# Multi-clue Consistency Learning to Bridge Gaps Between General and Oriented
Object in Semi-supervised Detection

Chenxu Wang  Nanjing University of Science and TechnologyNanjingChina
<EMAIL_ADDRESS>,  Chunyan Xu  Nanjing University of Science and
TechnologyNanjingChina ,  Ziqi Gu  Nanjing University of Science and
TechnologyNanjingChina and  Zhen Cui  Nanjing University of Science and
TechnologyNanjingChina

###### Abstract.

While existing semi-supervised object detection (SSOD) methods perform well in
general scenes, they encounter challenges in handling oriented objects in
aerial images. We experimentally find three gaps between general and oriented
object detection in semi-supervised learning: 1) Sampling inconsistency: the
common center sampling is not suitable for oriented objects with larger aspect
ratios when selecting positive labels from labeled data. 2) Assignment
inconsistency: balancing the precision and localization quality of oriented
pseudo-boxes poses greater challenges which introduces more noise when
selecting positive labels from unlabeled data. 3) Confidence inconsistency:
there exists more mismatch between the predicted classification and
localization qualities when considering oriented objects, affecting the
selection of pseudo-labels. Therefore, we propose a Multi-clue Consistency
Learning (MCL) framework to bridge gaps between general and oriented objects
in semi-supervised detection. Specifically, considering various shapes of
rotated objects, the Gaussian Center Assignment is specially designed to
select the pixel-level positive labels from labeled data. We then introduce
the Scale-aware Label Assignment to select pixel-level pseudo-labels instead
of unreliable pseudo-boxes, which is a divide-and-rule strategy suited for
objects with various scales. The Consistent Confidence Soft Label is adopted
to further boost the detector by maintaining the alignment of the predicted
results. Comprehensive experiments on DOTA-v1.5 and DOTA-v1.0 benchmarks
demonstrate that our proposed MCL can achieve state-of-the-art performance in
the semi-supervised oriented object detection task. The code will be available
at https://github.com/facias914/sood-mcl

##  1\. Introduction

The fully-supervised object detection in aerial images (Xia et al., 2018; Han
et al., 2021; Xie et al., 2021; Li et al., 2023) has achieved remarkable
success in the past few years. However, labeling a large amount of accurate
annotations is labour-consuming, especially for oriented dense objects. To
reduce the annotation burden, the semi-supervised object detection (SSOD)
attempts to leverage both labeled data and unlabeled data for boosting the
detector performance. Existing advanced SSOD methods, which mainly adopt the
self-training framework (Liu et al., 2021; Li et al., 2022a; Liu et al., 2022;
Wang et al., 2023) to employ these unlabeled data, have achieved significant
performance in general scenes. However, they encounter various challenges in
handling the oriented object detection task due to the tricky characteristics
such as arbitrary rotation angles, large aspect ratio changes and dense
arrangement. This prompts us to study the performance gaps between general and
oriented object detection when performing semi-supervised learning.

With comprehensive investigations in Section 3.2, we figure out that the
performance of SOOD is significantly hindered by three gaps and inconsistency
problems. Specifically, the sampling inconsistency represents that the
positive labels selected from labeled data are inconsistent with the
supervision information required by the oriented objects. It is caused by the
sub-optimal center-based label assignment and the gap in aspect ratio
distribution between general and oriented objects. That is to say, oriented
objects usually have more extreme aspect ratio distributions than general
ones, while the center-sampling strategy only focuses on the center region,
which results in the discriminative information of large aspect ratio objects
distributed at the edge being assigned as background, affecting the
optimization of the detector.

Figure 1. The pipeline of our MCL. To address the sampling inconsistency
issue, the Gaussian Center Assignment is introduced to select more accurate
pixel-level positive labels from labeled data. The Scale-aware Label
Assignment is proposed to select pixel-level pseudo-labels for objects with
various scales. The Consistent Confidence Soft Label is adopted to mitigate
the mismatch problem between classification and localization qualities through
maintaining the alignment of the predicted results.

In addition, the assignment inconsistency denotes that the predicted oriented
pseudo-boxes from unlabeled data are difficult to guide the semi-supervised
learning process, resulting in noisy label assignment. In general, most
advanced SSOD methods (Li et al., 2022a; Wang et al., 2023; Zhang et al.,
2023) follow the pseudo-boxes paradigm (Sohn et al., 2020) that using the
pseudo-boxes predicted by teacher model act as the supervised signals to
optimize the student model. However, the introduction of angle parameters in
rotated pseudo-boxes makes their localization quality less controllable than
that of horizontal ones. Under the guidance of low-quality rotated pseudo-
boxes, noisy labels are inevitably introduced during the label assignment
process. Moreover, even with the aid of NMS (Non-Maximum Suppression) and
threshold filtering, it is impossible to guarantee there are not redundant
boxes which will bring additional noisy labels.

On the other hand, the confidence inconsistency indicates that there exists
the mismatch between the predicted classification and localization qualities,
affecting the selection of pseudo-labels. Prior researches (Sun et al., 2021;
Xu et al., 2021; Li et al., 2022a) have validated that the classification
score is unable to measure the localization quality, and the lack of
interaction between the two confidences causes an inconsistency in
predictions, leading to sub-optimal pseudo-label selection results. Moreover,
while numerous researches have studied the proxy localization quality of
horizontal box, there is a lack of research for oriented boxes. Our
experiments show that there remains a gap in the representation of
localization quality between horizontal and oriented boxes, while sub-optimal
proxy localization quality also affects the performance of oriented object
detection.

