Entropy Teacher: Entropy-Guided Pseudo Label Mining for Semi-Supervised Small Object Detection in Panoramic Dental X-Rays

Abstract

Small-scale object detection remains a significant challenge in semi-supervised object detection (SSOD), particularly in panoramic dental X-rays. Due to the small lesion size, low contrast, and complex anatomical background, conventional teacher models often fail to extract accurate lesion features, leading to noisy pseudo labels and suboptimal detection performance. Additionally, most existing SSOD methods rely on high-confidence thresholds to select pseudo labels, which may mistakenly discard valuable predictions with low scores but accurate localization—especially for small-scale targets. To address these challenges, we propose Entropy Teacher, a novel SSOD framework specifically designed for small-scale dental disease detection. Our method introduces an Entropy-Guided Feature Pyramid that integrates entropy-guided representations to enhance fine-grained structural learning. Moreover, we develop a low-confidence pseudo-label mining (LCPLM) strategy with a class-adaptive thresholding mechanism to effectively recover high-quality pseudo labels below conventional confidence thresholds. Extensive experiments on the Dental Disease Dataset and ChestX-Det demonstrate that Entropy Teacher achieves state-of-the-art performance, surpassing the baseline Unbiased Teacher by +3.8 $A{P}_{50}$ and +4.5 $A{P}_S$. These results confirm the effectiveness of entropy-guided representations and low-confidence mining in improving small-scale lesion detection under limited supervision.

1. Introduction

Object detection in medical imaging plays a vital role in computer-aided diagnosis, enabling automated localization of abnormal regions [1]. In particular, panoramic dental X-rays (also known as orthopantomograms) are widely used in routine dental assessments due to their ability to capture comprehensive anatomical structures in a single scan. Accurate detection of dental diseases, such as caries, apical shadows, and high/low-density lesions, is crucial for early diagnosis and treatment planning. However, detecting these lesions remains challenging due to their small size, low contrast, and high similarity to surrounding tissues. Moreover, collecting large-scale, pixel-level annotated datasets in the medical domain is both time-consuming and labor-intensive [2,3,4,5], which severely limits the applicability of fully supervised detection frameworks [6,7,8,9] in real-world scenarios.

Semi-supervised object detection [10,11,12,13] (SSOD) has recently emerged as a promising paradigm to alleviate the reliance on extensive annotations by leveraging large amounts of unlabeled data. Most SSOD methods adopt a teacher–student framework [10,14], where the teacher model generates pseudo labels to supervise the student model on unlabeled images. Although this approach has shown impressive results on natural images, it faces two major limitations when applied to small-scale lesion detection in medical images.

Firstly, limitations of conventional feature pyramids for small-scale lesion detection. While Feature Pyramid Networks [15] (FPNs) are widely used in object detection for multi-scale representation, they often fail to capture the subtle appearance and boundary features of small-scale lesions in panoramic dental X-rays. This is due to the low contrast and high similarity between lesions and surrounding anatomical structures. As shown in Figure 1 [16], many lesions are tiny and blend into the background, leading to inaccurate localization and noisy pseudo labels. In contrast, entropy maps have demonstrated strong potential in highlighting regions with rich structural information. By quantifying local uncertainty and complexity, they enhance texture and boundary details, making them particularly effective for small object detection in low-contrast medical images [17,18]. As shown in Figure 2, entropy-enhanced features offer clearer discrimination between lesions and background, making them a promising alternative to conventional FPN enhancements. In Figure 2, we visualize the attention heatmaps before and after integrating entropy maps with the original view. Before incorporating entropy information, the model tends to focus on irrelevant anatomical structures, such as the outer edges of the panoramic image or the central areas of teeth, which are generally unrelated to most dental diseases. However, after fusing entropy-based representations, the model shifts its attention toward more diagnostically relevant regions, such as the tops, sides, and roots of teeth—areas where caries and apical shadows commonly occur. In addition, as shown in

Table 1. Experimental results of original view and original + entropy on Dental Disease Dataset.

View	${\mathit{AP}}_{50}$	${\mathit{AP}}_{\mathit{S}}$
Original	51.5	39.5
Original + Entropy	54.2 (+2.7)	42.4 (+2.9)

, we validate the effectiveness of entropy maps on the Dental Disease Dataset. It can be observed that integrating entropy-based features improves the overall detection accuracy $A{P}_{50}$ by 2.7 and enhances the performance on small-scale lesions $A{P}_S$ by 2.9. These demonstrate the effectiveness of entropy maps in guiding the model toward informative lesion features and reducing interference from background structures.

