A CTIVE L EARNING FOR O BJECT D ETECTION WITH E VIDENTIAL D EEP L EARNING AND H IERARCHICAL U NCERTAINTY A GGREGATION
Anonymous authors
Paper under double-blind review
A BSTRACT
Despite the huge success of object detection, the training process still requires an immense amount of labeled data.
Although various active learning solutions for object detection have been proposed, most existing works do not take advantage of epistemic uncertainty, which is an important metric for capturing the usefulness of the sample.
Also, previous works pay little attention to the attributes of each bounding box (e.g., nearest object, box size) when computing the informativeness of an image.
In this paper, we propose a new active learning strategy for object detection that overcomes the shortcomings of prior works.
To make use of epistemic uncertainty, we adopt evidential deep learning (EDL) and propose a new module termed model evidence head (MEH), that makes EDL highly compatible with object detection.
Based on the computed epistemic uncertainty of each bounding box, we propose hierarchical uncertainty aggregation (HUA) for obtaining the informativeness of an image.
HUA realigns all bounding boxes into multiple levels based on the attributes and aggregates uncertainties in a bottom-up order, to effectively capture the context within the image.
Experimental results show that our method outperforms existing state-of-the-art methods by a considerable margin.
I NTRODUCTION
Deep learning contributes to huge success in computer vision problems such as semantic segmentation (Long et al., 2015; Ronneberger et al., 2015;
Chen et al., 2018) and object detection (Liu et al., 2016; Lin et al., 2017; Redmon et al., 2016).
However, training a deep neural network typically comes with a cost of large labeled datasets.
Labeling data for complex vision problems requires intensive labor of human experts, which makes preparing practical application challenging.
Active learning, which gradually labels a set of samples based on the informativeness (e.g., uncertainty), is a promising solution for this problem due to its simplicity and high performance.
Although active learning has been extensively studied on image classiﬁcation, only a few prior works focused on object detection (Yuan et al., 2021;
Su et al., 2020; Haussmann et al., 2020; Yu et al., 2021) despite its practical importance.
Furthermore, existing works on active learning for object detection have two limitations.
First, when computing the informativeness of an image, most previous works only use the aleatoric uncertainty , not taking the epistemic uncertainty into account.
Epistemic uncertainty, also known as knowledge uncertainty, captures the lack of knowledge of a model (caused by a lack of data) and can be reduced when we have large amounts of data.
Aleatoric uncertainty, on the other hand, captures the noise inherent in the observed data and is irreducible.
As stated in (Nguyen et al., 2022; Hafner et al., 2018; H¨ullermeier & Waegeman, 2021), epistemic uncertainty can reﬂect the usefulness of samples and support active learning better than aleatoric uncertainty.
Secondly, previous works on active learning for object detection generally ignore the attributes of bounding boxes (e.g., nearest object, box size) when computing the informativeness of an image: informativeness is often deﬁned as the maximum or mean of the uncertainty values of all bounding boxes in the image.
This can be a problem because a cluttered image with many objects belonging to various categories can be enforced to have a similar uncertainty value relative to just a simple image with only a few objects belonging to a single category.
Goal and challenge.
The general goal of this paper is to propose an active learning strategy for object detection, that handles the above limitations of existing approaches.
First, we aim to build an algorithm which can compute epistemic uncertainty quickly yet correctly in object detection.
Some existing works on object detection (Haussmann et al., 2020; Feng et al., 2019) calculate epistemic uncertainty using multi-model based methods (e.g., model ensemble (Beluch et al., 2018), Monte
Carlo (MC) dropout (Gal & Ghahramani, 2016)).
However, these methods require multiple models or repetitive forward propagations for MC integration, and consequently make practical application difﬁcult.
Secondly, we aim to design an uncertainty aggregation scheme which can consider attributes of bounding boxes and understand the context within images.
This goal is meaningful since aggregation schemes of previous works (Yuan et al., 2021; Roy et al., 2018; Choi et al., 2021), which simply rely on the maximum/mean of all bounding boxes, are hard to reﬂect the context in images.
Main contributions.
Our ﬁrst key idea is to adopt Evidential Deep Learning (EDL) to effectively compute epistemic uncertainty, and to propose a new module that makes EDL highly compatible with object detection.
Introduced by (Sensoy et al., 2018; Amini et al., 2020), EDL is a useful tool for computing epistemic uncertainty since it enables to sample model ensembles almost instantly.
However, previous works on EDL have mainly been focused on image classiﬁcation and induce unconﬁdent prediction and unstable training when simply applied to object detection.
To this end, we propose a new module named as Model Evidence Head (MEH) to enable conﬁdent prediction and stable training of EDL.
Speciﬁcally, MEH predicts the expected difﬁculty, or model evidence, and is optimized independently of the object detector.
To our knowledge, this is the ﬁrst research to make EDL compatible with object detection on 2D image.
Another key ingredient for our solution is Hierarchical Uncertainty Aggregation (HUA), which makes use of attributes in bounding boxes for computing the informativeness of an image.
According to the attributes, HUA realigns boxes into multiple levels and aggregates uncertainties in a bottom-up order.
This helps to capture the context within the image and improves the quality of the expected informativeness of images.
Overall, our main contributions are summarized as follows:
• We make use of EDL to effectively compute epistemic uncertainty in object detection, and design a new module termed Model Evidence Head (MEH) which solely predicts the model evidence independently of the class conﬁdence to make EDL adaptable to the object detection.
