Oriented object detection in remote sensing images based on angle quality estimation

Abstract

Remote sensing has a large amount of content information and high complexity, making it difficult to annotate image, high demand for professional knowledge, and high economic cost. There are significant differences in the quality of data labels obtained, which poses various information limited challenges in object detection. Data labels with significant differences in quality pose various challenges with limited information for object detection. Therefore, a new oriented object detection technique based on angle quality estimation (AQE-detector) was designed to overcome the challenges of missing confidence information on oriented angle and insufficient object localization accuracy. Firstly, a periodic Gaussian distribution was used to model the oriented angle variable, transforming the angle regression into the distribution estimation, greatly improving the accuracy of the angle and implicitly estimating the potential confidence. Based on this, the non-maximum suppression based on angle quality (NMS-AQ) was proposed to alleviate the confirmation bias caused by existing methods that only use classification confidence to evaluate detection results. An angle loss function based on aspect-ratio perception (Double-A Loss) was designed to effectively improving the overall detection performance. The intelligent object detection technology under information limited conditions has been studied, facilitating the efficient application of object detection in major demand fields, such as remote sensing and non-destructive testing.

Introduction

At present, the emergence of satellite image sharing platforms such as Google Earth and Amap has led to an increasing scale of high-resolution images. Intelligent interpretation of remote sensing has received more attention in various fields. Object detection is widely used in locating targets of interest, such as airplanes and ships, and in many extensions such as military reconnaissance, road rescue, and environmental monitoring^1–3. The targets in remote sensing through on-board or satellite imaging sensors often exhibit arbitrary directional distributions. It is difficult to accurately locate remote sensing objects with oriented angles using general detection algorithms^4–6, which will cause problems such as overlapping between object bounding boxes and background within object boxes, greatly affecting the detection performance⁷.

Many detection methods based on oriented bounding box^8–12 have been proposed and have made encouraging progress. Wang et al.¹³ introduced an angle prediction branch based on the general object detector - Faster RCNN, accurately predicting the orientation of remote sensing objects. Song et al.¹⁴ introduced the angle prediction branch into the object candidate region generation network to generate a series of object candidate regions with oriented angles, enhancing the feature extraction ability for oriented objects. On this basis, Liu et al.¹⁵ fully explored the multi-scale features of remote sensing through a densely connected feature pyramid mechanism, overcoming scale fluctuations. Jin et al.¹⁶ used a model to automatically learn the parameter transformation relationship between candidate region boxes and the oriented objects, thereby accurately extracting oriented object features. Ravi et al.¹⁷ proposed an L1 loss function based on IoU to eliminate the inconsistency between angle loss function and localization performance. Mandi et al.¹⁸ proposed a modulation loss function for direct regression of target vertices, which avoids the inconsistency between the loss function of the oriented object and its localization performance by reordering each vertex. Zheng et al.¹⁹ designed an oriented feature refinement module to improve the detection performance of target regions. Furthermore, Chen et al.²⁰ proposed a sample allocation method to mitigate the difference between classification and the localization accuracy of detection box.

Although the above-mentioned algorithm based on oriented bounding box has made some progress, there are still three urgent challenges that need to be addressed: (1) Existing methods usually treat angles as ordinary variables for regression, without considering their periodic characteristics, resulting in inconsistency between the monotonicity of the loss function and the periodicity of angles. Although recent studies such as Gaussian Wasserstein Distance (GWD)²¹ and Circular Smooth Label (CSL)²² have attempted to address this issue from a distribution modeling perspective, they still have limitations. GWD converts the oriented bounding box into a 2D Gaussian distribution and calculates the distribution distance, which is a complex process and does not explicitly model the boundary problem of the angular period. CSL transforms angle regression into a classification problem. Although it avoids cycle jumps, its predictions are deterministic and cannot provide confidence (or quality) information for angle predictions. (2) Most existing algorithms only use classification confidence to evaluate the performance, while ignoring the quality of predicted angles that are significantly related to localization performance. Due to the inconsistent difference between classification confidence and localization accuracy, detection results with lower classification confidence but more accurate localization are suppressed. Most existing algorithms only use classification confidence to evaluate the quality of detection boxes, while ignoring the significant correlation between angle quality and localization accuracy. Although previous studies such as IoU-aware NMS or Quality-aware NMS have proposed using IoU or other quality indicators to assist NMS, these indicators are usually focused on horizontal boxes, and have not specifically evaluated the quality of the “angle” dimension in oriented object detection. (3) Most existing studies have overlooked the correlation between angle prediction and object aspect-ratio. Applying the same level of supervision to all objects can make it difficult to fully learn accurate angles for angle sensitive objects, and vice versa, it can generate redundant supervision information.

Therefore, a new oriented object detection technique based on angle quality estimation (AQE-detector) was proposed. This method overcomes the phenomenon of inconsistent loss function values and target localization results caused by periodic angles, thereby significantly improving the accuracy of angle prediction; Next, the process proposes the non-maximum suppression based on angle quality (NMS-AQ). By comprehensively considering the angle quality and classification confidence, the detection is comprehensively evaluated to alleviate the inconsistency in confidence and positioning between the two; In addition, the relationship between angle sensitivity and object aspect-ratio was quantitatively analyzed, and an angle loss function based on aspect-ratio perception (Double-A Loss) was designed.

1. A new oriented object detection technique based on angle quality estimation (AQE-detector) has been proposed. The problem of inconsistent optimization function values and object detection results caused by angle periodicity has been overcome, significantly improving the accuracy of angle prediction and implicitly estimating the quality information.

2. Non-maximum suppression based on angle quality (NMS-AQ) was designed. By comprehensively considering the angle quality and classification confidence, the detection is comprehensively evaluated to alleviate the inconsistency in confidence and positioning between the two.

3. An angle loss function based on aspect-ratio perception (Double-A Loss) was proposed. This function adaptively adjusts the loss weight of the angle prediction branch based on the aspect ratio, reducing redundant supervision information.