Secondly, the over-reliance on fixed high-threshold pseudo-label filtering limits the effectiveness of semi-supervised training for small-scale lesions. Most existing SSOD frameworks discard predictions with classification scores below a predefined threshold (e.g., 0.9). However, small lesions—due to their low contrast and subtle visual features—often yield low confidence scores even when correctly localized. As a result, many potentially valuable pseudo labels are mistakenly excluded, leading to insufficient supervision for small objects. Moreover, low confidence does not necessarily imply poor localization quality. In many cases, predictions with relatively low scores still correspond to accurate bounding boxes [19]. To address this, we propose a low-confidence pseudo-label mining (LCPLM) strategy combined with a class-adaptive threshold mechanism. This strategy adaptively identifies reliable pseudo labels below the traditional confidence threshold by evaluating the Entropy-Guided feature pyramid. It enables the model to retain high-quality supervisory signals from hard-to-detect lesions that would otherwise be discarded, ultimately improving detection performance on small-scale targets.

To address these challenges, we propose a novel SSOD framework, Entropy Teacher, specifically designed for small-scale dental disease detection in panoramic X-rays. Our approach introduces an Entropy-Guided Feature Pyramid that integrates entropy-based representations to enhance feature learning for subtle lesions. In addition, we develop a low-confidence pseudo-label mining (LCPLM) strategy with a class-adaptive thresholding mechanism, enabling effective utilization of high-quality pseudo labels with low confidence scores. Our main contributions are summarized as follows:

• We propose Entropy Teacher, a novel SSOD framework that combines entropy-guided feature fusion and low-confidence pseudo-label mining to improve the detection of small-scale lesions in panoramic dental X-rays.
• We design an Entropy-Information Aggregation (EIA) module to extract entropy-based features and fuse them with original image features, leading to enhanced fine-grained representations and more accurate localization of small-scale lesions.
• We introduce an LCPLM strategy with class-adaptive thresholding, which identifies and leverages reliable pseudo labels with low classification scores, thereby improving supervision for hard-to-detect lesions.

2. Related Works

2.1. Semi-Supervised Object Detection

In recent years, SSOD has gained significant attention as an effective approach to reducing reliance on large-scale labeled data. STAC [20] was the first to introduce pseudolabeling with strong data augmentation and consistency training in SSOD. However, this method employs a two-stage pseudo-label generation process, where pseudo-labels cannot be dynamically updated during training, thereby limiting performance improvement. Subsequently, various improvements based on the Mean Teacher framework have been proposed. Refs. [10,11,12,13,19,21,22,23] leverage the exponential moving average (EMA) mechanism to iteratively update pseudo-labels in the teacher network, enabling end-to-end pseudo-label generation.

For instance, Unbiased Teacher [10] adopts a confidence thresholdbased pseudo-labeling strategy to mitigate confirmation bias in SSOD. Soft Teacher [12] assigns classification confidence scores as classification loss weights to suppress the negative impact of missing potential objects in pseudo-labeling. PseCo [24] enhances pseudo-label reliability through a perturbation-consistency pseudolabeling strategy, effectively reducing noise and improving SSOD performance. Although these methods have achieved promising results in natural scene object detection, they struggle to address the complex multi-scale lesion distribution in panoramic dental X-rays. In particular, pseudo-label noise has a significant impact on detecting small lesion regions. Therefore, our research focuses on enhancing feature fusion with entropy image and mining low confidence but high-quality pseudo labels to enhance small-scale dental disease detection.

2.2. Semi-Supervised Learning in Medical Imaging

Due to the difficulty of obtaining precisely annotated medical data, semi-supervised learning has been widely adopted in the medical domain. For instance, Das et al. [2] introduced a Scale-Invariant Module and a Pseudo-Label Optimizer specifically designed to enhance disease detection accuracy in chest X-ray images. Saga et al. [25] utilized YOLOv6 and DeepLab v3+ for facial detection to assist in the treatment of speech disorders in children. Roy et al. [26] developed a semi-supervised human activity recognition system based on various clustering strategies.

Unlike these existing applications of semi-supervised learning in the medical field, our work focuses on detecting complex small-scale diseases in panoramic X-rays. Our goal is to improve the detection performance of small-scale lesions through a semi-supervised object detection framework, thereby assisting clinicians in making more effective diagnoses.