• We propose Hierarchical Uncertainty Aggregation (HUA) , which reorganizes all bounding boxes into several levels and aggregate uncertainties of each level in a bottom-up manner, to better capture the context within the image.
We validate the efﬁcacy of proposed methods using RetinaNet, SSD as base models on well-known datasets: PASCAL VOC, MS-COCO.
Extensive experiments demonstrate that the proposed methods signiﬁcantly improve performance achieving new state-of-the-art results.
R ELATED W ORKS
Active learning for object detection.
Active learning (Sinha et al., 2019; Yoo & Kweon, 2019;
Sener & Savarese, 2017; Gal et al., 2017; Wang et al., 2016) aims to select a small subset of informative unlabeled samples which is expected to be most effective.
Although active learning has been extensively studied for the classiﬁcation problem, only a few works focus on object detection (Yuan et al., 2021;
Su et al., 2020; Haussmann et al., 2020; Yu et al., 2021), despite its practical importance.
The authors of (Yuan et al., 2021; Su et al., 2020) train discriminators using unlabeled data to predict whether an image is from labeled set or unlabeled set.
LL4AL (Yoo & Kweon, 2019) trains an auxiliary module to predict loss of data samples, where a sample with high predicted loss is considered as the one with high informativeness.
The concurrent work CDAL (Agarwal et al., 2020) introduced a distance measure to select diverse samples in semantic and spatial context.
Recently, (Choi et al., 2021) predicts the parameter of Gaussian mixture model and computes epistemic uncertainty as the variance of Gaussian modes.
However, there is no guarantee that model uncertainty leads to variance in GMM, and the size of the model ensemble is ﬁxed to be small since the number of Gaussian modes is inhibited to change after training.
Overall, existing approaches do not fully take advantage of epistemic uncertainty and pay little attention to attributes of bounding boxes during uncertainty aggregation.
Our work resolves both limitations using novel and effective methods.
Bayesian deep learning.
In spite of huge success of deep learning, recent studies (Amini et al., 2020; Louizos & Welling, 2017) show typical DNN is often overconﬁdent on its decision and is difﬁcult to take advantage of uncertainty.
It naturally gives rise to the advent of Bayesian approach for modern deep learning (Gal & Ghahramani, 2015; Blundell et al., 2015; Gal & Ghahramani,
The goal of Bayesian deep learning is to build a credible machine that measures uncertainty on its decision as well.
In contrast to frequentist approach where model parameters are not random variables but ﬁxed quantities, Bayesian approach assumes prior distribution on model parameters and estimates posterior distributions based on given data.
Previous Bayesian deep learning methods such as Bayes by Backprop (Gal & Ghahramani, 2015; Blundell et al., 2015), MC dropout (Gal & Ghahramani, 2016) and Variational Inference (Blei et al., 2017; Hoffman et al., 2013; Kingma & Welling, 2013) often require costly sampling-based MC approximation to estimate posterior distribution.
Instead, our work adopts Evidential Deep Learning (EDL) (Sensoy et al., 2018;
Amini et al., 2020) to compute epistemic uncertainty through a single forward propagation.
Different from typical Bayesian approaches, EDL tries to predict prior distributions of posterior models without repetitive model sampling.
However, EDL has hardly been applied to complicated computer vision problems such as object detection yet, and it usually requires adversarial learning using regularization loss which makes training unstable.
In this work, we propose MEH to overcome aforementioned limitations of previous works.
P ROPOSED M ETHOD 3. P ROBLEM S ETUP AND O RGANIZATION
Active learning consists of multiple learning cycles.
At the ﬁrst cycle, a large unlabeled dataset Uand a small labeled dataset L 0 are given.
Once an object detector is trained using L 0 , the network selects the most informative images I 0 from U 0 , based on the informativeness .
Human oracles then manually label I 0 and construct new labeled/unlabeled sets for the next cycle as L 1 =
L 0 ∪ I 0 and
U 1 = U 0 \ I 0 .
The same process is repeated until the annotation budget is exhausted.
In this section, we describe our method for computing the informativeness of an image for active learning in object detection.
Section 3.2 describes how we estimate epistemic uncertainty of a bounding box using EDL and the proposed MEH.
Based on the results in Section 3.2, we describe how we compute the informativeness of an image using HUA, in Section 3.3.
3. E VIDENTIAL D EEP L EARNING FOR E PISTEMIC U NCERTAINTY
Overview of our approach.
Fig 1 shows the high-level descriptions of our approach under the EDL framework for computing epistemic uncertainty of a bounding box.
MEH in Fig.
1a is our new module that makes EDL adabtable to object detection.
Under the Dirichlet-Categorical Bayesian framework, we propose to predict class conﬁdences β
= { β k } Kk =1 and model evidence λ , to obtain concentration parameter α
= { α k } Kk =1 and construct prior Dirichlet distribution Dir ( θ | α ) for each bounding box.
Epistemic uncertainty is then computed using model ensembles θ ∼ Dir ( θ | α ) as the mutual information between predictions and model posterior as
[Equation]
where H denotes Shannon entropy and θ parameterizes categorical likelihood Cat ( θ ) .
p ( y | θ ) and p ( θ | α ) are probability functions of categorical and Dirichlet distributions.
Fig.
1b shows an example on how the 3 types of uncertainty in (1) change according to λ predicted from our MEH module.
Prior works on active learning without model sampling fail to take advantage of epistemic uncertainty U epi since p ( θ | α ) becomes a point estimate, enforcing U tot = U ale and U epi = 0 .