Methods

A new oriented object detection technique is studied for coping the inconsistency between angle periodicity and loss function monotonicity, inconsistency between classification confidence and localization accuracy, inconsistency between objects with different geometric characteristics and the same angle supervision intensity. Figure 1 shows the model structure. Figure 1 illustrates the overall architecture of the proposed AQE-Detector, which features three specialized branches for angle prediction: Angle Classification, Angle Regression, and Angle Quality Estimation. The Angle Classification branch follows the conventional approach similar to CSL²², predicting discrete angle categories through a 180-dimensional output representing probability distribution over angle classes. This branch provides a deterministic angle prediction based on the highest probability category. The Angle Regression branch employs direct regression to predict the continuous angle value, treating angle as an ordinary regression variable without considering its periodic nature. The Angle Quality Estimation (AQE) branch, which is the core contribution of this work, models the angle as a periodic Gaussian distribution. It predicts both the mean and variance parameters, with the 180-dimensional output representing the discretized probability density function of the continuous angle distribution. This probabilistic formulation naturally generates angle quality scores that reflect prediction uncertainty. During inference, the AQE branch’s mean prediction is used as the final angle estimate, while the variance-derived quality score is integrated with classification confidence in the proposed NMS-AQ to comprehensively evaluate detection quality.

Fig. 1.

Overall structure of oriented object detection.

This method overcomes the phenomenon of inconsistent loss function values and target localization results caused by periodic angles, thereby significantly improving the accuracy of angle prediction. Afterwards, the non-maximum suppression based on angle quality (NMS-AQ) was proposed. By comprehensively considering the angle quality and classification confidence, the detection is comprehensively evaluated to alleviate the inconsistency in confidence and positioning between the two. Finally, the relationship between angle sensitivity and object aspect-ratio was quantitatively analyzed, and an angle loss function based on aspect-ratio perception was designed. In the Double-A Loss illustration, the red oriented bounding boxes represent angle-sensitive objects with high aspect ratios (e.g., ships, large vehicles), which require stronger angle supervision; the blue dashed boxes represent angle-insensitive objects with low aspect ratios (e.g., storage tanks, roundabouts), for which the angle loss is adaptively reduced. The curve depicts how the loss weight adapts based on the object’s aspect ratio.

Angle quality estimation

Angle variable modeling: Gaussian distribution functions with periodicity are used to model angle variables. Specifically, an angle quality estimation branch was constructed to predict mean and variance:

FC _AQE represents the angle quality estimation branch, while F_obj is a feature map of the target area extracted by pooling operations on the region of interest using a backbone network²³. The variables µ and σ predicted by the fully connected layer are unbounded and cannot be directly used to characterize the variables under Gaussian distribution. θµ and θσ are the mean and standard deviation of the angle, respectively. They need to be limited to the range of angle definitions. To this end, the range of the mean value of the angle variable is limited to 0 to π, and its standard deviation is limited to 0 to 1:

The angle variable is modeled as:

Among them, α_θ is the periodic factor. After modeling the angle variable, θ_σ can implicitly reveal the quality information²⁴. Next, the true value label of the angle is modeled as a Dirac distribution:

At this point, the transformation from angle prediction task to distribution estimation task has been completed. N training samples are used to optimize the weight, so that the angle distribution P(θ) approaches the label distribution δ(θ):

Distance (|) is a metric function used to estimate the difference between two distributions. By representing angle variables in the form of periodic Gaussian distributions, the phenomenon of sudden changes in angle prediction loss values at the boundary of the defined range due to the inconsistency between angle periodicity and loss function monotonicity is avoided, thereby improving the accuracy of angle prediction.

Optimization of angle quality estimation branch: Converting the angle distribution into discrete variables reduces the difficulty of model optimization. Specifically, the angle continuous distribution established above is sampled at equal intervals to obtain an angle Gaussian vector of length M, which is called L_G(x):

Among them, , x represents the discrete value of angle, which is the sampling point used to calculate the probability density function of Gaussian distribution. Gaussian random vector with angular direction is calculated:

Among them, the resolution R_θ of the angle variable was set to 1 through parameter experimental analysis. Similarly, the label distribution δ(θ) is also encoded:

Through this approach, the distribution estimation task has been successfully simplified into a classification problem, making it easier to train and optimize the model²⁵.

Angle quality estimation branch inference: In the inference stage, the model’s predicted θ_µ from the AQE branch is directly and solely regarded as the object’s oriented angle to generate the final detection results. The predictions from the Angle Classification and Angle Regression branches are only utilized during the training phase to enrich feature learning and provide auxiliary supervision. Based on the predicted θ_σ, the angle quality information is calculated using the following formula:

Based on angle quality, AQ-NMS is constructed in the subsequent stage. The angle quality and classification confidence are comprehensively considered to re evaluate the detection results.

Theoretical analysis: A theoretical analysis was conducted on whether the variable θ_σ can represent the quality information. The objective function based on cross entropy loss in Θ is transformed into:

Among them, can be simplified and decomposed into²¹:

According to α_θ, it can be deduced that . Therefore, the above equation can be rewritten:

Among them, needs to be minimized, so θ_σ will converge to 0. On the other hand, needs to be maximized. According to α_θ, when θ_σ approaches θ_gt, α_θ will tend towards 0. Therefore, can be rewritten as , resulting in θ_µ and θ_σ tending towards θ_gt and 1, respectively. Therefore, as θ_µ approaches θ_gt, θ_σ decreases^25,26.

Angle Quality Estimation (AQE) is fundamentally different from works such as Gaussian Wasserstein Distance (GWD)²¹ and Circular Smooth Label (CSL)²². CSL is a deterministic classification method based on label smoothing, whose output is the probability of each angle category, but it cannot provide continuous estimation of angle uncertainty. The core advantage of the AQE lies in: (1) Directness: Directly modeling the one-dimensional probability distribution of the angle as a periodic variable, the principle is more intuitive; (2) Information richness: The mean (θ_µ) and uncertainty (θ_σ) of angle prediction are naturally generated, namely angle quality; (3) Integration: The quality score of the output can be directly and seamlessly used to improve post-processing processes (such as non-maximum suppression based on angle quality). This “modeling-estimation-application” closed loop is the unique contribution of this study.