3. Materials and Methods

In the problem of semi-supervised object detection, a model is trained with a labeled $D_L=\left\{\left(X_i^S,Y_i^S\right){|}_{i=1}^N\right\}$ and an unlabeled image set $D_u=\left\{X_j^u{|}_{j=1}^M\right\}$, where N and M are the numbers of labeled and unlabeled data. $X_i^S$ represent the i-th labeled image; $Y_i^S$ denote the label of the i-th labeled image, including the bounding box and class information; $X_j^u$ represent the j-th unlabeled image. The goal is to make use of both labeled and unlabeled data to learn the object detection model. Built upon the pseudo labeling framework, our method follows a score filtering mechanism [10] to generate pseudo labels $Y^u$ for unlabeled image $X^u$.

An overview of our approach is illustrated in Figure 3. We propose Entropy Teacher to mitigate pseudo-label noise and enable accurate detection of small-scale dental diseases in panoramic X-rays. Specifically, we introduce an Entropy-Guided Feature Pyramid, which incorporates an EIA module to fuse entropy map features and enhance representations in low-contrast regions. In addition, we adopt an LCPLM strategy to identify high-quality pseudo labels with low confidence scores. To further improve recall, a class-adaptive threshold strategy is employed, which dynamically adjusts pseudo-label selection based on the confidence distribution of each category. Although our framework is model-agnostic, we adopt Faster R-CNN [6] with FPN [15] to ensure consistency with previous SSOD works in medical imaging.

3.1. Basic Pseudo-Labeling Framework

Following standard practice in SSOD, we adopt a pseudo-label-based teacher–student framework for training. Specifically, each training batch is composed of both labeled and unlabeled data, sampled at a ratio of 1:4. The labeled data are used to supervise the student model via standard supervised loss with ground-truth annotations, while the unlabeled data rely on pseudo labels generated by the teacher model. 

Since unlabeled data lack annotations, the teacher model provides supervision by generating pseudo labels. Its weights are updated through the exponential moving average (EMA) of the student’s parameters. For each unlabeled sample, the teacher model generates pseudo labels on a weakly augmented view of the image, which are then used to supervise the student model on the strongly augmented view. The student model is updated using both the labeled and unlabeled samples. The overall training objective is defined as follows:

$$\mathcal{L}={\mathcal{L}}_s+\alpha ·{\mathcal{L}}_u$$

(1)

where ${\mathcal{L}}_s$ and ${\mathcal{L}}_u$ denote supervised loss of labeled images and unsupervised loss of unlabeled images respectively, $\alpha$ controls contribution of unsupervised loss.

In this framework, the teacher model parameters ${\theta }^{\prime }$ are updated by the student model parameters using EMA, as follows:

$${\theta }_t^{\prime }=m{\theta }_{t-1}^{\prime }+\left(1-m\right){\theta }_t$$

(2)

where t represents the current time step, and the momentum decay is defined as 0.999.

3.2. Entropy-Guided Feature Pyramid

In panoramic dental X-rays, small-scale lesions often exhibit low contrast and weak semantic cues, making them difficult to localize using traditional visual features alone. To address this issue, we introduce an EIA module that integrates structural information from entropy maps with semantic features extracted from the original image. Entropy maps are capable of capturing local uncertainty and texture complexity, thereby highlighting regions that are rich in structural detail. By aggregating these representations with standard visual features, our EIA module enhances the model’s ability to focus on diagnostically relevant regions. The module is lightweight, plug-and-play, and trained in an end-to-end manner alongside the base detector. As shown in Appendix A, we calculate the local entropy map of the image by sliding the window. In addition to the provided code, we have now cited the original publication by Robert Haralick [27], who first introduced entropy features in the context of image analysis.

Given an unlabeled image $X^u$, we introduce its corresponding entropy map, which shares the same spatial resolution as $X^u$. Using the feature encoder $f\left(\theta \right)$, we extract multi-scale feature pyramids $\left\{P_i^{+}\right\}$ from the original image and $\left\{P_i^E\right\}$ from the entropy map, where each $P_i^{+}\in {\mathbb{R}}^{256\times H\times W}$ and $P_i^E\in {\mathbb{R}}^{1\times H\times W}$.

To achieve this, inspired by [28], we first compute a spatial attention map $SA$ based on the entropy features by EIA. Specifically, we invert the normalized entropy features $(1-P_i^E)\in {\mathbb{R}}^{1\times H\times W}$ to emphasize stable, low-entropy regions that are typically more reliable for detection. This inversion reduces the impact of noisy, high-entropy background areas while amplifying well-structured lesion regions.