Our two-stage Bayesian framework based on EDL enables us to sample θ almost instantly, which is signiﬁcantly faster than multi-model-based Bayesian methods such as MC-dropout (Gal & Ghahramani, 2016) and model ensemble (Haussmann et al., 2020).
In the following, we start by applying
EDL to object detection to describe our algorithm with details.
Applying EDL to object detection.
Inspired by EDL (Sensoy et al., 2018; Amini et al., 2020; Zhao et al., 2020), compared to typical object detectors where classiﬁcation head predicts parameters θ of categorical distribution, we instead predict high-order Dirichlet distribution Dir ( θ | α ) which is a conjugate prior of lower-order categorical likelihood Cat ( θ ) .
To ﬁt our evidential model to data, we maximize the marginal likelihood, also known as maximum likelihood Type II.
Marginal likelihood p r o [Figure] a
[Figure]
ili t y
C1 C2 C C1 C2 C
[Figure]
r o
[Figure]
ili
[Figure]
y
[Figure]
Unlabeled Image
Backbone
Cls.
Head
MEH
Reg.
Head 𝛽 𝜆 𝛼
[Figure]
p r
[Figure]
a
[Figure]
ili t y
C [Figure] C
C
[Figure]
p r
[Figure]
a
[Figure]
ili t y
[Figure]
Unlabeled Image
Backbone
Cls.
Head
MEH
Reg.
Head 𝛽 𝜆 𝛼 𝛼
[Figure]
=
[Equation]
exp 𝛽 i σ
[Equation]
exp 𝛽 j | 𝑘 ∈ {1,2,...,K}
[Figure]
for a bounding box y i can be obtained by marginalizing over the likelihood parameter θ as
[Equation]
The ﬁrst term in the integral comes from categorical distribution, while the second term is from
Dirichlet distribution; the integration can be interpreted as the marginalization over every possible categorical model θ ∼ Dir ( θ | α ) .
Thanks to the Dirichlet-Categorical conjugacy, the integral can be written in a closed-form as follows:
[Equation]
The network is then optimized to minimize negative log marginal likelihood L cls = − (cid:80)
k ¯ y k log( p ( y = k | α )) , where ¯ y is an one-hot label vector.
At inference, the expected probability for the k -th category is computed as ˆ p k
= α k /S , where
S =
(cid:80) k
α k is the Dirichlet strength.
Issues.
When the EDL method used for image classiﬁcation is directly applied to object detection, several problems arise: (i) training becomes unstable due to the adversarial regularization loss, and (ii) the prediction becomes unconﬁdent due to the use of ReLU as an hypothesis function.
Given class conﬁdences β = { β i } Ki =1 , previous works (Sensoy et al., 2018; Zhao et al., 2020; Hemmer et al., 2022) adopt ReLU to compute the concentration parameter as α (cid:48) k = ReLU ( β k )+1 .
Although
ReLU performs well in image classiﬁcation with simple datasets, it noticeably decreases the mAP score in object detection where the number of classes is large and conﬁdent prediction is important.
For example, in the case of 80-way classiﬁcation, β k should be at least 7820 to achieve ˆ p k
=
.even
when β i =
for all i (cid:54)
= k , according to α (cid:48) k = ReLU ( β k ) + 1 and (3).
MEH module.
To overcome the aforementioned issues, we propose MEH and introduce several techniques.
As a ﬁrst step, we apply softmax as α k = exp( β k ) (cid:80) c exp( β c ) instead of ReLU to produce sufﬁciently conﬁdent prediction.
However, although softmax enables conﬁdent prediction, it enforces the Dirichlet strength S =
(cid:80) k
α k to be 1.
This makes the entropy of Dirichlet distribution unchangeable and deprives the model of the ability to predict model evidence.
To tackle this issue, we propose a new module termed MEH, which solely predicts model evidence λ .
When λ is obtained from MEH and class conﬁdences { β k } Kk =1 are obtained from classiﬁcation head, we propose to re-scale the concentration parameter α as
[Equation]
where β c is the class conﬁdence for class c .
The above re-scaling process with λ transforms
Dir ( θ | α ) to be either concentrated or ﬂat.
Epistemic uncertainty is then computed based on the re-scaled Dir ( θ | α ) via (1).
Fig.1b illustrates the effect of λ on epistemic uncertainty.
The effects of softmax and λ are validated via experiments in Section 4.
MEH loss function.
We separate the training of MEH from the primary object detector with a novel loss function for stability.
For a Bayesian model to work properly, it must be able to recognize the “I don’t know” state i.e., the model should generate low model evidence for difﬁcult samples.
To this end, previous works on EDL (Hemmer et al., 2022; Sensoy et al., 2018) shrink the model evidence for singletons which do not correspond to target category, via the following regularization loss
[Equation]
where ˆ α = ¯ y
+ ( 1 − ¯ y ) (cid:12) α is the concentration parameter where the element for target category is disregarded.
However, this loss enforces the non-target elements to be one, no matter how large an error is detected, since the uniform Dirichlet distribution Dir ( θ | < 1 , ..., 1 > ) is considered as a constant supervisory signal.
Furthermore, this adversarial regularization loss suppresses the overall model evidence and makes training unstable.
To overcome these issues, we propose a simple yet effective solution: we utilize the continuous loss score from the classiﬁcation head as a target value.
Speciﬁcally, when classiﬁcation loss l s,i is given for bounding box i at scale s , the proposed loss function for MEH is deﬁned as
[Equation]
This loss encourages MEH to decrease model evidence
λ s,i when the classﬁcation loss l s,i is large; similarly, MEH is guided to increase λ s,i for small l s,i .