Based on the above observations, we propose a Multi-clue Consistency Learning
(MCL) framework to boost the performance of the SOOD task through bridging
multi-gaps between general and oriented object detection in semi-supervised
learning process. Figure 1 illustrates the pipeline of MCL. Specifically, to
address the sampling inconsistency problem, we introduce the Gaussian Center
Assignment (GCA) strategy to select more accurate positive labels from the
limited annotated data. Here each oriented object region can be represented as
a $2D$ Gaussian Distribution (Yang et al., 2022) according to its
corresponding ground truth box, which can be adopted to guide the pixel-level
positive label selection. In addition, the normalized distance to the center
of the object (termed centerness) can be formulated as a $2D$ Gaussian
distribution, which is used to better measure the localization quality of each
pixel-level positive label. Compared to other label assignment strategies
(Ming et al., 2021; Hou et al., 2022; Xu et al., 2022, 2023) for fully-
supervised detection, our designed GCA can not only extract more comprehensive
target information from limited labeled data but also avoid the performance
degradation caused by the sampling inconsistent supervision of large-ratio
aerial objects.

To mine accurate potential information from a large amount of unlabeled data,
we would resist the assignment and confidence inconsistency. As for the
assignment inconsistency, we propose the Scale-aware Label Assignment (SLA)
method to select pixel-level pseudo-labels instead of unreliable pseudo-boxes,
which adopts a divide-and-rule strategy to develop different pseudo-labels
selection rules for objects with different scales. For small objects, a
coarse-to-fine pseudo-label selection is used to filter high quality pseudo
labels from dense features, which can preserve only a few candidates with both
high classification and localization qualities. For large-scale objects with
sparse features, we just use a score threshold filtering mechanism to maintain
scale balance. Different from the previous dense pseudo-labels assignments
(Zhou et al., 2022; Liu et al., 2023a) used in general scenes, our proposed
SLA is more suitable for various scale objects in oriented object detection
and then select more reliable pixel-level pseudo-labels from the unlabeled
data.

To address the confidence inconsistency problem, we employ the soft label (Li
et al., 2020) that the value at the ground-truth category index indicates its
corresponding localization quality, replacing the one-hot label to supervise
the classification branch learning. However, there is a gap in the proxy
representations of localization quality between horizontal and oriented boxes.
Through experimental analysis in Section 3.2, we find that centerness (Tian et
al., 2019) can effectively represent the localization quality of the oriented
box and outperforms the predicted IoU (Intersection over Union) used on the
horizontal box (Li et al., 2020; Liu et al., 2023a). Thereby we propose the
Consistent Confidence Soft Label (CCSL) based on centerness to further promote
the selection of pseudo-labels through mitigating the inconsistency problem.
Prior to this, we have not seen any work on the localization quality
representation of oriented box. In conclusion, our contributions are
summarized as follows:

  * •

We look deep into the gaps between general and oriented object detection in
semi-supervised learning, and then propose a multi-clue consistency learning
framework to improve the performance of SOOD task.

  * •

To address three inconsistency problems, we specially design the Gaussian
Center Assignment, the Scale-aware Label Assignment, and the Consistent
Confidence Soft Label methods to mine more instructive supervised signals from
the annotated data and unlabeled training data.

  * •

Comprehensive evaluations and comparisons demonstrate that our MCL achieves
state-of-the-art performance on DOTA-v1.5 and DOTA-v1.0 benchmark (Xia et al.,
2018).

##  2\. RELATED WORK

Semi-supervised Object Detection. Most of previous methods (Liu et al., 2021;
Yang et al., 2021; Li et al., 2022c, d; Liu et al., 2023b; Zhang et al., 2023;
Nie et al., 2023) are inherited from the Mean Teacher paradigm (Tarvainen and
Valpola, 2017), where the teacher model is updated via Exponential Moving
Average (EMA) of the student weights and produce pseudo labels over unlabeled
data as ground truth for training the student model. Under this scheme, the
quality and precision of pseudo labels play a substantial role. ISMT (Yang et
al., 2021) maintains a memory bank to ensure the consistency of pseudo labels
across various iteration stages. Unbiased Teacher (Liu et al., 2021) applies
Focal Loss (Lin et al., 2017b) to tackle the class-imbalance pseudo labels
issues. Soft Teacher (Xu et al., 2021) employs a box jittering argumentation
to select reliable pseudo labels. For misleading instances, Unbiased Teacher
v2 (Liu et al., 2022) selects pseudo labels through utilizing uncertainty
predictions. Consistent Teacher (Wang et al., 2023) dynamically adjusting the
threshold for pseudo labels filtering. Mix Teacher (Liu et al., 2023b)
enhances the quality of pseudo labels through mixed-scale prediction.
Different from these, some methods (Zhou et al., 2022; Li et al., 2022b; Liu
et al., 2023a) directly use the dense predictions of the teacher model as
pixel-level pseudo-labels for semi-supervised learning. However, since the
usage scenarios of oriented object detection are more complex, there still
exist the performance gaps when applying these SSOD methods in semi-supervised
oriented object detection.

Semi-supervised Oriented Object Detection. Oriented object detection requires
predicting rotated bounding boxes by adding an angle parameter in the
regression task, posing significant challenges for controlling the quality and
accuracy of pseudo boxes. SOOD (Hua et al., 2023) uses the absolute distance
of the predicted angle between the teacher and student models to weight the
regression loss. Additionally, it introduces the optimal transport cost
(Monge, 1781) to evaluate the global similarity of layouts between the
predictions of teacher and student. However, SOOD fails to recognize the root
issue hindering semi-supervised learning in oriented object detection, which
lies in how to eliminate inconsistency issues caused by the divergence of
general and oriented object detection. In this work, we dive into the
performance gaps between SSOD and SOOD methods, proposing a multi-clue
consistency learning method for semi-supervised learning in oriented object
detection.