We then use a two-layer convolutional subnetwork to model spatial dependencies and adaptively learn attention weights. The architecture consists of a 1 × 1 convolution that expands the feature to an intermediate dimension 16, followed by a ReLU activation, and then a second 1 × 1 convolution that projects back to a single-channel attention map. Concretely,

$$SA=\sigma \left(W_{SA}^2·\delta \left(W_{SA}^1·(1-P_i^E)+b_{SA}^1\right)+b_{SA}^2\right),$$

where $W_{SA}^1\in {\mathbb{R}}^{16\times 1\times 1\times 1}$ projects the input to 16 channels, $W_{SA}^2\in {\mathbb{R}}^{1\times 16\times 1\times 1}$ reduces it back to a single channel, $\delta (·)$ denotes the ReLU function, and $\sigma (·)$ is the Sigmoid function that normalizes the attention map to [0, 1]. As a result, $SA\in {\mathbb{R}}^{1\times H\times W}$.

We apply this attention map to fuse the original and entropy features in a soft attention manner:

$$P_i^{\times }=SA·P_i^{+}+(1-SA)·P_i^{E^{\prime }},$$

where $P_i^{E^{\prime }}\in {\mathbb{R}}^{C\times H\times W}$ is obtained by expanding $P_i^E$ through channel-wise replication and a 1 × 1 convolution for channel alignment.

This fusion strategy allows the model to dynamically prioritize structural cues from the entropy map in uncertain or ambiguous regions, while retaining semantic richness from the original view in well-understood areas. The final fused features $P_i^{\times }$ and the original features $P_i^{+}$ are used to generate predictions ${\widehat{y}}^{\times }$ and ${\widehat{y}}^{+}$, respectively.

Notably, the EIA module is lightweight, requiring only two pointwise convolution layers and a few activation functions, resulting in negligible additional computation and parameters.

3.3. Low-Confidence Pseudo-Label Mining Strategy

Semi-supervised object detection frameworks typically filter pseudo labels using a fixed high-confidence threshold ${\tau }_h$ (e.g., 0.9). However, this approach is suboptimal for small-scale lesion detection, where subtle features and low contrast often result in low classification scores—even for accurately localized objects.  To address this, we adopt a two-threshold scheme: a fixed lower threshold ${\tau }_l=0.5$ and a class-adaptive upper threshold ${\tau }_h$ (introduced in Section 3.3.1). Based on these thresholds, pseudo labels are categorized as follows:

• High-confidence pseudo labels ($s\ge {\tau }_h$): directly used to supervise the student model.
• Weak pseudo labels (${\tau }_l\le s<{\tau }_h$): potentially valuable but uncertain, evaluated by our mining strategy.
• Low-confidence pseudo labels ($s<{\tau }_l$): discarded as unreliable.

We then propose a two-stage strategy to leverage both confident and weak pseudo labels: (1) a class-adaptive thresholding mechanism to compute ${\tau }_h$ for each class, and (2) a Quality-Aware Mining strategy to select high-quality weak pseudo labels based on cross-view consistency. This design improves both recall and robustness in detecting small lesions.

3.3.1. Class-Adaptive Threshold for Pseudo-Label Filtering

Instead of using a fixed threshold across all classes, we dynamically adjust the upper threshold ${\tau }_h$ based on the average classification confidence of each class. Specifically, given the set of foreground $N_c^{fg}$ and background predictions $N^{bg}$ for a class c, wo define ${\tau }_h$ as follows:

$${\tau }_h={\left({\displaystyle \frac{\frac{1}{N_c^{fg}}{\sum }_{i=1}^{N_c^{fg}}{S}_i^{fg}}{\frac{1}{N^{bg}}{\sum }_{j=1}^{N^{bg}}{S}_j^{bg}}}\right)}^{\gamma }$$

(3)

where $S_i^{fg}$ and $S_j^{bg}$ are the classification scores of the i-th foreground and j-th background prediction boxes, respectively, and $\gamma$ is a hyperparameter controlling the threshold scaling (we set $\gamma =0.05$). The intuition behind this design is to avoid setting an overly low threshold at the early training stages, as this may introduce a large number of noisy pseudo labels. By applying a power function with a small exponent (e.g., $\gamma =0.05$), even low foreground-to-background confidence ratios produce relatively high thresholds, which leads to conservative pseudo-label selection at the beginning. As training progresses and the model becomes more confident in foreground predictions, the ratio increases, and the threshold grows more slowly. This allows more pseudo labels to be accepted without significantly increasing the risk of noise, thus improving recall while maintaining quality.

3.3.2. Quality-Aware Mining of Low-Confidence Pseudo Labels

To recover reliable pseudo labels from low-confidence predictions, we define a lower threshold ${\tau }_l$ (empirically set to 0.5) and consider all candidate boxes within the interval ${\tau }_l\le s<{\tau }_h$ For each candidate, we assess its quality based on the consistency of classification scores across two views: the original view and the entropy-guided fused view.