L MEH has the same effect as previous regularization loss (5) in that it prevents overconﬁdence and helps the model to predict uncertainty better; however, by using the target loss as a changeable supervisory signal, L MEH is able to dynamically penalize the model to better predict the model evidence.
Stability.
Note that we deliberately supervise only model evidence λ independently of Dirichlet parameters { α k } Kk =1 to train MEH.
λ is utilized only for re-scaling the Dirichlet strength and λ has no effect on p ( x | θ ) or ˆ p k , since λ will naturally vanish when division α k /S occurs.
Hence, the
MEH network Φ MEH and remaining network Φ \ Φ MEH can be updated in a disjoint manner.
We in turn optimize Φ MEH and Φ \ Φ MEH , thus training of Φ MEH never affects the performance of the primary object detector; this resolves the stability issue of previous EDL approaches.
Applications to recent models.
Our method is not limited to softmax-based object detectors like
SSD (Liu et al., 2016), but also applicable to sigmoid-based detectors like RetinaNet (Lin et al., 2017).
Given sigmoid-based prediction p ∈ [0 , 1] , focal loss can be deﬁned as FL ( p t ) =
− (1 − p t ) γ log( p t ) where p t = p if y = 1 , p t = 1 − p otherwise.
To enable evidential learning, we replace sigmoid-based binary prediction p by Dirichlet-Categorical multiclass prediction p ( x | α ) of equation (3).
We train RetinaNet with the modiﬁed evidential focal loss and report its performance in Fig.
3. H IERARCHICAL U NCERTAINTY A GGREGATION
Based on the epistemic uncertainty of a bounding box, we propose HUA: a new method for computing the ﬁnal informativeness score of an image.
Recent active learning methods for object detection (Yuan et al., 2021; Choi et al., 2021; Yu et al., 2021) typically compute the informativeness of an image as the mean or maximum of all bounding boxes.
To this end, we propose a generalized framework that can apply different kinds of aggregation functions based on the level of information (predicted category, box size, nearby object) of each bounding box, as described in Fig.
Filtering bounding boxes.
Single-stage object detectors such as RetinaNet and SSD generate bounding boxes at every scale, pixel and anchor.
Since most boxes correspond to background, we ﬁrst ﬁlter out background boxes whose max k
(ˆ p k ) is lower than threshold γ score .
Realigning bounding boxes.
Besides the uncertainty score, each bounding box contains much more information: predicted object, scale and category it belongs to.
Based on these information, we propose to realign the boxes into a hierarchical structure.
First, boxes are matched to the nearest object depending on the IoU score.
For example, in Fig.
2a, the blue box is matched to “object”, but the green box is ignored since IoU is lower than the threshold γ IoU .
Secondly, boxes are further grouped based on the scale to which they belong.
Lastly, boxes are divided based on the category ( argmax k ˆ p k ) to which they belong.
See Fig.
2b for the resulting hierarchy of bounding boxes.
Uncertainty aggregation.
Once the bounding boxes are fully realigned, individual uncertainty scores are uniﬁed in a hierarchical order.
As shown in Fig.
2b, uncertainties of the boxes in a lower level (e.g., class) are aggregated into a single value through a predeﬁned aggregation function;
[Figure]
human human human cow horse cow cow horse objectobjectobject𝑏𝑜𝑥 𝑏𝑜𝑥 𝑏𝑜𝑥 𝑏𝑜𝑥 𝑏𝑜𝑥 𝑏𝑜𝑥 𝑏𝑜𝑥 𝑏𝑜𝑥 sum sum sum
[Figure]
the aggregated value is then passed to an upper level (e.g, scale).
This aggregation repeats from the “class level” to “object level”.
Note that HUA can be viewed as a generalized scheme where different types of aggregation functions can be adopted at different levels of information; it can cover aggregation methods of previous works (Choi et al., 2021; Yuan et al., 2021) where identical functions (max or mean) are applied to the every level.
As discussed in Appendix, we speciﬁcally propose to adopt sum operation when aggregating the uncertainties at the object level, since this reﬂects the number of objects in ﬁnal informativeness of the image.
We also propose to apply sum operation to the class level.
Given that ambiguous bounding boxes are often classiﬁed into more than one class, considering these classes altogether helps to increase the uncertainty score of the difﬁcult object.
By considering the attributes of each bounding box, HUA effectively captures the context within the image in the informativeness score.
3. S ELECTION OF I NFORMATIVE I MAGE
Now the epistemic uncertainties of all unlabeled images can be computed at each active learning cycle.
While previous works typically select the top- k uncertain images, we propose to select from the ﬁltered-out images as well.
These images are also valuable since the model was incapable of sensing any objects due to lack of knowledge.
Composing a certain fraction of selections with these images further improves the performance, where the detailed analysis is provided in Appendix.
E XPERIMENTS 4. E XPERIMENTAL S ETUP
Dataset.
Our work is validated on PASCAL VOC (Everingham et al., 2010) and MS-COCO (Lin et al., 2014).
As to PASCAL VOC, VOC07+12 trainval is used for training and VOC07 test is used for evaluation.
While mAP50 is used for evaluation metric in PASCAL VOC, mean of mAP at IOU=.50:.05:.95 is used for MS-COCO.
In the ﬁrst cycle for PASCAL VOC, 5% from 16, samples are randomly selected.
Then 2.5% of samples are labeled at each cycle until reaching 20%.
As for MS-COCO with 117,267 samples, labeled sets increased from 2% to 10% in steps of 2%.
Implementation details.