Differentiation from Multi-branch Angle Prediction: The proposed AQE-detector incorporates three parallel branches for angle prediction, each with distinct characteristics and purposes. The Angle Classification branch, similar to CSL²², provides discrete angle predictions but lacks uncertainty quantification. The Angle Regression branch offers continuous angle estimates but suffers from periodicity boundary issues. In contrast, the AQE branch uniquely combines the advantages of both: it provides continuous angle estimation through probabilistic modeling while naturally generating quality scores that reflect prediction confidence. This multi-branch design allows for comprehensive angle representation: the classification branch captures discrete angular patterns, the regression branch provides direct continuous estimates, and the AQE branch offers probabilistic uncertainty awareness. During training, all three branches contribute to the learning process, but during inference, only the AQE branch’s predictions are utilized, as they encapsulate both angle estimation and quality assessment in a unified framework. This represents a significant advancement over single-branch approaches like CSL²² or pure regression methods, enabling more robust and reliable oriented object detection.

Non-maximum suppression based on angle quality

Non-maximum Suppression (NMS) is usually applied to a series of candidate detection boxes. The conventional non-maximum suppression operation only uses the detection box as the evaluation criterion, suppressing detection boxes with lower classification confidence²⁷. However, some oriented detection boxes with lower classification confidence actually have higher localization accuracy, making it difficult to accurately preserve high-precision detection boxes. Considering the impact of angle prediction on the localization, the non-maximum suppression based on angle quality (NMS-AQ) is proposed.

Specifically, any detection box is represented as . AQ-NMS combines the classification confidence with the angle quality to generate a comprehensive confidence S:

Among them, score_cls are classification scores, and ξ is a weight factor used to control the fusion ratio of classification confidence and angle quality²⁸. AQ-NMS can effectively filter out inaccurate detection boxes.

Non-maximum Suppression (NMS) is a key step in post-processing of object detection. Traditional NMS relies solely on classification confidence ranking, which has many limitations. Therefore, a series of improvement methods have been proposed. Soft-NMS²⁹ alleviates dense target problems through attenuation rather than inhibition; Methods such as IoU-aware NMS³⁰ and Fitness-NMS³¹ introduce IoU or fit between predicted and real boxes as new scoring criteria to better reflect localization accuracy. These methods can be collectively referred to as Quality-aware NMS.

Comparison with Existing NMS Methods. The proposed NMS-AQ is fundamentally different from and addresses specific limitations of existing NMS methods in the context of oriented object detection. Traditional & Soft-NMS²⁹: These methods rely solely on classification confidence (score_cls) for ranking and suppression. This often leads to the suppression of detection boxes with high localization accuracy but slightly lower classification scores, due to the common mismatch between classification and localization confidence. Quality-aware NMS (e.g., IoU-aware³⁰, Fitness-NMS³¹: These methods introduce a general localization quality metric (e.g., IoU) to form a combined score (e.g., S = score_cls × IoU). While this is an improvement, the IoU is a holistic measure resulting from all bounding box parameters (center point, width, height, and angle). It cannot specifically and explicitly quantify the uncertainty or quality of the angle prediction alone, which is crucial for oriented objects. Proposed NMS-AQ: Our method introduces a dedicated angle quality score (quality_θ) derived directly from the probabilistic output of the AQE branch. This score explicitly measures the reliability of the angle prediction. By fusing quality_θ with score ~ cls~ (i.e., S = score_cls + ξ · quality_θ), NMS-AQ can prioritize boxes with highly reliable orientations. This is particularly advantageous for elongated objects (e.g., ships, vehicles) where a small angle error can cause a significant IoU drop, ensuring that detections with precise angles are preserved even if their classification scores are not the highest.

Angle loss function based on aspect-ratio perception

Objects are highly sensitive to angle changes, such as large vehicles and ships in ports, so slight deviations in oriented angles can lead to significant differences in their localization accuracy. In existing detection methods, the same level of angle supervision is usually applied to various types of objects, which makes it difficult for angle sensitive objects to receive sufficient training, and generates a lot of redundant supervision information for angle insensitive objects. Specifically, for angle insensitive objects, the correlation between their localization accuracy and oriented angle is weak^32,33. Therefore, applying too much supervision information to these objects is redundant, resulting in excessive redundant supervision information. For angle sensitive objects, angle prediction requires the application of more supervisory information. An angle loss function based on aspect-ratio perception (Double-A Loss) is proposed to address the above issues, dynamically adjusting the weight in combination with the geometric structure of different objects. The name ‘Double-A’ signifies that the loss incorporates dual considerations of Aspect-ratio and Angle, which are the core factors it adapts to.

The coefficients λ_L, λ_Q, λ_G, ζ_L, ζ_Q, and ζ_G for the linear, quadratic, and Gaussian transformation functions were determined through a curve fitting process. A theoretical relationship between aspect ratio and desired angle sensitivity was defined: sensitivity should peak at very high and very low aspect ratios and be lowest for near-square objects. The idealized trend curve was plotted. Subsequently, the least squares method was employed to optimize the parameters of each candidate function (linear AS_L, quadratic AS_Q, and Gaussian AS_G³² to best fit this idealized curve. Using a series of transformation functions (AS_L, AS_Q, and AS_G) to characterize the trend of change, and approximating the curve using the least squares method:

Among them, the values λ_L = -1.376, λ_Q = -2.013, λ_G = -3.386, ζ_L = 1.078, ζ_Q = 0.916, and ζ_G = -0.044, respectively, are the optimal parameters resulting from this fitting process, which minimizes the total squared error between the function output and our predefined trend. By using this conversion function, it is possible to adaptively adjust the angle supervision strength of objects with different aspect ratios, thereby reducing redundant angle losses, as shown below:

In addition, although AS_* effectively adjusts its angle loss intensity for different objects, it neglects the adjustment of the loss proportion between simple and difficult samples³³. A well-known solution to the easy/hard sample imbalance problem is the Focal Loss³⁴. While Double-A Loss adopts a similar modulating factor (γ) to dynamically scale the loss, its core purpose and application are fundamentally different. Focal Loss addresses the foreground-background class imbalance by down-weighting the loss for well-classified background examples (easy negatives). In contrast, Double-A Loss addresses the disparity in angle sensitivity among different objects. The modulating factor here is applied to down-weight the angle loss for objects that are inherently less sensitive to angle errors (typically those with low aspect ratios), regardless of their class. Therefore, the innovation of Double-A Loss lies not in the modulating mechanism itself, but in its novel integration with the aspect-ratio-sensitive weighting (AS_*). It creates a unified loss function that simultaneously addresses sample-level difficulty (easy/hard) and object-level geometric property (angle sensitivity), which is a new challenge specific to oriented object detection. The loss weights of each objective are adaptively adjusted, and the final angle loss function is:

Using angle sensitivity control to penalize difficult samples can effectively avoid redundant angle supervision on objects with lower aspect ratios and improve overall detection accuracy³⁵.

Multi-task joint optimization

A plug and play angle prediction method has been studied, which can be combined with any object detector. The construction of the multi-task loss function refers to the classical object detector Faster-RCNN:

Among them, Loss_cls, Loss_bbox, and Loss_Double−A represent the classification loss, regression loss, and prediction loss, respectively³⁶. For angle prediction loss, the proposed Double-A Loss function is used. The hyperparameters λ_c, λ_b, and λ_θ, which balance the multi-task loss function, were determined through a grid search on the validation set (DOTA validation split). We aimed to find a combination that allows all tasks (classification, regression, and angle prediction) to converge harmoniously. The search range for parameter λ_c is [0.1, 0.5, 1.0, 2.0, 3.0]; the search range for parameter λ_b is [0.1, 0.5, 1]; the search range for parameter λ_θ is [0.1, 0.2, 0.3, 0.4, 0.5]. The final combination (λ_c = 2.0, λ_b = 1.0, λ_θ = 0.2) was selected as it yielded the highest overall mAP, indicating a good balance between the different learning objectives.

It is important to note that during inference, the model operates in a streamlined manner. Only the predictions from the AQE branch (θ_µ for the angle and score_cls for classification) are used to form the final oriented bounding boxes. The Angle Classification and Regression branches are disabled at this stage. This approach allows us to leverage the benefits of multi-task learning during training—where each branch contributes to learning a more generalized feature representation—while maintaining a simple and efficient inference pipeline that capitalizes on the superior accuracy and inherent quality estimation of the AQE method.

Experimental setup

Data and setup

Different algorithms were evaluated on three datasets: DOTA³⁷, HRSC2016³⁸, and ICDAR2015³⁹.

1. HRSC2016 is an oriented objects dataset. This dataset mainly includes two scenarios: offshore ships and nearshore ships. The images are divided into a training set (617 images) and a testing set (444 images), with a resolution of 300 × 300 pixels ~ 1500 × 900 pixels.

2. DOTA is an oriented objects dataset. The dataset is divided into training dataset (10276 images), validation dataset (2957 images), and testing dataset (10833 images), with a resolution of 1024 × 1024 pixels.

3. To further validate the effectiveness in other detection fields, it was validated on the ICDAR2015 dataset. ICDAR2015 is divided into a training set (1000 images) and a testing set (500 images), with a resolution of 720 × 1280 pixels, used for detecting and recognizing oriented text in the scene.

The operating system used in the experiment is Ubuntu 16.04LTS, the processor model is Intel Xeon(R) CPU E5-2680v4@2.40 GHz×51, the memory size is 128GB, and the graphics card is NVIDIA Ge Force GTX2080Ti. The programming language used in the experiment is Python 3.7, and the deep learning framework is PyTorch. The software tools used include Python 3.7 (https://www.python.org), PyTorch (deep learning framework, https://pytorch.org), OpenCV 4.5.4 (image processing, https://opencv.org), and Matplotlib 3.5.1 (visualization, https://matplotlib.org). The pre trained weights on ImageNet are used to initialize the backbone network (i.e. ResNet), and the weight parameters of other network layers are randomly initialized using a zero mean normal distribution with a standard deviation of 0.01. Stochastic Gradient De-scent (SGD) was selected to optimize the model and set the initial learning rate to 0.01. The learning rate decreased by 10 times in the 8th and 11th training batches, with a total of 24 training batches trained and the batch size set to 4. Data augmentation techniques including random horizontal flipping, random rotation, and random scaling are adopted to enhance the robustness of the detector, and the target detection threshold is set to 0.001.

Evaluation metrics

The average accuracy indicators of categories include the conventional accuracy indicator mean average precision (mAP) when the IoU is 0.5, and the high-precision indicator mAP75 when the IoU is 0.75.

Among them, N_R is set to 11, and R and P respectively represent recall (R) and precision (P):

Among them, TP, FP, and FN respectively represent the number of true positives, false positives, and false negatives. If the IoU between the detection result and the target box exceeds the threshold, the detection result is considered a true positive, otherwise it is considered a false positive.

Results analysis

Ablation experiment

1. Effectiveness of the angle quality estimation module (AQE).

The experimental results in Table 1 are all reproduced under the same conditions, with each row showing the best performance highlighted in bold, and the underlined numbers representing the second best performance. Table 1 presents the experimental results of models with different modules added on different types of targets. The different modules of our method have been proven to significantly improve the comprehensive detection efficiency of various targets. As this method overcomes the inconsistency between angle periodicity and loss function monotonicity, it makes the model localization performance more accurate. Meanwhile, it can be observed that the introduction of the angle quality estimation module demonstrates greater improvement in the high-precision metric mAP75. This method has significant advantages for angle sensitive objects, such as large vehicles, ships, and harbor, achieving detection accuracy improvements of 6.22%, 7.91%, and 3.01%.

Table 1.