Label Assignment in Oriented Object Detection. Previous works have (Zhang et
al., 2020; Ge et al., 2021; Kim and Lee, 2020) revealed that label assignment
plays a crucial role in object detection. For oriented object detection, DAL
(Ming et al., 2021) introduce matching degree to select anchors with high
prior and regression qualities. SASM (Hou et al., 2022) set dynamic IoU
thresholds decided by object shapes to filter prior anchors. In order to
achieve scale-balance learning for tiny objects, RFLA (Xu et al.,
2022)replaces the IoU-based or center sampling assignment with hierarchical
label assignment built on gaussian respective field, while DCFL (Xu et al.,
2023) develops the dynamic priors instead of static priors. Although these
assignment methods are effective, they are limited to fully-supervised
settings. With such over-designed label assignment strategies, the model is
insufficient to learn perfect target information from sparse labeled data. In
this work, we show that a simple changed sampling prior significantly improves
the performance of SOOD task.

Representation of Localization Quality. The representation of localization
quality has attracted increasing attention in general object detection task.
FCOS (Tian et al., 2019) utilize a separate branch to perform localization
quality estimation in the form of centerness. After that, GFL (Li et al.,
2020) points out that centerness is easier to get very small values in object
edge by its definition, making it perform consistently worse than IoU. In SSOD
task, several researches (Liu et al., 2022; Li et al., 2022a; Liu et al.,
2023a) also focus on accurately measuring the localization quality of pseudo
labels. For instance, PseCo (Li et al., 2022a) measures the localization
quality of pseudo labels by estimating the consistency of predicted proposals
(Ren et al., 2015) for two-stage detectors. Unbiased Teacher v2 (Liu et al.,
2022) reveals that the centerness is not reliable for reflecting whether a
prediction is a positive sample due to lack of background supervision. Thereby
it uses the predicted localization uncertainty of four box boundaries instead.
ARSL(Liu et al., 2023a) also replaces the centerness branch with the IoU
branch following the VFNet(Zhang et al., 2021) and GFL(Li et al., 2020).
However, none of these works are designed for rotating bounding boxes in
oriented object detection. In this work, we figure out that centerness is
still the best choice as the proxy localization quality and we will verify
this in Section 3.2.

##  3\. METHODOLOGY

To study the gaps between the general and oriented object detection in the
semi-supervised learning, we start from the classic SSOD framework (Tarvainen
and Valpola, 2017), as introduced in Section 3.1. We then experimentally
analyze the three inconsistency issues (Section 3.2). To mitigate the
inconsistency and bridge the gaps, we subsequently propose a Multi-clue
Consistency Learning (MCL) framework for the SOOD task. It mainly comprises
three modules: Gaussian Center Assignment (Section 3.3), Scale-aware Label
Assignment (Section 3.4), and Consistent Confidence Soft Label (Section 3.5).

###  3.1. The Basic SSOD Framework

We introduce the classic Pseudo-labeling SSOD framework inherited from Mean
Teacher (Tarvainen and Valpola, 2017) as our baseline, which adopts a rotated
FCOS version (Tian et al., 2019) as the detector. In general, the SSOD
framework comprises two branches: one dedicated to the supervised learning
branch and the other to the unsupervised learning branch. In the burn-in
stage, the student model undergoes pre-training with the limited annotated
data, where the supervised loss $\mathcal{L}^{s}$ is minimized by combining
classification, centerness, and regression. Simultaneously, the learned
weights of the student model are mirrored onto the teacher model. In the self-
training stage, the unlabeled training data with weak data augmentation is fed
into the teacher model to generate pseudo-labels. Subsequently, the student
model is further optimized with these generated pseudo-labels (i.e.,
supervised by $\mathcal{L}^{u}$), while the input comprises unlabeled data
augmented more aggressively. Meanwhile, the supervised learning with
$\mathcal{L}^{s}$ is maintained on the student network. The overall loss
function is thus formulated as
$\mathcal{L}=\mathcal{L}^{s}+\beta\mathcal{L}^{u}$, where $\beta$ is a hyper-
parameter regulating the impact of unsupervised learning. The network
parameters of the student model are continually updated onto the teacher
network through an exponential moving average (EMA) mechanism at each
iteration.

###  3.2. Inconsistency Analysis

Figure 2. Analysis of the sampling inconsistency on the general COCO and
aerial DOTA-v1.5 datasets. (a) Statistics of object aspect ratio distribution
on both datasets. (b) The class activation mapping of an aerial object with
large aspect ratio. (c) The positive label selection of an aerial object by
the common center sampling strategy, where the red points and blue points
represent negatives and positives, respectively.

Since oriented objects in aerial images have some specific characteristics
(e.g., the bird’s-eye view perspective, the complex environment, and the
variant scales of objects), the standard SSOD framework would encounter
various challenging problems when directly applied to the SOOD task. We
attempt to analyze the core components of the SSOD framework (including
positive label assignment and pseudo-label selection), and then find some
gaps/inconsistencies between general and oriented object detection in the
semi-supervised learning. Specifically, we conduct a series of experimental
analysis on two datasets representing general scenes and aerial perspectives,
namely COCO (Lin et al., 2014) and DOTA-v1.5 (Xia et al., 2018), respectively.
To ensure a fair comparison, we use the FCOS as the object detector on both
datasets.