For fair comparisons with previous works (Yuan et al., 2021; Agarwal et al., 2020; Yoo & Kweon, 2019), we adopt RetinaNet (Lin et al., 2017) and SSD (Liu et al., 2016) which use ResNet50 and VGG16 as backbones, respectively.
The structure of MEH is the same as the regression head except that the dimension of the output layer is one.
As for RetinaNet, we follow the setting of (Yuan et al., 2021) and set epoch to be 26, batch size to be 2; also, we follow the setting of (Yoo & Kweon, 2019; Agarwal et al., 2020) for SSD and set epoch to be 300, batch size to be 32.
In both experiments on PASCAL VOC and MS-COCO, SGD optimizer is used with a learning rate of 0 .
001 ; (cid:96) 2 weight decay rate of 0 . 0001 ; momentum of 0 . 9 ; warm-up strategy for the early 500 steps.
As for the backbones, ResNet50 and VGG16 are pretrained on ImageNet.
Note that at every cycle, the object detector is trained from scratch with the pretrained backbone.
We implement our framework using Pytorch 1.5.0 and mmdetection 2.13.0.
In every experiment, single NVIDIA
GeForce RTX 2080Ti is used.
We set the conﬁdence threshold for box ﬁltering γ score to 0.3, and
IoU threshold for object grouping γ IoU to 0.5.
500 ensemble members θ are sampled for uncertainty [Figure] [Figure] estimation.
For our scheme, (sum, max, sum) operations are adopted for each information level (object, scale, class) when applying HUA.
Ablation studies with different operations are provided in Appendix.
We compose 15% of selections with ﬁltered images, where the results with various selection ratios are reported in Appendix.
Baselines.
We compare our work with state-of-the-art works: MI-AOD (Yuan et al., 2021), CDAL (Agarwal et al., 2020), LL4AL (Yoo & Kweon, 2019), Core-set (Sener & Savarese, 2017), CALD (Yu et al., 2022).
Also, as basic baselines, Entropy Sampling (Roy et al., 2018), Random Sampling with vanilla RetinaNet/SSD are considered as well.
For Core-set, features from backbone (ResNet50/VGG16) are used following the setting of (Yoo & Kweon, 2019; Choi et al., 2021).
While Random Sampling randomly selects unlabeled samples to be labeled for the next cycle, Entropy Sampling selects the samples based on Shannon entropy; the average value of Shannon entropy among all of bounding boxes is regarded as the informativeness as done in (Yuan et al., 2021; Choi et al., 2021; Roy et al., 2018).
Five independent networks are trained with different seeds and the averaged performance is reported with 95% conﬁdence interval.
4. M AIN E XPERIMENTAL R ESULTS
Comparison with state-of-the-arts.
Fig.
3 shows mAP scores under various settings.
Our proposed method exhibits a clear edge over other baselines giving the best performance.
In Figs.
3a and 3c, the proposed method shows superiority in early cycles, proving that the proposed evidential focal loss is effective when labeled data is extremely limited.
It is noteworthy to consider our method is trained only on labeled set, while MI-AOD beneﬁts from semi-supervised learning using unlabeled set as well.
In Fig.
3b, the reason SSD has lower initial performance than RetinaNet comes from the difference of the loss function.
Unlike RetinaNet trained with focal loss, SSD is trained with
CE loss.
As in equation (3), since we calculated α using a softmax, the loss expression does not change at all in the case of SSD.
Still, it is remarkable that our proposed methods (MEH and HUA) gradually increase the performance by selecting informative images even with the same loss.
Comparison with multi-model based Bayesian methods.
In recent active learning works, multimodel based methods are used to compute epistemic uncertainty.
Here, we compare existing methods and our work.
As for baselines, we ﬁrst consider MC-dropout; following (Beluch et al., 2018;
Choi et al., 2021), dropout layers whose rate is 0.1 are added to the convolutional layers andforward passes are sampled to compute epistemic uncertainty using equation (1).
Secondly, model ensemble is considered, where we follow (Haussmann et al., 2020; Choi et al., 2021) and train three independent models to construct an ensemble.
Lastly, we consider the work of (Choi et al., 2021); it predicts the parameter of Gaussian mixture model (GMM) and regards the variance of Gaussian modes as the epistemic uncertainty.
In every baseline, we average uncertainties from all bounding boxes for the computation of the ﬁnal image-level uncertainty, as done in (Yuan et al., 2021; Choi et al., 2021; Roy et al., 2018).
In Fig.
4, we ﬁrst observe that multi-model based methods yield higher scores than random sampling, underlying the importance of epistemic uncertainty.
Still, large performance gap between the baselines and our work conﬁrms the beneﬁts of the proposed techniques: MEH and HUA.
It is noteworthy that baselines ignore the hierarchy between bounding boxes, which implies there possibly exists important yet underestimated boxes.
4. A BLATION S TUDIES AND D ISCUSSIONS
Effects of MEH and HUA.
Table 7 shows ablation studies on the proposed methods.
While Random and Entropy use vanilla RetinaNet with focal loss, proposed methods use the proposed evidential focal loss.
While ReLU computes α with ReLU as done in (Sensoy et al., 2018;
Zhao et al., 2020;
Hemmer et al., 2022), Softmax uses softmax.
All methods except HUA compute uncertainty of an image as the mean of all boxes, as in (Yuan et al., 2021; Choi et al., 2021).
At every cycle, proposed methods (Softmax, MEH, HUA) increase the performance by a large margin.
The results indicates that informativeness of images can be captured much better via our proposed methods.