Results of AQE-Detector on DOTA validation set (mAP and mAP75).

	mAP				mAP75
AQE	×	√	√	√	×	√	√	√
Double-A Loss	×	×	√	√	×	×	√	√
NMS-AQ	×	×	×	√	×	×	×	√
Plane	90.01	90.00	90.00	89.55	66.23	69.61	67.09	69.87
BD	76.97	77.53	78.85	79.26	27.72	31.16	28.19	33.21
Bridge	45.61	47.54	47.18	47.30	6.29	7.94	11.77	10.70
GTF	69.52	69.10	72.31	72.51	39.76	41.48	41.87	42.03
SV	65.81	66.06	66.10	66.30	26.15	26.80	27.87	28.14
LV	78.05	79.05	79.45	80.22	38.52	44.74	46.21	46.26
Ship	87.17	88.11	88.22	88.25	34.72	42.63	42.41	42.76
TC	90.84	90.86	90.87	90.85	79.92	81.02	79.82	83.98
BC	64.28	69.56	69.00	68.88	49.33	52.90	57.69	57.76
ST	87.95	87.63	87.68	87.68	55.30	54.75	56.66	56.73
SBF	72.51	72.64	77.84	78.27	46.32	48.66	43.75	44.58
RA	65.91	69.14	70.01	70.19	35.36	34.37	35.01	34.66
Harbor	64.81	65.46	65.23	65.83	12.39	15.40	20.30	20.96
SP	64.36	64.37	64.81	65.41	5.30	11.60	11.53	11.92
HC	48.33	50.23	56.19	55.45	5.88	10.47	13.94	15.93

*Plane, plane; Ship, ship; ST, storage tank; BD, baseball diamond; TC, tennis court; BC, basketball court; GTF, ground track field; Harbor, harbor; Bridge, bridge; LV, large vehicle; SV, small vehicle; HC, helicopter; RA, roundabout; SF, soccer field; SP, swimming pool.

The best performancehighlighted in bold, and the italic numbers representing the second best performance.

To quantitatively dissect the contribution of each proposed module, we conduct a comprehensive ablation study following a progressive integration path, with results summarized in Table 2. Case 1: Baseline - no any modules; Case 2: adding AQE; Case 3: adding AQE and Double-A Loss; Case 4: adding AQE, Double-A Loss and NMS-AQ (Ours).

Table 2.

Ablation results of different modules on DOTA validation set (mAP and mAP75).

Module	mAP (%)	mAP75 (%)	ΔmAP75 (vs. Baseline)
Case 1: Baseline	71.47	35.28
Case 2: Baseline + AQE	72.49	38.24	+ 2.96
Case 3: Baseline + AQE + Double-A Loss	73.58	38.94	+ 3.66
Case 4: Baseline + AQE + Double-A Loss + NMS-AQ (Ours)	73.73	39.97	+ 4.69

1. Contribution of Angle Quality Estimation (AQE): Comparing Case 2 (AQE only) with the Baseline (Case 1), we observe a significant gain of 2.96% in mAP75. This substantial improvement under a high IoU threshold underscores that modeling angle as a periodic distribution fundamentally enhances angle prediction accuracy, which is the cornerstone for high-precision localization.

2. Synergy between AQE and Double-A Loss: When both AQE and Double-A Loss are employed (Case 3), the performance (38.94% mAP75) surpasses the sum of their individual gains, achieving a synergistic improvement of + 3.66% over the baseline. This indicates that high-quality angle prediction (AQE) and aspect-ratio-aware supervision (Double-A Loss) are complementary and mutually reinforcing.

3. Contribution of NMS-AQ: Finally, integrating the NMS-AQ module (Case 4, Full Model) pushes the mAP75 to 39.97%, an overall gain of 4.69%. This final step demonstrates that leveraging the angle quality score to refine the post-processing stage effectively selects detection boxes with more reliable orientations, thereby translating accurate predictions into superior final results.

Figure 2 presents the ablation experiments on the HRSC2016 dataset. According to the table, compared to the benchmark model Faster-RCNN, the insertion angle quality estimation module significantly improves the detection performance of ship objects, achieving an 8.31% improvement in the mAP. Ship objects usually have higher aspect ratios, so precise detection of these objects requires higher accuracy in angle prediction. Data augmentation alone, while beneficial, does not specifically address the core challenges of angle prediction periodicity or the mismatch between classification and localization confidence. Thus, the improvement in mAP75 (from 38.92% to 50.04%) is more modest compared to the full model with AQE and other modules, which explicitly enhance angle estimation and localization accuracy. This highlights the necessity of our proposed modules for high-precision oriented object detection. Due to the improved optimization process of the angle prediction branch in this method, its detection performance has been significantly improved. At the same time, the improvement it brings increases with the improvement of detection standards. Under the more accurate detection standard mAP75, a performance improvement of 11.20% can be achieved.

Fig. 2.

Trend of models with different modules on the HRSC2016 test set.

To analyze the cost introduced by the angle quality estimation module, experimental comparisons were conducted in Table 3 between the angle regression based method (RetinaNet)³⁴, the angle classification based method (CSL)⁴⁰, our own method (AQE-Detector), and other methods. Among them, RetinaNet³⁴ was selected as the baseline model, with an input image size of 800 × 800. As illustrated in Table 3, the proposed AQE-Detector achieves an excellent balance between accuracy and efficiency. Parameter Efficiency: AQE-Detector introduces a very lightweight Angle Quality Estimation branch. Consequently, AQE-Detector has a highly competitive number of parameters (36.15 M), which is comparable to the lightweight RetinaNet⁴⁰ (36.13 M) and significantly lower than other complex detectors like Faster R-CNN (41.55 M), RoI-Transformer (43.82 M), and ReDet (45.66 M). This demonstrates the parameter efficiency of our design. Computational Cost: GFLOPs of AQE-Detector (128.37G) are comparable to Faster R-CNN and significantly lower than more complex detectors like RoI-Transformer and ReDet. This indicates that our added modules incur negligible additional computational burden during the forward pass.

Table 3.

Comparison of model parameters and training costs on the HRSC2016 test set.