Sampling Inconsistency: When employing these limited annotated data, the
common center sampling strategy is adopted to select positive labels for
general objects, but it is not suitable for oriented objects with larger
aspect ratios. For an intuitive understanding, we statistically analyze the
aspect ratio distributions of targets on the COCO and DOTA-v1.5 datasets, as
shown in Figure 2(a). More than 90% of objects are with the aspect ratios
exceeding 0.5 on the COCO dataset, thus the center sampling strategy can be
adopted to select positive points of the general objects, thereby providing
sufficient supervision signals. However, more than 70% of objects exhibit
aspect ratios less than 0.5 on the DOTA-v1.5 dataset, especially for some
objects with extreme aspect ratios (seen in Figure 2(b)) in the bird’s-eye
view perspective. As seen in Figure 2(c), only these blue points can be
selected as pixel-level positive points with the common center sampling
strategy, while these unselective red points would be seen as negative
background information, leading to incorrect guidance for the model
optimization. Therefore, the inconsistency between the shape-agnostic center
sampling and objects with large aspect ratios would cause the performance
degradation in the SOOD task.

Assignment Inconsistency. Compared with the horizontal object detection in the
general images, the localization of oriented objects in aerial images is more
challenging due to their arbitrary rotation angles. To elucidate this, we
conduct evaluations with the FCOS detector on the DOTA-v1.5 and COCO datasets,
and then utilize the Intersection over Union (IoU) metric between predicted
boxes and the corresponding ground-truth boxes to assess the localization
quality of the pseudo-boxes. As shown in Figure 3(a), we use different IoU
thresholds to obtain the pseudo-box precision under the same recall rate on
the DOTA-v1.5 and COCO datasets, respectively. With a lower IoU threshold, we
can achieve a higher precision on the DOTA-v1.5 dataset compared to the COCO
dataset, but the pseudo-boxes with the poor localization quality would affect
the detection optimization. Under the guidance of low-quality rotated pseudo-
boxes, noisy labels are inevitably introduced during the label assignment
process. When improving the requirement of localization quality by increasing
the IoU threshold (from 0.5 to 0.9) on both datasets, the detection precision
would severely drop from 84% to 17% on the DOTA-v1.5 dataset, while it will be
also reduced from 76% to 54% on the COCO dataset. A large number of redundant
noisy boxes caused by reduced precision can also introduce the noisy labels.
Hence, it’s hard to achieve a trade-off between the precision and localization
quality of rotated pseudo-boxes, and the assignment inconsistency problem
should be addressed to guide the semi-supervised learning process.

Figure 3. Investigation on the assignment and confidence inconsistency
problems. (a) The pseudo-box precision of the DOTA-v1.5 dataset and COCO
dataset under different IoU thresholds. (b) The top heat-map illustrates the
consistency of centerness and IoU between ground truth boxes and their
corresponding true positive boxes on the DOTA-v1.5 dataset, while the bottom
one is on the COCO dataset.

Confidence Inconsistency: Prior research (Li et al., 2020; Liu et al., 2023a)
has validated that the confidence inconsistency problem is existing between
the predicted classification and localization qualities. To enhance the
correlation between them, most previous horizontal object detectors (Li et
al., 2020; Liu et al., 2023a) use the IoU-based soft label to supervise the
classification branch. However, predicting a confidence IoU value is difficult
for the oriented objects due to the increased uncertainty introduced by the
rotation angle parameter. Meanwhile, we discover that centerness can well
represent the localization quality of oriented bounding boxes. As in Figure
3(b), we statically analyze the IoU and centerness between all ground truth
boxes and their corresponding true positive boxes on the DOTA-v1.5 dataset
(the top subfigure) and the COCO dataset ((the bottom subfigure). Compared to
the COCO dataset, the correlation between the IoU and centerness values is
significantly higher on the DOTA-v1.5 dataset. Therefore, to address the
confidence inconsistency problem, we utilize the predicted centerness value to
measure the localization quality of oriented objects.

###  3.3. Gaussian Center Assignment

To deal with the sampling inconsistency problem, we attempt to select more
suitable positive labels from the following aspects: 1) making full use of
sparse annotated data; 2) taking the shape information of oriented objects
into consideration. For the first condition, the optimal solution is to
leverage these sparse annotations to assign more positive samples, hence some
carefully designed label assignment strategies are excluded. Also considering
the second condition, we propose a shape-aware method named Gaussian Center
Assignment (GCA) to selectpixel-level positive labels for oriented object
detection in semi-supervised learning.

Concretely, We model the object as a $2D$ Gaussian distribution that can well
reflect the shape and direction of the aerial object. We denote a rotated
bounding box as $B=\left(x_{c},y_{c},w,h,\theta\right)$, where $\theta$
represents the angle parameter; $(x_{c},y_{c})$, $w$, and $h$ represent the
center coordinates, width, and height of the oriented box, respectively. The
coordinate of the center point $(x_{c},y_{c})$ serves as the mean vector of
$2D$ Gaussian distribution $\boldsymbol{\mu}_{g}=(x_{c},y_{c})^{\top}$, and
the co-variance matrix $\boldsymbol{\Sigma}_{g}$ can be formulated as:

(1)
$\boldsymbol{\Sigma}_{g}=\left[\begin{array}[]{cc}\cos\theta&-\sin\theta\\\
\sin\theta&\cos\theta\end{array}\right]\left[\begin{array}[]{cc}\frac{w^{2}}{4}&0\\\
0&\frac{h^{2}}{4}\end{array}\right]\left[\begin{array}[]{cc}\cos\theta&\sin\theta\\\
-\sin\theta&\cos\theta\end{array}\right].$

We then define a point coordinate as $\boldsymbol{P}=(x,y)^{\top}$ and
determine whether it is a positive label based on the following formula:

(2) $\text{ label }=\left\\{\begin{array}[]{ll}1,&\text{ if
}(\boldsymbol{P}-\boldsymbol{\mu}_{g})^{\top}\boldsymbol{\Sigma}_{g}^{-1}(\boldsymbol{P}-\boldsymbol{\mu}_{g})\leq
1\\\ 0,&\text{ otherwise }.\end{array}\right.$

This label assignment ensures that positive labels cover not only the central
region but also the edge region of the target, thereby avoiding the omission
of discriminative features for aerial objects with large aspect ratios.
Moreover, a large number of sub-optimal positive samples (pixels near the
boundaries) also provide sufficient supervision information for the detector
optimization. For the oriented object, the new expression of centerness is
formulated as follows:

(3) $\text{ centerness
}^{*}=1-(\boldsymbol{P}-\boldsymbol{\mu}_{g})^{\top}\boldsymbol{\Sigma}_{g}^{-1}(\boldsymbol{P}-\boldsymbol{\mu}_{g}).$

According to the prior that pixels located around the center of the object are
more representative than those near the object boundaries, we establish a new
normalized distinction in the object region to represent the pixel-wise
localization quality. The Gaussian Center Assignment (GCA) can select
comprehensive supervision signals from the sparse annotated data to guide the
learing, and further improve the performance for objects with large aspect
ratios.