Interestingly, it can be seen that ReLU method performs even worse than Random .
This result conﬁrms that previous works of EDL for image classiﬁcation cannot be simply applied to object detection.
[Table]
Comparison of computing costs.
In Table 2, we compare computing costs of the proposed method with multi-model based baselines (MC-dropout, Ensemble ) and Entropy baseline.
Speciﬁcally, the ﬁrst column indicates the latency time for uncertainty calculation of a single image with a 95% conﬁdence interval and the second column shows the size of all parameters in the models.
It can be seen that the proposed method has a similar model size to that of MC-dropout and Ensemble baselines; a slight increase is due to the MEH module.
With respect to the latency time, multi-model based methods require signiﬁcant computing cost because of multiple forward propagations for MC integration.
Speciﬁcally, MC-dropout and Ensemble takes 25 and 3 forward passes, respectively.
In comparison, our method requires much less latency time, although it samples 500 ensemble members Cat ( θ ) .
This is because our method requires only single forward propagation and each ensemble member is sampled virtually (i [Table] e., θ ∼ Dir ( θ | α ) ).
Note that Entropy has the lowest latency, since this method dose not use epistemic uncertainty and there is no need to sample ensemble members. [Table]
Visualization analysis of model evidence λ .
To clearly understand the role of model evidence λ , we illustrate the effect of the λ in Fig.
In the 2 nd column, when model evidence λ is not considered, uncertain regions are observed over a wide area inside the object.
On the other hand, in the 3 rd column, MEH estimates high λ only around the center of objects.
This is because the difﬁculty of classiﬁcation increases as the center of the bounding box moves away from the center of objects due to ambiguity.
The MEH output, λ , is used to readjust the prior Dirichlet distribution Dir ( θ | α ) .
As noted in Section 3.2, high λ increases Dirichlet strength and make D ( θ | α ) concentrated.
It makes similar θ ∼ Dir ( θ | α ) be sampled and decreases the epistemic uncertainty according to equation (1).
For example, in the 4 th column, it can be seen that the uncertainty of the central part of the object is reduced due to high λ ; conversely, the uncertainty of the edge part of the object is preserved high.
[Figure]
Examples of easy and hard samples.
In Fig.
6, for intuitive understanding, we compare uncertainties of easy and hard samples with Entropy Sampling (Roy et al., 2018), and MI-AOD
(Yuan et al., 2021) which represent SoTA.
In all methods, easy examples tend to have just one unoccluded object; however, hard examples tend to have numerous objects, which are unclear or heavily occluded.
One interesting thing to note is that the difference in informativeness scores between the easy samples and the hard samples.
In previous methods, the range of scores between images is not wide, since these methods average the uncertainties of all bounding boxes to get a single score.
On the other hand, in the proposed method, it can be seen that the informativeness scores of the hard examples are more than 50 times higher than those of the easy examples.
This is because the proposed uncertainty aggregation scheme (HUA) adds up informativeness scores of meaningful bonding boxes with consideration for additional information (e [Figure] g., the number of objects, categories in images).
[Figure]
C ONCLUSION
We proposed a new active learning strategy for object detection.
With the evidential deep learning framework and model evidence head, our scheme effectively estimates the epistemic uncertainty of a bounding box.
Also, our hierarchical uncertainty aggregation provides a new guideline for computing informativeness of an image.
Our scheme presents an up-and-coming direction for active object detection [Figure] where estimating epistemic uncertainty accurately yet quickly is of crucial importance [Figure]
R EPRODUCIBILITY S TATEMENT
To ensure reproducibility, we provide theoretical proof and implementation details in Appendix.
Speciﬁcally, our experimental setup including hyperparameter setting is described in Appendix and our source codes are included in Supplementary Material.
A A PPENDIX B A DDITIONAL E XPERIMENTAL S ETUP
In this section, we provide more detailed information on our experimental setting.
Following previous works, two well-known object detectors are chosen as base models: RetinaNet (Lin et al., 2017) and SSD (Liu et al., 2016).
First, RetinaNet adopts ResNet-50 which is pretrained on ImageNet as backbone.
ResNet-50 has four stages and output of each stage is passed to the neck structure.
Output dimension of each stage is 256, 512, 1024, 2048, respectively.
Parameters of the backbone in the ﬁrst stages are frozen during training.
As for the neck structure, Feature Pyramid Network (FPN) with ﬁve stages is adopted.
FPN takes the output of ResNet as input and returns 256-dimensional features at the every stage.
Output of FPN is then goes through a classiﬁcation head and a regression head, independently.
Structure of the classiﬁcation head and the regression head are the same as that of vanilla RetinaNet (Lin et al., 2017) which consist of three convolutional modules and one last convolutional layer for classiﬁcation and regression, respectively.
Following (Lin et al., 2017; Yuan et al., 2021), we utilize an bounding box generator whose octave base scale is 4; scales per octave is 3; ratios of bounding boxes are (0.5, 1.0, 2.0).
Base sizes of boxes are (8, 16, 32, 64, 128) from the lowest scale to the highest scale.
Coordinates of bounding boxes and ground truth are encoded to the delta and considered as the target value of regression head.
Speciﬁcally, given central coordinates ( x, y ), width ( w ) and height ( h ) are given for the bounding box ( px, py, pw, ph ) and the ground truth ( gx, gy, gw, gh ), values of delta is computed as:
[Equation]
py ph , dw = log ( gwpw ) , dh = log ( ghph ) .
Regression heads are supervised to predict the encoded value ( gx, gy, gw, gh ) and these values are decoded to the coordinates of the uppermost left corner and the lowermost right corner to make the ﬁnal prediction.