Methods	Model parameter (MB)	GFLOPs	Training time/iteration	mAP	mAP75
Faster R-CNN18	41.55	137.42	0.3592	72.47	56.81
RoI-Transformer41	43.82	225.67	0.3700	81.54	62.44
ReDet42	45.66	239.23	0.4833	76.52	70.28
RetinaNet34	36.13	128.09	0.2495	83.21	50.72
CSL40	40.15	181.79	0.3870	85.40	60.20
AQE-Detector	36.15	128.37	0.3468	86.28	72.32

In summary, the AQE-Detector provides a significant accuracy improvement over the baseline and other methods while maintaining a model complexity (in terms of parameters and GFLOPs) on par with the most efficient detectors like RetinaNet. This makes it a highly efficient and practical solution for oriented object detection tasks.

• 2.Effectiveness of angle loss function based on aspect-ratio perception (Double-A Loss).

As shown in Table 1, introducing an angle loss function based on aspect-ratio perception (Double-A Loss) can effectively improve detection performance. The detector improved by 1.09% and 0.70% on the mAP and mAP75 of the DOTA dataset, respectively. This study improved the optimization process of the model and enhanced the recognition efficiency of rare low-frequency objects. Figure 2 shows the detection results on the HRSC2016 dataset. Introducing the new loss function based on aspect-ratio perception on the basis of the angle quality estimation module can bring additional improvements of 0.77% and 4.34% on the mAP and mAP75 metrics, demonstrating its effectiveness.

• 3.Effectiveness of Non-Maximum Suppression based on Angle Quality (NMS-AQ).

The estimated angle quality is used to perform post-processing operations on the model detection results, comprehensively evaluating the quality of each detection bounding box. Table 1 indicate that the non-maximum suppression based on angle quality (NMS-AQ) can effectively improve the detection performance, especially for the high-precision mAP75, the use of NMS-AQ brought a 1.03% improvement. Figure 2 indicate that the introduction of NMS-AQ improves the model performance on the HRSC2016 dataset, achieving gains of 0.92% and 4.01% on the mAP and mAP75, respectively.

Finally, all the modules mentioned above were integrated. As shown in Fig. 2, without adding any data augmentation, the AQE-Detector proposed achieved a 19.55% improvement in mAP75 on the HRSC2016 dataset. Despite using the data augmentation techniques, AQE-Detector still achieved a significant improvement of 25.08% on the mAP75, and AQE-Detector can further enhance its high-precision detection performance. For the DOTA dataset, AQE-Detector improved the mAP and mAP75 by 2.26% and 4.89% respectively, indicating the effectiveness for oriented objects of any category. For further comparison, the visualizations were visualized in Figs. 3 and 4, indicating that AQE-Detector can bring significant advantages. As shown, Faster R-CNN and RoI-Transformer produces inaccurate oriented boxes, particularly for densely packed and elongated objects like ships. With the introduction of the AQE module, the angle predictions become significantly more precise, leading to better-aligned bounding boxes. The integration of the Double-A Loss further refines the detection, especially for angle-sensitive high-aspect-ratio objects. Finally, our full model with NMS-AQ demonstrates the best performance, effectively suppressing duplicate detections while retaining the most accurately oriented boxes, resulting in the cleanest and most precise detection results.

Fig. 3.

Visualizations of ablation experiments on DOTA validation set. The base image is based on DOTA dataset and visualized using Python 3.7, OpenCV 4.5.4 (https://opencv.org), and Matplotlib 3.5.1 (https://matplotlib.org) software.

Fig. 4.

Visualizations of ablation experiments on the HRSC2016 test set. The base image is based on HRSC2016 dataset and visualized using Python 3.7, OpenCV 4.5.4 (https://opencv.org), and Matplotlib 3.5.1 (https://matplotlib.org) software.

Parameter analysis

1. Hyperparameter analysis of angle resolution.

The impact of angular resolution on model detection was compared under different angular resolution settings. Setting the angular resolution R_θ to 10, 5, and 1 respectively, Table 4 shows the model detection at different R_θ. According to Table 4, when the angular resolution is set to 10, the iteration time is only 0.3440s. Due to the low angular resolution allowing the model to make ambiguous predictions, the detection model achieved the lowest mAP accuracy. When the angular resolution is set to 5, the mAP and mAP75 increase to 72.64% and 37.50%, respectively. Due to the low computational cost introduced by the AQE during the training phase, it has almost no impact on the time cost. The model maintains an approximate training time at an angular resolution of 1, indicating that this method can ensure overall efficiency with almost no increase in time cost.

Table 4.

Parameter analysis of AQE on DOTA validation set.

Method	R θ	Training time/iteration	mAP	mAP75
AQE-Detector	10	0.3440	72.29	33.04
	5	0.3442	72.64	37.50
	1	0.3468	73.73	39.97

• 2.Hyperparameter analysis of NMS-AQ.

ξ is crucial in non-maximum suppression based on angle quality (NMS-AQ), and is set to 0, 0.05, 0.1, 0.2, and 0.5, respectively. Table 5 shows that when ξ is set to 0.1, this method reaches the optimal detection accuracy. After introducing NMS-AQ, the mAP increased by 0.15%, and the mAP75 increased by 0.66%. Overall, with the change of ξ, the mAP75 consistently outperforms the model without NMS-AQ, verifying its effectiveness.

Table 5.

Parameter analysis of NMS-AQ on DOTA validation set.

Method	NMS-AQ	ξ	mAP	mAP75
AQE-Detector	×	0	73.58	38.94
	√	0.05	73.69	39.60
	√	0.1	73.73	39.97
	√	0.2	73.58	39.75
	√	0.5	72.63	39.58

• 3.Hyperparameter analysis of Double-A Loss.

Angle sensitivity function and weight factor γ are key parameters in the angle loss function. As mentioned earlier, three conversion functions were selected for the angle sensitivity in this experiment. Table 6 shows that the fitted Gaussian function has significant effectiveness in characterizing the relationship between angle sensitivity and object aspect ratio. For the weight factor γ, this experiment sets it to 2, 5, and 10 for comparison. When γ is set to 5, the model achieves a better balance between simple and difficult samples.

Table 6.

Parameter analysis of Double-A loss on DOTA validation set.