###  3.4. Scale-aware Label Assignment

Figure 4. Analysis on difference feature maps and the object centerness. (a)
Score imbalance between feature maps at different levels. (b) For centerness-
based soft label, condition 1 introduce ambiguities while condition 2 is more
suitable.

To tackle the assignment inconsistency problem, we conduct the pixel-level
pseudo-label selection based on the feature level predictions of the teacher
model rather than the post-processed pseudo-boxes. According to multi-level
prediction with FPN (Lin et al., 2017a), different sizes of objects can be
detected on different levels of feature maps (i.e.,
$P_{3},P_{4},P_{5},P_{6},P_{7}$). However, as shown in Figure 4(a), there is a
score imbalance problem between feature maps at different levels, where the
higher level feature map tend to predict the lower scores. To balance the
allocation of pseudo-labels for oriented targets with different scales, we
propose Scale-aware Label Assignment (SLA) to improve the quality of pseudo-
labels by employing different sampling rules for different level feature maps.

For the low-level feature maps (i.e., $P_{3},P_{4}$) with dense features, we
design a coarse-to-fine rule to predict these small-scale objects with two
following stages. In the coarse selection stage, the joint confidence (denoted
as the multiplication of score and centerness) is used to rank all pixels and
the top-k sorted pixels will be selected as candidate pseudo-labels. The joint
confidence is expected to select samples with the high classification and
localization qualities. As has been proven that the joint confidence is
dominated by centerness due to its higher value than classification score (Liu
et al., 2022), a high centerness value is unreliable to determine whether a
pixel is positive since the centerness branch lacks supervision from negative
instances. Therefore, we further filter these candidates through a score
threshold to ensure the precision.

For the high-level feature maps (i.e., $P_{5},P_{6},P_{7}$) with the lower
predicted scores, we only use the score threshold to filter high-confidence
pseudo-labels, thereby avoiding the unbalanced pseudo-labels allocation across
various scales. Here the unsupervised loss consists of three parts:

(4)
$\mathcal{L}_{u}=\frac{1}{N_{all}}\sum_{i}^{N_{all}}\mathcal{L}_{i}^{cls}+\frac{\alpha}{N_{pos}}\sum_{j}^{N_{pos}}w_{j}(\mathcal{L}_{j}^{cen}+\mathcal{L}_{j}^{reg})$

where $\alpha$ is a weighting parameter, $N_{all}$ represents the number of
pixels across five level feature maps, $N_{pos}$ denotes the number of
selected pseudo-labels. We apply the quality focal loss (Li et al., 2020), the
binary cross-entropy loss and the smooth-l1 Loss for guiding the
classification, centerness and regression branches, respectively. Besides, the
localization weights $w$ are determined by the following formula:

(5) $w_{j}=\left\\{\begin{array}[]{ll}s_{j}\times c_{j}&j\in[P_{3},P_{4}]\\\
s_{j}&j\in[P_{5},P_{6},P_{7}]\end{array}\right.$

where $s$ and $c$ denote the score and centerness, respectively. Since the
pseudo-labels selection is based on model predictions, the existence of false
positive labels is inevitable and the localization task is more sensitive to
such noisy samples. Through employing the weight $w$, we reduce the
contribution of low-confidence samples to the overall loss.

###  3.5. Consistent Confidence Soft Label

In this part, we focus on alleviating the confidence inconsistency issue.
Based on the analysis in Section 3.2, we design a centerness-based soft label
to supervise the classification branch. The soft label have to satisfy two
conditions: (1) being positively correlated with centerness; (2) the score
variance among all points within the target should not be too large,
especially for small targets. Therefore, we propose the Consistent Confidence
Soft Label (CCSL) strategy to align the classification and localization
confidences.

The core idea of CCSL is to replace the value of one-hot label at
corresponding category index with a float value $y\in[0,1]$, which satisfies
the condition that the covariance calculated with centerness equal to 1. The
soft label $y\in[0,1]$ is given as follows:

(6) $\text{ y
}=[1-(\boldsymbol{P}-\boldsymbol{\mu}_{g})^{\top}\boldsymbol{\Sigma}_{g}^{-1}(\boldsymbol{P}-\boldsymbol{\mu}_{g})]^{\gamma}$

where $\gamma$ is a scale factor designed for the second condition. As shown
in Figure 4(b), all points belonging to a small object have smaller stride,
resulting in very similar point features. We hope that the score values of all
points within the target are very close. Therefore, we weight them with the
scale factor $\gamma$, which is formulated as $\sqrt[\beta]{(h\times
w)/(H\times W)}$. $h$ and $w$ represent the height and width of the oriented
box, $H$ and $W$ denote the height and width of the whole image, while $\beta$
controls the smoothing degree of $\gamma$. $\gamma$ can help prevent confusion
during model training caused by excessive differences in point scores within
the target. The proposed CCSL can bridge the gap between horizontal and
oriented boxes in localization quality, and effectively mitigate the mismatch
between classification and localization confidences, thereby bolstering the
semi-supervised learning performance.