Regarding the loss, as stated in the main paper, Focal loss (Lin et al., 2017) with marginal likelihood is adopted.
Hyperparameters for focal loss ( γ, α ) are set to 2.0 and 0.25, respectively.
As to assigning positive/negative boxes, bounding boxes whose IoU scores with the ground truth are higher than 0.5 are assigned to the positive box; boxes with iou scores greater than 0.4 and less than 0.5 are assigned as negative boxes and all remaining boxes are ignored.
As for evaluation, 1000 bounding boxes with the highest conﬁdence are used for Non-Maximum Suppression (NMS).
IoU threshold for NMS is set to 0.5 and the number of boxes after NMS is at most 100.
Secondly, SSD adopts VGG-16 which is pretrained on ImageNet as backbone.
Following (Liu et al., 2016), the backbone of SSD has extra layers to generate multi-scale feature maps.
After these layers, six levels of features are created with dimensions of (512, 1024, 512, 256, 256, 256) and these features are taken as inputs to the classiﬁcation head and the regression head.
The same encoding/decoding scheme as RetinaNet was used.
Different from RetinaNet, hard negative mining is applied to assign positive/negative boxes; speciﬁcally, three times more negative boxes than positive boxes are assigned.
As for evaluation, the same NMS scheme is adopted as RetinaNet except the number of bounding boxes after NMS is set to 200.
For both models, SGD optimizer is used with learning rate of 0.001; momentum of 0.9 and weight decay of 0.0001.
C A LGORITHM D ESCRIPTION
The detailed procedure of the proposed active object detection method is given in Algorithm 1.
D P ROOF OF M ARGINAL L IKELIHOOD L OSS
We consider Dirichlet-Categorical Bayesian framework where low-order predictive distribution parameters θ are sampled from the high-order prior distribution (i.e., θ ∼ Dir ( θ | α ) and θ parameterizes categorical likelihood Cat ( θ ) .)
To train our evidential model, we maximize the marginal likelihood which is given as below:
[Equation]
which is equivalent to
[Equation]
The above integral can be simpliﬁed using an useful trick.
Given Dir ( θ | α ) , integrating probability density function over θ results in one:
[Equation]
Dividing the above equation by a constant part which is not involved in the integration gives the following result:
[Equation]
Now we can regard equation (8) as the integration over ”shifted parameter” (i.e., α j + 1 { y j = i } ).
This shift of parameter changes the equation (10) to:
[Equation]
Considering the case when y j = i separately, the above equation (11) can be written as:
[Equation]
Now we can use the fact that Γ( x + 1) =
x Γ( x ) to simplify the above equation as:
[Equation]
By substituting the result of the above equation in the integral of equation (8)
[Equation]
we obtain:
[Equation]
E A NALYSIS OF T HRESHOLD V ALUES
To understand the HUA better, we investigate the effect of each threshold value: γ score , γ IoU .
We vary the thresholds and report the results in Table 3.
Note that aggregate functions (Sum, Max,
Sum) is applied to information levels (Object, Scale, Class) in all tries for fair comparison.
It can be seen that higher γ IoU increases the performance.
This is because excessively low thresholds cause too many unnecessary bounding boxes to be taken into account, thus deteriorating the quality of estimated informativeness.
Otherwise, too high or too low γ score impairs the quality of ﬁltering and degrades the ﬁnal performance. [Table] [Table]
[Table]
F A NALYSIS OF HUA
Fig.
7 visualizes how HUA works in detail.
Note that aggregation functions (Sum, Max, Sum) is chosen for (Object, Scale, Class).
First, it can be seen that unclear or occluded objects have high uncertainty.
For example in left image, occluded boats in the left side show higher uncertainty than the one in the right side.
It can also be seen that uncertainties of numerous objects within left image are summed and contribute to the higher informativeness score.
Note that since aggregation function for ”Class” is ”Sum”, bounding box which is classiﬁed into multiple classes simultaneously is supposed to have high uncertainty.
For example in the right image, a head of horse in the right image is classiﬁed into horse and cow at the same time; bounding boxes which predict either category are separated into independent groups, and uncertainty for each category group is computed independently and summed together.
[Figure]
G C OMPARISON WITH OTHER L OSS T YPE FOR MEH
For the training of MEH, Mean Square Error ( MSE ) loss is adopted for regression of the target loss.
In this section, we further investigate performances of other typical losses which are well-known for the regression problem.
Table 4 compares the mAP50 score on PASCAL VOC with RetinaNet as the base model.
The method MAE indicates Mean Absolute Error; given prediction ˆ y and ground truth y , Loss ( y, ˆ y )
=
| y − ˆ y | .
The MSLE method refers to Mean Squared Logarithmic Error, (i.e., Loss ( y, ˆ y )
= ( log ( y + 1) − log (ˆ y + 1)) 2 ).
Experimental results show that general losses for regression are all effective, yet MSE loss shows the best result.
[Table]
H A NALYSIS ABOUT THE S ELECTION R ATIO OF F ILTERED S AMPLES
In this section, we compare performance of the proposed method varying the selection ratio of ﬁltered samples.
Note that bounding boxes whose conﬁdence value is lower than γ score are ﬁltered out to ignore predictions for background.
This scheme naturally makes the informativeness score of any image to zero, if all bounding boxes in the image are unconﬁdent.
We stress that these images with zero informativeness are important since the object detector is unable to ﬁnd any object due to its lack of knowledge.
