N_t$ is the size of the training set. Afterward, we use the methodology as in the Mahalanobis distance baseline to obtain a scoring function for each of the detected objects. We used a hyperparameter of $R = 9$ for all experiments. For Faster-RCNN, the chosen latent layer was the RPN intermediate convolutional layer as in Arnez et al. [2024]; for Yolov8, it was the final layer of the backbone, after evaluation of each layer. For RT-DETR the chosen hidden layer was the first encoder module, similarly, after evaluation of each layer.

# G Details on the training of architectures

This section provides details on the training of Yolov8 Sohan et al. [2024] and RTDETR Zhao et al. [2024]. Both architectures were trained on a single GPU Nvidia A100 40G. The achieved mAP by both models in each ID dataset is found in Table 3.

## G.1 Yolov8

We trained the nano version of Yolov8 for both ID datasets (BDD100k and Pascal-VOC). We used the same hyperparameters for both models. Most of them corresponded to the default hyperparameters. They were trained for 100 epochs, using the AdamW optimizer with momentum of 0.937 and weight decay of $5 \times 10^{-4}$. The learning rate was $10^{-3}$, and was controlled by a cosine scheduler. The batch size was 16, and we used the copy-paste augmentation, on top of the mosaic, translate, scale, erase, and flip-lr default augmentations. For the training, we used the Ultralytics library Jocher et al. [2023].

## G.2 Real-Time DETR

We fine-tuned a version of RT-DETR that was pre-trained on COCO for both ID datasets (BDD100k and Pascal-VOC). The pretrained version can be found in Huggingface: RT-DETR. Both versions used early stopping with a patience of 16 epochs. The hyperparameters for both models can be found in Table 26.
<table><caption>Table 26: Hyperparameters for training RT-DETR with ID datasets BDD100k and Pascal-VOC</caption><thead><tr><th>Parameter</th><th>ID: BDD</th><th>ID: VOC</th></tr></thead><tbody><tr><td>Batch size</td><td>8</td><td>8</td></tr><tr><td>Inference threshold</td><td>0.25</td><td>0.25</td></tr><tr><td>Learning rate backbone</td><td>4 × 10<sup>-6</sup></td><td>2 × 10<sup>-6</sup></td></tr><tr><td>Max epochs</td><td>60</td><td>60</td></tr><tr><td>Num queries</td><td>100</td><td>100</td></tr><tr><td>Random seed</td><td>40</td><td>40</td></tr><tr><td>Learning rate</td><td>4 × 10<sup>-5</sup></td><td>2 × 10<sup>-5</sup></td></tr></tbody></table>

## H Further discussion on the similarities and differences between OOD-OD and OSOD methods

Building upon the detailed presentation of how Out-of-Distribution Object Detection (OOD-OD) methods operate in Section 2 and Appendix F, which draws from previous works Du et al. [2022b], Wilson et al. [2023], Ammar et al. [2024], Han et al. [2022], we can conclude that the two approaches for handling unknown objects in object detectors are distinct yet they are like two sides of the same coin.

In simpler terms, the current formulation of OOD-OD serves as a monitoring function for the base object detector. It aims to verify that the detected objects are indeed In-Distribution (ID) categories, rather than actively seeking out unknown objects in images. Nevertheless, it can identify unknown objects and label them as Out-of-Distribution (OOD). The ability of OOD-OD methods to detect objects was not assessable in the previous benchmark, but it can now be quantified precisely using the new FMIYC benchmark, which employs OSOD metrics calculated with respect to the ground truth labels.

Conversely, open set object detection (OSOD) methods do not rely on monitoring functions. Instead, they incorporate an "unknown" class directly into the object detector, adding specific loss terms and usually training with labeled or pseudo-labeled examples of "unknowns" Joseph et al. [2021], Dhamija et al. [2020], Gupta et al. [2022]. OSOD has developed several metrics, already presented in Section 4.2 and Appendix D, to measure how well OSOD methods can identify and localize both unknown and known objects simultaneously. The OOD-OD community lacks this type of evaluation, which we believe can significantly enrich the field and is provided by the present benchmark.

We believe the OOD-OD field has substantial potential for future developments, particularly in enhancing a method's ability to localize unknown objects. The main bottleneck is perhaps the filtering of predictions by the confidence threshold in the base model *M* because the model is trained to ignore unknown objects. Therefore, finding ways to encourage models to retrieve more predictions that will be post-processed anyway by OOD scoring functions can be an interesting research direction. This could be done perhaps by adjusting the confidence threshold *t*\* so that a model can retrieve more objects, rather than just maximizing the mAP of the ID test dataset.

Another research direction that may impact the field is the use of VLMs, which have a broader semantic knowledge and, therefore, may be able to localize several categories of objects beyond a definite set of ID classes. In any case, precise detection of unknown objects must be rigorously evaluated, since this capability is crucial for applications beyond identifying incorrect predictions. Without proper evaluation, OOD-OD methods lack a realistic assessment of their performance for real-world scenarios.

## I Societal Impact

This work fosters positive societal impacts by enhancing the safety and trustworthiness of object detection systems in safety-critical applications like autonomous driving and medical imaging. By providing a more rigorous benchmark and nuanced metrics for evaluating how well systems detect out-of-distribution objects, it helps prevent overconfidence in deployed models and pushes the field towards developing AI that is more trustworthy and reliable. However, as systems improve in identifying "unknown" or "novel" entities through enhanced evaluations like this, there are several
potential downsides to consider. Enhanced capabilities in detecting unspecified "unknowns" could inadvertently enable more pervasive or intrusive surveillance systems, potentially tracking atypical (though not necessarily illicit) activities or objects without clear justification. Furthermore, if the definition of "known" within the training data or benchmark inherently contains biases, such as curation biases, objects or individuals deviating from these biased norms might be disproportionately flagged as "unknown," leading to unfair scrutiny or misclassification for certain groups. There's also a risk that an over-reliance on these improved systems, even with better benchmarking, could lead to a false sense of safety & security, potentially delaying human intervention when truly critical and unanticipated failures occur, or encouraging the deployment of systems in environments where the range of true "unknowns" far exceeds what any benchmark can capture i.e., existence of *unknown-unknowns* in the wild real-word that cannot be foreseeing by any evaluation benchmark.