Given proposal sets ${\left\{C_i^{\times }\right\}}_{i=1}^M$ from the entropy-fused features and ${\left\{C_j^{+}\right\}}_{j=1}^N$ from the original features, both having IoU > 0.7 with the candidate, we define the improvement score $\Delta q$ as

$$\Delta q={\displaystyle \frac{1}{M}}\sum _{i=1}^M{C}_i^{\times }-{\displaystyle \frac{1}{N}}\sum _{j=1}^N{C}_j^{+}$$

(4)

A higher $\Delta q$ indicates that the prediction has significantly benefited from entropy-based enhancement, suggesting its underlying reliability. If $\Delta q$ exceeds a promotion threshold $\delta$, the candidate is selected as a valid pseudo label and incorporated into the training set. This mechanism enables the model to retain informative but uncertain predictions, improving recall and robustness—especially for small-scale lesions. Owing to the enhanced feature representation enabled by the entropy-guided feature pyramid, we believe that the observed improvement in the score of $\Delta q$ reflects a genuine pseudo label quality gain.

3.4. Loss Function of Entropy Teacher

In our framework, the final pseudo labels generated by the teacher model are used to supervise the student detector on unlabeled data. Specifically, the student model makes predictions using two separate feature branches: one from the original augmented image view and another from the entropy-guided feature fusion. Both branches are supervised using the same set of pseudo labels. The overall unsupervised loss is formulated as

$${\mathcal{L}}_u={\lambda }_1{\mathcal{L}}_u^1\left(y^1,\widehat{y}\right)+{\lambda }_2{\mathcal{L}}_u^2\left(y^2,\widehat{y}\right)$$

(5)

where $y^1$ and $y^2$ denote the predictions from the original-view feature pyramid and the entropy-fused feature pyramid, respectively, and $\widehat{y}$ represents the pseudo labels produced by the teacher model. These pseudo labels include both high-confidence predictions (above the class-adaptive threshold ${\tau }_h$) and additional low-confidence pseudo labels selected through our LCPLM strategy. ${\lambda }_1$ and ${\lambda }_2$ are weighting coefficients that balance the two loss terms.

For labeled data, the standard supervised loss ${\mathcal{L}}_s$ is computed using the ground-truth annotations. The final training objective combines both supervised and unsupervised components:

$${\mathcal{L}}_{\mathrm{total}}={\mathcal{L}}_s+\alpha ·{\mathcal{L}}_u$$

(6)

where $\alpha$ is a hyperparameter that controls the relative contribution of the unsupervised loss. In all experiments, we follow the baseline setting [10] for the design of detection losses, including classification and bounding box regression terms.

As shown on the right side of Figure 3, to ensure fair comparison during inference, all auxiliary components—such as entropy maps and the EIA module—are discarded, and predictions are made using only the original image view.

4. Results

4.1. Dataset and Evaluation Metrics

To evaluate the effectiveness and generalization capability of our method, we tested it on two datasets: Dental Disease Dataset [16] and ChestX-Det dataset [29].

Dental Disease Dataset: This comprises 245 annotated panoramic X-rays from patients with dental diseases and 1000 unlabeled panoramic X-rays. These images contain a total of 1157 annotated disease instances, categorized into four types: low-density shadow, high-density shadow, root tip shadow, and obstructed teeth. Following the definition in MS COCO [30], we classify lesions based on their pixel area: small-scale diseases are those with an area smaller than $32\times 32$ pixels, medium-scale diseases fall within the range of $32\times 32$ to $96\times 96$ pixels, and large-scale diseases exceed $96\times 96$ pixels. The dataset statistics are presented in

Table 2. The distribution of small (≤32 × 32), medium (>32 × 32 and ≤96 × 96), and large (>96 × 96) diseases in the Dental Disease Dataset.

Dataset	Abnormalities	Small	Medium	Large
Dental Disease Dataset	high-density shadow	164	274	60
	low-density shadow	114	57	0
	root tip shadow	110	92	10
	obstructed teeth	3	177	96

, showing that the majority of instances belong to the small-scale category. For the Dental Disease Dataset, due to the difficulty of annotating small-scale diseases and the resulting scarcity of labeled data, we used all available labeled images for training.

ChestX-Det Dataset: This dataset consists of 3578 chest X-ray images, annotated by three board-certified radiologists with 13 common disease or abnormality categories. For the ChestX-Det dataset, we randomly sampled 10%, 30%, and 50% of the images as labeled data, with the remaining images used as unlabeled data accordingly. Following standard practice, we performed five-fold cross-validation for each experimental setting and reported the average results.