Method	Angle sensitivity function	γ	mAP	mAP75
AQE-Detector	Linear function	5	72.75	38.55
	Quadratic function	5	73.12	37.98
	Gaussian function	5	73.73	39.97
	Gaussian function	2	73.20	38.78
	Gaussian function	10	73.25	39.16

Comparison results

This section conducted a comprehensive experimental comparison between our method (AQE-Detector) and currently advanced methods on three datasets: DOTA, HRSC2016, and ICDAR2015. As shown in Table 7, AQE-Detector achieved a detection accuracy of 78.35% on the mAP, significantly better than most other comparison methods. Compared to the baseline model⁴¹, this method achieved an improvement of 25.42% on mAP, verifying its superiority. When using RoI-Transformer⁴², this method achieved 80.87% on mAP, outperforming all existing methods. In addition, compared with the most advanced methods^34,43,44, the evaluation indicators of AQE-Detector have improved by 3.33%, 3.02%, and 2.18% in terms of results, respectively. As shown in Fig. 5, this method can identify oriented objects in complex and dense scenes at different scales. In addition, the proposed algorithm can be combined with any existing method to improve its detection performance. As shown in Table 8, AQE-Detector can improve the overall efficiency of RetinaNet³⁴, Faster-RCNN¹⁸, RoI-Transformer⁴², and ReDet⁴³.

Table 7.

Comparative results on DOTA test set.

Methods	Plane	BD	Bridge	GTF	SV	LV	Ship	TC	BC	ST	SBF	RA	Harbor	SP	HC	mAP
FR-O	79.09	69.12	17.17	63.49	34.20	37.16	36.20	89.19	69.60	58.96	49.40	52.52	46.69	44.80	46.30	52.93
R-DFPN	80.92	65.82	33.77	58.94	55.77	50.94	54.78	90.33	66.34	68.66	48.73	51.76	55.10	51.32	35.88	57.94
R2CNN	80.94	65.67	35.34	67.44	59.92	50.91	55.81	90.67	66.92	72.39	55.06	52.23	55.14	53.35	48.22	60.67
RRPN	88.52	71.20	31.66	59.30	51.85	56.19	57.25	90.81	72.84	67.38	56.69	52.84	53.08	51.94	53.58	61.01
ICN	81.40	74.30	47.70	70.30	64.90	67.80	70.00	90.80	79.10	78.20	53.60	62.90	67.00	64.20	50.20	68.20
RoI-Transformer	88.64	78.52	43.44	75.92	68.81	73.68	83.59	90.74	77.27	81.46	58.39	53.54	62.83	58.93	47.67	69.56
CAD-Net	87.80	82.40	49.40	73.50	71.10	63.50	76.70	90.90	79.20	73.30	48.40	60.90	62.00	67.00	62.20	69.90
DRN	88.91	80.22	43.52	63.35	73.48	70.69	84.94	90.14	83.85	84.11	50.12	58.41	67.62	68.60	52.50	70.70
DAL	88.61	79.69	46.27	70.37	65.89	76.10	78.53	90.84	79.98	78.41	58.71	62.02	69.23	71.32	60.65	71.78
SCRDet	89.98	80.65	52.09	68.36	68.36	60.32	72.41	90.85	87.94	86.86	65.02	66.68	66.25	68.24	65.21	72.61
R3Det	89.49	81.17	50.53	66.10	70.92	78.66	78.21	90.81	85.26	84.23	61.81	63.77	68.16	69.83	67.17	73.74
Gliding Vertex	89.64	85.00	52.26	77.34	73.01	73.14	86.82	90.74	79.02	86.81	59.55	70.91	72.94	70.86	57.32	75.02
Mask OBB	89.56	85.95	54.21	72.90	76.52	74.16	85.63	89.85	83.81	86.48	54.89	69.64	73.94	69.06	63.32	75.33
CSL	90.25	85.53	54.64	75.31	70.44	73.51	77.62	90.84	86.15	86.69	69.60	68.04	73.83	71.10	68.93	76.17
DCL	89.14	83.93	53.05	72.55	78.13	81.97	86.94	90.36	85.98	86.94	66.19	65.66	73.72	71.53	68.69	76.97
ReDet	88.81	82.48	60.83	80.82	78.34	86.06	88.31	90.87	88.77	87.03	68.65	66.90	79.26	79.71	74.67	80.10
AQE-Detector	89.49	85.89	55.46	77.32	74.17	80.33	87.65	90.82	86.99	86.52	66.58	69.06	77.12	78.35	69.51	78.35
RoI-Transformer +AQE-Detector	89.23	85.35	60.26	80.13	80.27	85.58	88.46	90.88	87.51	88.07	69.80	70.32	80.97	82.16	74.03	80.87

Fig. 5.

Visualization on DOTA test set. The base image is based on DOTA dataset and visualized using Python 3.7, OpenCV 4.5.4 (https://opencv.org), and Matplotlib 3.5.1 (https://matplotlib.org) software.

Table 8.

Algorithm transferability analysis.

Methods	Networks	AQE-Detector	mAP	mAP75
RetinaNet34	ResNet−50	×	64.31	36.40
		√	66.86 (+ 2.55)	38.04 (+ 1.64)
Faster-RCNN18	ResNet−50	×	71.47	35.28
		√	73.73 (+ 2.26)	39.97 (+ 4.69)
RoI-Transformer42	ResNet−50	×	75.54	47.02
		√	76.31 (+ 0.77)	48.33 (+ 1.31)
ReDet43	ReResNet−50	×	76.52	51.73
		√	76.81 (+ 0.29)	52.03 (+ 0.30)

The Double-A Loss adaptively adjusts the supervision intensity based on an object’s aspect ratio. This design is particularly beneficial for objects whose localization accuracy is highly sensitive to angle prediction. Categories with extremely high or low aspect ratios, such as Large Vehicle (LV), Ship, and Harbor, show consistent improvements. For instance, Helicopter (HC) achieves a remarkable gain of 5.96% in mAP with Double-A Loss. This can be attributed to the fact that helicopters, while sometimes appearing near-square, often have distinct orientations due to their tail boom, making them moderately angle-sensitive. The Double-A Loss provides more nuanced supervision than a one-size-fits-all loss, allowing the model to learn more accurate angles for such targets. Conversely, for categories with more balanced aspect ratios like Storage Tank (ST) or Tennis Court (TC), which are less sensitive to angle errors, the gains from Double-A Loss are smaller, as expected. This confirms that our method intelligently allocates learning resources.