##  4\. Experiment

###  4.1. Experimental Setup

Dataset: The experiments are conducted on DOTA-v1.5 (Xia et al., 2018) and
DOTA-v1.0 (Xia et al., 2018). DOTA-v1.5 comprises 16 categories which contains
400$k$ annotated oriented instances. DOTA-v1.5-train, DOTA-v1.5-val, and
DOTAv1.5-test contain 1411, 458, and 937 images, respectively. DOTA-v1.0 uses
the same images as DOTA-v1.5 and the number of annotated instances is half the
DOTA-v1.5’s, with targets having a pixel area smaller than 10 being ignored.
We include three evaluation protocols: 1) DOTA1.5-Partial. Following SOOD
method (Hua et al., 2023), we randomly sample10%, 20%, and 30% images from
DOTA-v1.5-train as labeled data and set the remaining images as unlabeled
data. 2) DOTA1.5-Full. We set DOTA-v1.5-train as labeled data, DOTA-v1.5-test
as unlabeled data and perform the evaluation on the DOTA-v1.5-val. 3)
DOTA1.0-Full. The DOTA-v1.0-train and DOTA-v1.0-test are employed as labeled
data and unlabeled data respectively, while the DOTA-v1.0-val is set as the
evaluation dataset. For all evaluation protocols, the mAP (Xia et al., 2018)
is adopted as the evaluation metric.

Implementation Details: We adopt the FCOS (Tian et al., 2019) as the detector
and ResNet-50 (He et al., 2016) pretrained on ImageNet (Deng et al., 2009) as
the backbone. Following the previous works (Li et al., 2023; Xie et al., 2021;
Han et al., 2021), we crop the original images into patches of size 1024
$\times$ 1024, with an overlap region of 200 pixels between adjacent patches.
To ensure a fair comparison, the MCL is trained on 2 RTX4090 GPUs with 3
images per GPU (2 labeled images and 1 unlabeled image). The SGD optimizer is
applied with an initial learning rate of 0.0025, a momentum of 0.9, and a
weight decay of 0.0001. For 30% partial and full setting experiments, the MCL
is trained for 180$k$ iterations, and the learning rate is divided by 10 at
120k and 160k. For 10% partial and 20% partial setting experiments, we train
the MCL for 120$k$ iterations, while the learning rate is divided by 10 at 80k
and 110k. We follow the same pipeline in (Hua et al., 2023; Zhou et al.,
2022), employing a burn-in strategy to initialize the parameters of the
teacher model and applying the EMA strategy to update its parameters. The weak
data augmentation strategy for the teacher model and strong data augmentation
strategy for the student model are also consistent with them (Hua et al.,
2023; Zhou et al., 2022).

Table 1. Performance comparison with other state-of-the-art methods on the DOTA-v1.5-Partial dataset. ${\circ}$ and ${\dagger}$ denotes the base detector is Faster RCNN and FCOS respectively. |  | mAP(%) $\uparrow$
---|---|---
Task | Method | 10% | 20% | 30%
OD | Faster RCNN (Girshick, 2015) | 43.43 | 51.32 | 53.14
FCOS (Tian et al., 2019) | 42.78 | 50.11 | 54.79
SSOD | Unbaised Teacher∘ (Liu et al., 2021) | 44.51 | 52.80 | 53.33
Soft Teacher∘ (Xu et al., 2021) | 48.46 | 54.89 | 57.83
Dense Teacher† (Zhou et al., 2022) | 46.90 | 53.93 | 57.86
PseCo∘ (Li et al., 2022a) | 48.04 | 55.28 | 58.03
DualPolish∘ (Zhang et al., 2023) | 49.02 | 55.17 | 58.44
ARSL† (Liu et al., 2023a) | 48.17 | 55.34 | 59.02
SOOD | SOOD*† (Hua et al., 2023) | 48.63 | 55.58 | 59.23
PST∘ (Wu et al., 2024) | 49.63 | 57.39 | 60.40
MCL†(Ours) | 52.98 | 59.63 | 62.63
Table 2. Performance comparison on DOTA-v1.5-Full and DOTA-v1.0-Full, while numbers in font of the arrow indicate the result of supervised baseline Method | DOTA-v1.5-Full | DOTA-v1.0-Full
---|---|---
Unbiased Teacher (Liu et al., 2021) | 66.12 $\xrightarrow{-1.27}$ 64.85 | -
Soft Teacher (Xu et al., 2021) | 66.12 $\xrightarrow{+0.28}$ 66.40 | -
Dense Teacher (Zhou et al., 2022) | 65.46 $\xrightarrow{+0.92}$ 66.38 | 66.72 $\xrightarrow{+3.58}$ 70.30
SOOD* (Hua et al., 2023) | 65.46 $\xrightarrow{+2.24}$ 67.70 | 66.72 $\xrightarrow{+4.09}$ 70.81
MCL(Ours) | $\textbf{65.46}\xrightarrow{\textbf{+3.62}}\textbf{69.08}$ | $\textbf{66.72}\xrightarrow{\textbf{+6.91}}\textbf{73.63}$

###  4.2. Comparison with State-of-the-Arts

To validate the effectiveness of MCL, we compare it with previous methods
under DOTA1.5-Partial, DOTA1.5-Full and DOTA1.0-Full evaluation protocols. For
distinguishing with SOOD task, the SOOD (Hua et al., 2023) method is termed as
SOOD*. Moreover, some SSOD methods with their oriented version also
participate in comparison.