The evaluation follows the standard metrics of the PASCAL VOC dataset [31], including $A{P}_{50}$, $A{P}_S$, $A{P}_M$, $A{P}_L$ and $AR$. Specifically, $A{P}_{50}$ represents the mean average precision across all categories at an IoU threshold of 0.5, while $A{P}_S$, $A{P}_M$ and $A{P}_L$ correspond to the average precision for small-, medium-, and large-scale diseases at the same IoU threshold. Higher values indicate better detection performance. The definition of $AP$ and $AR$ is as follows:

$$P={\displaystyle \frac{TP}{TP+FP}}$$

(7)

$$R={\displaystyle \frac{TP}{TP+FN}}$$

(8)

$$AP={\int }_0^{1}P\left(R\right)dR,AR={\displaystyle \frac{1}{N}}\sum _{i=1}^N{R}_i$$

(9)

where $TP$ denotes the number of detected bounding boxes with an IoU greater than the specified threshold, while $FP$ represents the number of detected bounding boxes with an IoU below the threshold. $FN$ refers to the number of missed ground-truth boxes.

4.2. Implementation Details

Following the mainstream choices in semi-supervised object detection, we adopt Faster R-CNN [6] with a ResNet-50 [32] backbone and a FPN [15] as our detection model. Our proposed method is built upon the Unbiased Teacher framework [10], and we reuse its data augmentations and hyperparameters without any additional modifications to ensure a fair comparison. The entire framework is implemented in Python 3.8 using PyTorch 1.12.1, and the detector is developed based on the MMDetection toolbox (version 2.28.2). We employ standard libraries such as NumPy 1.23.5, OpenCV 4.5.5, and scikit-image 0.20.0 for image processing and entropy map computation. All models are trained on two NVIDIA RTX 4090 GPUs under Ubuntu 20.04 with CUDA 11.7, using a base learning rate of 0.01. The training configurations for each dataset are as follows:

ChestX-Det Dataset: Under the partial-label settings, all models are trained for 180,000 iterations, with each iteration using one labeled image and four unlabeled images per GPU. The learning rate is decayed by a factor of 0.1 at 120K and 160K iterations.

Dental Disease Dataset: Due to the scarcity of labeled data, models are trained for 20,000 iterations with a constant learning rate, using one labeled image and four unlabeled images per GPU at each iteration.

4.3. Effectiveness of Our Approach

We evaluate the effectiveness of our proposed Entropy Teacher framework on two challenging medical datasets: the Dental Disease Dataset and ChestX-Det. As shown in

Table 3. Comparison of different methods on the Dental Disease Dataset. Metrics include $A{P}_{50}$, $AP$, and $AR$ across small, medium, and large objects.

Model	${\mathit{AP}}_{50}$	${\mathit{AP}}_{\mathit{S}}$	${\mathit{AP}}_{\mathit{M}}$	${\mathit{AP}}_{\mathit{L}}$	${\mathit{AR}}_{\mathit{S}}$	${\mathit{AR}}_{\mathit{M}}$	${\mathit{AR}}_{\mathit{L}}$
FCOS [9] (Supervised)	31.0	11.2	36.9	52.0	34.5	62.7	66.9
ARSL [33]	31.6	23.2	41.8	45.2	45.8	58.3	56.0
Dense Teacher [34]	44.3	32.6	47.9	53.6	51.0	60.2	69.4
Faster R-CNN [6] (Supervised)	41.2	25.7	42.3	70.8	52.0	63.0	76.9
Unbiased Teacher [10]	51.5	39.5	58.9	56.2	56.2	69.9	70.0
Soft Teacher [12]	52.2	39.0	57.3	57.4	60.0	75.7	72.0
MixTeacher [19]	54.4	41.2	59.5	62.4	62.8	74.1	78.5
LabelMatch [35]	52.6	41.1	53.3	70.4	59.8	68.1	75.4
PseCo [24]	53.3	40.8	60.7	61.1	64.2	71.9	74.0
Entropy Teacher (Ours)	55.9	45.3	59.4	70.7	68.1	75.2	80.5

and 

Table 4. Comparison of different methods on ChestX-Det under 10%, 30%, and 50% labeled data. Metric is $A{P}_{50}$.