In Table 5, it can be seen that taking some portion of these images of zero informativeness into account helps to increase the performance.
This is because training with ﬁltered images provides the model to experience difﬁcult objects from unfamiliar categories.
However, including too much ﬁltered images into the labeled set of the next stage rather impair the performance.
This is because some objcets with low conﬁdence are too small/large or heavily occluded enough to interfere with training of the detector.
[Table]
I C OMPARISON OF AGGREGATION FUNCTION
An obvious question in HUA is: which combination of aggregation functions yields the best performance?
In Table 6, we compare three types of functions: Avg, Max, Sum.
In all tries, γ score , γ IoU is set to 0.3, 0.9, respectively.
We try various combinations applying different aggregation functions in each level of information.
It can be seen (Sum, Max, Sum) gives the best performance exhibiting a large margin over naive aggregation schemes of (Choi et al., 2021; Yuan et al., 2021).
Besides, sum operation is observed to perform the best for “Object”, since it reﬂects the number of objects inside an image.
Likewise, sum operation shows the best result for “Class”.
It conﬁrms the importance of considering uncertainties from ambiguous classes together.
Otherwise, max operation prevails for “Scale”.
Since predictions can appear at various scales depending on the shape of the object regardless of the amount of information, it seems that the quality of uncertainty is rather impaired if all scales are considered.
Function
Ratio (%) of Labeled Samples (Obj, Scale, Class) 5.
[Table]
[Table] [Table]
) (Yuan
[Table]
(Avg, Avg, Sum) 52. (Avg, Sum, Sum) 52.
(Avg, Max, Sum) 52. (Max, Avg, Sum) 52.
(Max, Max, Max) (Choi et al., 2021)
[Table]
(Sum, Sum, Sum)
[Table]
(Sum, Max, Avg) [Table] [Table]
[Table]
J D ETECTION OF N OISY L ABELS
[Figure]
In active learning work, generally, it is assumed that a perfect oracle generates 100% accurate labels to unlabeled samples, so that the main focus of existing active learning works (including our work) becomes effectively seleting the informative samples under the assumption with no label noise.
In this section, we deal with an interesting question: how should we handle the label noise issue when human annotations are not 100% accurate?
Orthogonal to the existing active learning methods, a simple way is to utilize a new module that identiﬁes the noisy labels and re-label them or exclude them during training.
As illustrated in works of (Bernhardt et al., 2022; Younesian et al., 2021), cross-entropy is commonly adopted to detect the mislabeled samples in noise-robust learning literatures.
To demonstrate the capability our model of detecting noisy labels, we present simple toy examples in Figure 8.
To reproduce the noisy label, we change labels ( y ) of some bounding boxes to other similiar categories (e.g., horse → cow), and compute the cross entropy using the probability distribution ( ˆ y ) of Equation 3 for comparison.
As can be seen in Figure 8, bounding boxes with wrong labels show much higher cross entropy, ensuring opportunities to cope with noisy labels.
[Figure]
K A NALYSIS ON HUA WITH RESPECT TO THE NUMBER OF OBJECTS
As can be seen in Figure 6, HUA calculates image informativeness considering various information inside the image (number of objects, difﬁculty of each object), which makes the uncertainty scores of hard examples signiﬁcantly higher than those of easy examples.
However, this characteristic of HUA raises the following question: Does HUA favor only complex images with many objects?
Wouldn’t it be possible to replace HUA by simply selecting images in which many objects appear?
To answer these question, we investigated the relationship between the number of objects in the image and the uncertainty score, and found that a large number of objects does not always lead to a high uncertainty score, as shown in Figure 9.
This is because the resulting uncertainty of an image depends not only on the number of objects but also on the uncertainty value of each object .
For example, in the image on the left of Figure 9, there exists two objects, but the total uncertainty is higher than that of the right image, because the bounding boxes corresponding to the objects are classiﬁed as people and motorbikes at the same time.
On the other hand, since the objects in the right image are easy objects that are clearly classiﬁed only as people, the uncertainty of all ﬁve objects is not too large.
L A NALYSIS ON THE ORDER OF HUA
In this section, we investigate the effect of the aggregation order in HUA to provide additional insight.
Under the same conditions as the experiment conducted in the main manuscript, we only changed the order of scale and class, i.e., the aggregation hierarchy in HUA is changed from ”object (sum) ← scale (max) ← class (sum)” to ”object (sum) ← class (sum) ← scale (max)”.
As shown in the table below, the performance is degraded compared to the proposed scheme when we switch the order.
[Table]
We interpret this result as follows: 1) Since most objects do not span to multiple scales (they mostly span to 1 ∼ 2 scales), there is little difference even if the order of class and scale have changed. 2)
If the order is changed, uncertainty values from multiple scales may be mixed into a single informativeness score of one object.
Rather, it seems more appropriate to focus on a single informative scale to compute the score of the image.
Overall, both intuitively and experimentally, the original order is more powerful and makes more sense.
M A NALYSIS ON GENERALITY OF HUA
To demonstrate the generality of the proposed HUA, we conducted additional experiments.
We combined traditional methods (Roy et al., 2018; Yuan et al., 2021) with HUA and reported the performance gain in Table 8.
[Table]
As shown in the table, HUA generally improves the performance in both cases.
This is because
HUA helps to better understand the context within images by considering the information hierarchy (e.g., class, object, scale), than just taking the maximum value of the uncertainties of all bounding boxes as done in (Roy et al., 2018; Yuan et al., 2021).
This result conﬁrms the intuition that existing works can be enhanced by adopting HUA for uncertainty aggregation.