DOTA-v1.5-Partial: Experiment results under the DOTA-v1.5-Partial protocol are
presented in Table 1. In SOOD task, SSOD methods typically underperform
compared to SOOD methods, which exhibits the necessity of bridging the gap
between horizontal boxes and oriented boxes in semi-supervised detection.
SOOD* (Hua et al., 2023) and PST (Wu et al., 2024) are specifically designed
for the characteristics of oriented boxes and remote sensing images, yet the
performance gains are marginal. By bridging the gaps and addressing the
concerns of inconsistency, our MCL achieves remarkable enhancements over the
supervised baseline FCOS and outperforms all SOOD methods under all
proportions. It scores 52.98, 59.63 and 62.63 mAP on 10% 20% 30% experiments,
respectively, largely surpassing the state-of-the-arts method PST by 2 $\sim$
3.5 mAP, validating the necessity of our analyses and methods.

DOTA-v1.5-Full and DOTA-v1.0-Full: Table 2 gives the comparison results in
terms of mAP on the DOTA-v1.5-Full and DOTA-v1.0-Full configurations. Our MCL
demonstrates remarkable advancements over existing methods on the
DOTA-v1.5-Full and DOTA-v1.0-Full experiment settings. Compared to the state-
of-the-art SOOD* using the same detector, the MCL can achieve the notable
improvement: 1.38% on the the DOTA-v1.5-Full setting, and 2.82% on the
DOTA-v1.0-Full setting, exhibit its effectiveness.

Figure 5. Some visualization results from the DOTA-v1.5 dataset. The first and
the last rows are the results of Dense Teacher and MCL respectively. True
Positive, False Negative, and False Positive predictions are marked in green,
red, and blue respectively.

Visualization Analysis: The visualization results under the 30% setting of
DOTA-v1.5-Partial are shown in Figure 5. Compared with the Dense Teacher (Zhou
et al., 2022), MCL shows an enhancement in the detection of targets with large
aspect ratios aided by the GCA module. Additionally, supported by the SLA
module, the MCL demonstrates an improved capability in handling targets of
various sizes in remote sensing scenarios. Moreover, the CCSL module assists
the MCL in identifying high-quality pseudo-labels in densely populated target
scenes, effectively reducing the incidence of False Negative predictions. This
collective integration of GCA, SLA, and CCSL within the MCL not only refines
its detection precision but also establishes a robust approach for enhancing
object detection in complex remote sensing images.

###  4.3. Ablation Studies

Subsequently, we delve into the detailed analysis of each module. All the
ablation experiments are performed on the 30% setting of DOTA-v1.5-Partial
without special instructions. We set the Dense Teacher (Zhou et al., 2022) as
the baseline. It also uses pixel-level pseudo labels by sorting all pixels
according to classification scores and selects the top ratio(%) ones. The
original parameter setting sets ratio to 1%, and we set ratio to 3% by default
to maximize the performance.

Table 3.  Performance comparison with different modules.  |  |  |  | mAP(%) $\uparrow$
---|---|---|---|---
| GCA | SLA | CCSL | 10% | 20% | 30%
baseline | $\times$ | $\times$ | $\times$ | 49.71 | 55.64 | 59.65
MCL | $\checkmark$ | $\times$ | $\times$ | 51.12 | 56.74 | 60.62
$\times$ | $\checkmark$ | $\times$ | 51.84 | 57.16 | 61.32
$\checkmark$ | $\checkmark$ | $\times$ | 52.02 | 57.28 | 61.46
$\checkmark$ | $\checkmark$ | $\checkmark$ | 52.98 | 59.63 | 62.63

The effect of each module: We study the effectiveness of our proposed three
modules (GCA, SLA, CCSL) under different experiment settings (i.e., 10% 20%
30% ). The results are shown in Table 3. After comprehensively extracting
supervision information from annotated data, GCA facilitates a performance
enhancement for MCL. Furthermore, SLA enhances the quality of unsupervised
information extracted from unlabeled data and also contributes to performance
improvement. The CCSL can further improve the precision of pseudo-labels by
mitigating the inconsistency between classification and localization
confidence, thereby the participation of the CCSL leads to additional
performance improvement for MCL.

All Sampling vs GCA: To evaluate the effective of the GCA in SOOD task, we
compare GCA with the center sampling strategy used in FCOS (Tian et al., 2019)
and the all sampling strategy that labels all pixels insides ground-truth
boxes as positives and the remaining pixels as negatives. The detailed
comparable results are shown in Table 5. Although the aim is to fully utilize
labeled data to extract more positive supervision information, all sampling
strategy still shows performance degradation compared to center sampling. We
speculate that this is due to all sampling introducing excessive background at
the target’s edges. In contrast, GCA can provide sufficient positive
supervision information while accounting for the target’s aspect ratio without
introducing excessive noise, thereby improving the performance.

Table 4. Performance comparison between GCA and All Sampling strategy.

Sampling strategies | mAP
---|---
Center Sampling | 59.65
All Sampling | 58.49
GCA | 60.62

Table 5. Performance comparison between Mean Teacher and Dense Teacher.