Model	10%	30%	50%
FCOS [9] (Supervised)	8.6	13.1	17.1
ARSL [33]	7.9	12.1	17.5
Dense Teacher [34]	18.5	26.7	29.2
Faster R-CNN [6] (Supervised)	9.5	17.6	19.7
Unbiased Teacher [10]	20.6	30.0	37.3
Soft Teacher [12]	19.5	30.1	33.8
MixTeacher [19]	21.8	33.0	36.4
LabelMatch [35]	15.2	21.7	28.4
PseCo [24]	18.0	29.7	32.2
Entropy Teacher (Ours)	22.2	34.1	37.9

, our method consistently outperforms both supervised and recent state-of-the-art semi-supervised object detection approaches under various settings.

Table 3 presents the detailed comparison results on the Dental Disease Dataset. Our Entropy Teacher achieves the highest performance across almost all metrics, with a significant improvement in both precision and recall for small-scale lesions. Specifically, our method reaches 55.9 $A{P}_{50}$, surpassing the strongest baseline MixTeacher (54.4) by 1.5 points, and achieves the best $A{P}_S$ of 45.3, indicating superior performance on small objects—a known challenge in dental disease detection. This notable improvement can be attributed to our low-confidence pseudo-label mining strategy, which effectively recovers valuable small object proposals that are often discarded by high-threshold filters. Additionally, our class-adaptive thresholding mechanism dynamically adjusts confidence thresholds for different categories based on the model’s current learning state, further improving the inclusion of high-quality pseudo-labels for small-scale diseases. In terms of recall, our model achieves the highest $A{R}_S$ of 68.1 and $A{R}_L$ of 80.5, showing its robustness across scales. This indicates that the Entropy-Guided Feature Pyramid design allows the model to better aggregate spatial and semantic cues, benefiting both small and large lesion localization.

As shown in Table 4, under low-label regimes (10%, 30%, and 50% labeled data), our Entropy Teacher consistently outperforms all competing methods. With only 10% labeled data, it achieves 22.2 $A{P}_{50}$, outperforming the previous best MixTeacher (21.8) and Unbiased Teacher (20.6). When the amount of labeled data increases to 50%, our method still leads with 37.9 $A{P}_{50}$, achieving +0.6 absolute gain over Unbiased Teacher and +1.5 over MixTeacher. These results validate the generalization capability of our method to different medical imaging domains. The integration of Entropy-Guided information (e.g., combining original and enhanced views) improves feature robustness, especially under limited supervision. Moreover, the low-confidence mining strategy enables the model to discover more reliable training signals, which is particularly beneficial when high-quality annotations are scarce.

4.4. Ablation Study

In this section, we conducted experiments on the Dental Disease Dataset to analyze and validate our method in detail.

4.4.1. Investigation of Designed Components

We conduct a step-by-step ablation study to validate the effectiveness of each component in our framework, as shown in

Table 5. An ablation analysis of our method, where LCPLM refers to low-confidence pseudo-label mining strategy. ✔ represents the use of this module.

FPN			LCPLM	${\mathit{AP}}_{50}$	${\mathit{AP}}_{\mathit{S}}$
${\mathit{P}}^{+}$	${\mathit{P}}^{\mathit{E}}$	EIA
				39.6	34.8
✔				51.5 (+11.9)	39.5 (+4.7)
✔	✔			53.5 (+13.9)	41.7 (+6.9)
✔	✔	✔		54.2 (+14.6)	42.4 (+7.6)
✔	✔	✔	✔	55.9 (+16.3)	45.3 (+10.5)

. Starting with a fully supervised model trained solely on labeled data, the $A{P}_{50}$ reaches 39.6. After introducing unlabeled data and integrating the augmented view feature pyramid $P^{+}$, performance improves significantly to 51.5 $A{P}_{50}$ and 39.5 $A{P}_S$, demonstrating the benefits of cross-view feature enrichment. Next, the addition of entropy modality features $P^E$—even with a simple addition-based fusion—brings further gains of 2.0 in $A{P}_{50}$ and 2.2 in $A{P}_S$. This confirms the utility of entropy-guided features for capturing subtle cues of small-scale dental lesions. Building upon this, incorporating the EIA module for adaptive fusion leads to a further increase in both $A{P}_{50}$ and $A{P}_S$ (54.2 and 42.4, respectively), highlighting EIA’s effectiveness in enhancing the model’s sensitivity to small-scale features. Finally, introducing the low-confidence pseudo-label mining (LCPLM) strategy achieves the largest performance boost, reaching 55.9 $A{P}_{50}$ and 45.3 $A{P}_S$. The synergy between the Entropy-Guided Feature Pyramid and LCPLM allows the model to identify informative yet uncertain pseudo-labels, thus enriching supervision for small object regions and improving overall detection accuracy.