The gains from AQ-NMS are most pronounced in cluttered scenes containing multiple instances of elongated objects. For example, in the Ship and Large Vehicle (LV) categories, where objects are densely packed and have high aspect ratios, a small angle error can lead to a significant drop in IoU. AQ-NMS effectively prioritizes boxes with more reliable angle predictions, leading to noticeable improvements in mAP75 (e.g., + 2.05% for Ship). Conversely, for isolated objects or categories with more compact shapes (e.g., Basketball Court (BC) or Baseball Diamond (BD)), the classification confidence and IoU are already strong indicators of box quality. In these cases, the angle quality provides less additional information, resulting in more limited gains from AQ-NMS. This is not a failure but rather an expected behavior, demonstrating that AQ-NMS selectively provides the most value in complex, dense scenarios where angle precision is critical.

Table 9 shows the overall comparison of different models on the HRSC2016 dataset. Proposed AQE-Detector achieved an accuracy of 90.02% in the mAP, significantly better than the baseline model by 34.32%, demonstrating the detection advantage of AQE-Detector for larger aspect-ratio objects. In addition, compared with the most advanced methods^{40,42,43,45,46}, this method has improved by 3.82%, 1.82%, 0.76%, 0.45%, and 0.40%, respectively. Figure 6 visually illustrates the performance of AQE-Detector, as most ships have a large aspect ratio, have accurate recognition.

Table 9.

Comparative results on HRSC2016.

Methods	Size of image input	mAP
Fast-RCNN + SRBBS	–	55.70
BL2	–	69.60
R2CNN	800 × 800	73.07
IENet	1024 × 1024	75.01
RC1&RC2	–	75.70
RRPN	800 × 800	79.05
RRD	384 × 384	84.30
RoI-Transformer	512 × 800	86.20
Gliding Vertex	–	88.20
R3Det	800 × 800	89.26
DCL	800 × 800	89.46
GRS-Det	800 × 800	89.57
CSL	800 × 800	89.62
DAL	800 × 800	89.77
AQE-Detector	800 × 800	90.02

Fig. 6.

Visualization on the HRSC2016 test set. The base image is based on HRSC2016 dataset and visualized using Python 3.7, OpenCV 4.5.4 (https://opencv.org), and Matplotlib 3.5.1 (https://matplotlib.org) software.

The proposed AQE-Detector was evaluated on ICDAR2015. This benchmark contains many directed texts and complex backgrounds. To demonstrate the performance of AQE-Detector, it was compared with SOTAs^40,47,48 and some common text detection methods^49–53. As shown in Table 10, in terms of F1 Measure, this method achieved 84.58% performance, significantly better than other methods. Compared with SCRDet⁴⁷, this method improved F1 Measure by 4.50%. Compared with DAL⁴⁸ and CSL⁴⁰, this method still has good performance when facing oriented text objects and complex backgrounds.

Table 10.

Comparative results on ICDAR2015.

Methods	Precision	Recall	F1-Measure
CTPN	74.22	51.56	60.85
Seglink	73.10	76.80	75.00
RRPN	82.17	73.23	77.44
EAST	78.33	83.27	80.72
SCRDet	81.30	78.90	80.08
RRD	85.60	79.00	82.20
DAL	84.40	80.50	82.40
CSL	84.30	83.00	83.65
AQE-Det	85.65	83.53	84.58

Conclusion

A new oriented object detection technique based on angle quality estimation (AQE-detector) was proposed to solve the problems of missing confidence and insufficient localization accuracy in object detection for remote sensing, effectively improving the high-precision detection performance of remote sensing objects. Using periodic Gaussian distribution to model angle variables, the detection task was transformed into a distribution estimation task, overcoming the problem of inconsistent loss function values and object localization results caused by angle periodicity, while implicitly estimating the confidence information of the predicted angle. Non-maximum suppression based on angle quality (NMS-AQ) was proposed. By comprehensively considering angle confidence and classification confidence, the bias in evaluating detection results was reduced. In addition, the relationship between the angle sensitivity and aspect-ratio was quantitatively analyzed, and an angle loss function based on aspect-ratio perception (Double-A Loss) was constructed to flexibly adjust the loss weight. The intelligent object detection technology under information limited conditions has been studied, facilitating the efficient application of object detection in major demand fields.

In future work, in-depth research will be conducted from the following aspects. (1) Object detection based on cross modal information. This study only uses single modal image data, and lacks the comprehensive utilization of multimodal image information. How to fully explore the complementary information contained in different modal data is crucial for improving object detection performance. (2) Sustainable detection based on mixed supervision information. The actual application scenarios are usually dynamically open, and target data with new categories and appearances will emerge over time. Object detection models based on single training and lifelong use are difficult to meet the ever-changing practical needs. Therefore, it is crucial to research a sustainable object detection method that can be updated online and learn incrementally. (3) Benchmarking and performance validation with the latest methods. In response to the potential obsolescence of the comparative methods used in this study, we plan to systematically conduct large-scale comparative experiments with the latest advanced methods published in 2024–2025 in future work to further validate the competitiveness and generality of AQE detector. This will include performance evaluation and ablation studies on multiple datasets to ensure that our approach can continuously address the challenges of field development.

Author contributions

C. Li: Writing - origin draft, Investigation, Data curation, Formal analysis, Conceptualization, Resources. All authors reviewed the manuscript.

Funding

No Funding.

Data availability

The datasets used in this article are public datasets.The DOTA dataset is available at https://captain-whu.github.io/DOTA.The HRSC2016 dataset is available at https://aistudio.baidu.com/datasetdetail/54106.The ICDAR 2015 dataset is available at http://www.robots.ox.ac.uk/~vgg/data/text/.

Declarations

Competing interests

The authors declare no competing interests.