Method | mAP
---|---
FCOS(base) | 54.79
Mean Teacher | 26.02 (-28.77)
Dense Teacher | 59.65 (+4.86)

Table 6. Ablation studies on SLA. | ratio | thr | topk | Recall | Precision | mAP
---|---|---|---|---|---|---
score | 1% | - | - | 40.08 | 30.76 | 57.86
3% | - | - | 69.44 | 17.76 | 59.65
score $\times$ center | 3% | - | - | 70.38 | 18.01 | 60.45
SLA | - | 0.01 | 1500 | 90.35 | 12.74 | 59.97
0.02 | 88.76 | 19.50 | 60.61
0.03 | 87.15 | 24.03 | 60.59
- | 0.01 | 2000 | 93.72 | 12.39 | 60.34
0.02 | 91.89 | 19.13 | 61.32
0.03 | 90.04 | 23.69 | 60.89

The analysis of SLA: To verify the impact of SLA hyper-parameters and
demonstrate the advantages of SLA over other selection strategies, we conduct
the experiments with the pixel-level recall and precision as the metrics. In
detail, we denote the selected points from the ground truth boxes as ground
truth points. The selected pseudo-labels that coincide with ground truth
points are denoted as true positives and the remaining ones are false
positives. The computation forms of pixel-level recall and precision are
consistent with the previous work (Lin et al., 2014). The experimentation is
shown in Table 6. It can be observed that the performance of semi-supervised
learning improves 1.79% mAP when recall increases from 40.08% to 69.44%,
demonstrating that maintaining high recall of pseudo-labels is crucial for
ensuring the performance of SOOD task. In addition, replacing score selection
used in Dense Teacher (Zhou et al., 2022) with joint confidence selection can
slightly enhances both recall and precision, thereby improving the performance
from 59.65 mAP to 60.45 mAP. However, it is still not the optimal solution. By
considering the imbalance between scores of objects of different scales and
the disparity between scores and centerness values, SLA significantly enhances
recall while maintaining satisfactory precision, thereby markedly improving
SOOD performance.

The analysis of CCSL: To validate our analysis in Section 3.2 that predicted
centerness is a more suitable proxy localization quality of oriented box than
predicted IoU, we perform the comparative experiment between them. As shown in
Table 7, compared to predicting the uncontrollable IoU, predicting the
centerness with considering the scale information improves the SOOD
performance. In addition, the scale factor $\gamma$ is also a critical
component. The central and edge features of extremely small objects are very
similar, leading to significant differences in the predicted centerness values
confuse the algorithm’s training. By combining the scale factor $\gamma$, the
variance of the target internal center distribution can be dynamically
adjusted according to the target scale. Therefore, compared to vanilla
centerness, centerness with the scale factor can better enhance the detection
performance.

Table 7. Ablation studies on CCSL. Localization Quality | $\beta$ | mAP
---|---|---
IoU | - | 60.98
Centerness | 0 | 60.87
0.1 | 61.38
0.2 | 62.63
0.25 | 62.26
Table 8. The impacts of GCA on objects with large aspect ratios.  | HB | BD | GTF | mAP
---|---|---|---|---
| Recall | mAP | Recall | mAP | Recall | mAP
FCOS | 81.7 | 71.8 | 60.8 | 40.1 | 72.6 | 55.2 | 65.5
+GCA | 84.6 | 74.1 | 66.5 | 45.7 | 83.0 | 62.5 | 67.2

###  4.4. Inconsistency Mitigation

Sampling Inconsistency: We conduct additional experiments to demonstrate the
effectiveness of GCA in sampling inconsistency mitigation. The metric is the
detection performance for objects with large aspect ratios. The models are
trained on the DOTA-v1.5-train and evaluated on the DOTA-v1.5-val. We extract
the three categories with the highest aspect ratio from the 16 categories in
DOTA-v1.5, namely HB (harbor), BD (bridge), and GTF (ground-track-field). The
experimental results are shown in Table 8. With the support of GCA, there is a
notable enhancement in both recall and mAP for these objects with the large
aspect ratios, which verifies that GCA can effectively alleviating the
sampling inconsistency, enhancing the performance of large aspect ratio object
detection.

Assignment Inconsistency: To verify the necessity of using pixel-level pseudo-
labels to eliminate assignment inconsistency as discussed in Section 3.2, we
compare the performance of the pseudo-boxes-based method Mean Teacher(we
follow the Consistent Teacher (Wang et al., 2023) that call the vanilla
pseudo-boxes framework Mean Teacher) and the pixel-level pseudo-labels-based
method Dense Teacher (Zhou et al., 2022) on FCOS (Tian et al., 2019). As shown
in Table 5, Mean Teacher exhibits a significant performance drop due to the
fact that dense object detectors adopt a binary label assignment strategy,
making them highly sensitive to the overall quality of the oriented pseudo-
boxes which is difficult to guarantee. In contrast, pixel-level pseudo-labels
greatly alleviate the assignment inconsistency introduced during label
assignment, thereby improving the performance.

Confidence Inconsistency: To assess the effectiveness of CCSL in eliminate
confidence inconsistency, we train two FCOS detectors on DOTA-v1.5-train, one
of which is supervised with one-hot label as usual and the other with CCSL. We
visualize the score-centerness heatmaps of all ground truth points on the
DOAT-v1.5-val set, which is shown in Figure 6. As highlighted in the blue
squares, with the incorporation of CCSL, there is an improvement in the
positive correlation between classification scores and centerness that
represents the localization quality, which demonstrates that the CCSL is
effective in eliminating the inconsistency between classification and
localization qualities.

##  5\. Conclusion

In this work, we propose a Multi-clue Consistency Learning (MCL) framework to
boost the performance of semi-supervised oriented object detection. We attempt
to bridge the gaps between general and oriented object detection in semi-
supervised learning through investigating three inconsistency issues. To
mitigate the sampling inconsistency, we design the Gaussian Center Assignment
to consider various shapes of aerial objects by employing the limited
annotation data. The proposed Scale-aware Label Assignment and Consistent
Confidence Soft Label strategies to mine more accurate supervised information
from a large amount of unlabeled data, which can further promote the semi-
supervised learning. Extensive experimental results on the public DOTA-v1.0
and DOTA-v1.0 datasets clearly demonstrate our proposed MCL is effective to
bridge the gaps between the general and oriented object detection in the semi-
supervised learning.

Figure 6. Illustrated analysis of CCSL. (a) The heatmap of the scores and
centerness of positive samples trained based on CCSL. (b) The heatmap of the
scores and centerness of positive samples trained based on one-hot label.

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