There exists a certain degree of class imbalance in the Dental Disease Dataset; for instance, there are only three instances of small-scale obstructed teeth. Our method partially addresses this issue through two key mechanisms. First, the class-adaptive thresholding (CAT) module adjusts confidence thresholds based on the score distributions of each class, thereby avoiding the use of uniform and overly stringent thresholds for rare categories. Second, the LCPLM strategy enhances supervision for underrepresented classes by selectively mining reliable low-confidence predictions, which provides additional training signals for categories with limited samples, such as obstructed teeth.

4.4.2. Generalization to Other Semi-Supervised Frameworks

Detecting small-scale diseases remains a major challenge in semi-supervised detection. To evaluate the generalization capability of our proposed Entropy-Guided Feature Pyramid (EGFP), we integrate it into three representative frameworks: Unbiased Teacher, Soft Teacher, and PseCo. The results are shown in

Table 6. Generalization study of our Entropy-Guided Feature Pyramid (EGFP) integrated into different semi-supervised frameworks.

Method	${\mathit{AP}}_{50}$	${\mathit{AP}}_{\mathit{S}}$	${\mathit{AP}}_{\mathit{M}}$	${\mathit{AP}}_{\mathit{L}}$
Unbiased Teacher	51.5	39.5	58.9	56.2
Unbiased Teacher + EGFP	54.2 (+2.7)	42.4 (+2.9)	58.1	69.8
Soft Teacher	52.2	39.0	57.3	57.4
Soft Teacher + EGFP	54.8 (+2.6)	43.3 (+4.3)	57.1	68.6
PseCo	53.3	40.8	60.7	61.1
PseCo + EGFP	54.1 (+0.8)	42.9 (+2.1)	59.1	71.1

. For Unbiased Teacher and Soft Teacher, which originally adopt only a unimodal augmented-view feature pyramid, we directly replace their feature extraction module with our EGFP. In contrast, PseCo already incorporates multi-view scale-invariant learning; thus, we retain its original design and augment it by adding the entropy-based modality as an additional input. Experimental results show that integrating the proposed EGFP leads to consistent improvements across all three frameworks. Notably, Soft Teacher benefits the most, with a significant increase in $A{P}_S$, suggesting that the combination of Soft Teacher’s region-level supervision with entropy-aware modality yields stronger guidance for small-scale object learning.

4.4.3. Impact of Pseudo-Label Confidence Threshold ${\tau }_h$ on Detection Performance

In the LCPLM strategy, we use the classification score threshold ${\tau }_h$ to filter pseudo labels and select low-confidence candidates. This makes the setting of ${\tau }_h$ particularly critical, as it directly influences which pseudo labels are preserved or discarded. To investigate its impact, we conduct an ablation study comparing fixed thresholds with our proposed class-adaptive threshold (CAT), as shown in

Table 7. Ablation study on pseudo-label filtering thresholds ${\tau }_h$. CAT denotes the proposed class-adaptive threshold.

${\mathit{\tau }}_{\mathit{h}}$	${\mathit{AP}}_{50}$	${\mathit{AP}}_{\mathit{S}}$	${\mathit{AP}}_{\mathit{M}}$	${\mathit{AP}}_{\mathit{L}}$
0.8	54.3	43.4	58.4	69.9
0.85	55.5	44.9	58.8	71.2
0.9	54.8	44.1	58.1	70.3
CAT	55.9	45.3	59.4	70.7

. Results show that among the fixed thresholds, ${\tau }_h=0.85$ achieves the best performance, outperforming both 0.8 and 0.9. However, CAT surpasses all fixed values, achieving the highest AP across all scales, especially on small objects (45.3 $A{P}_S$), validating the effectiveness of dynamically adjusting the threshold according to class-wise confidence distributions.

4.4.4. Impact of Lower Threshold ${\tau }_l$ in LCPLM Strategy

To assess the impact of the lower threshold ${\tau }_l$ in our LCPLM strategy, we conduct an ablation study using different ${\tau }_l$ values. As shown in

Table 8. Ablation study on lower threshold ${\tau }_l$ of LCPLM.

${\mathit{\tau }}_{\mathit{l}}$	${\mathit{AP}}_{50}$	${\mathit{AP}}_{\mathit{S}}$	${\mathit{AP}}_{\mathit{M}}$	${\mathit{AP}}_{\mathit{L}}$
0.5	55.9	45.3	59.4	70.7
0.6	54.3	44.9	58.4	70.2
0.7	53.5	42.9	57.5	69.3

, setting ${\tau }_l=0.5$ yields the best performance across all metrics, achieving 55.9 in $A{P}_{50}$ and 45.3 in $A{P}_S$. Increasing the threshold to 0.6 and 0.7 results in consistent performance drops, especially on small-scale lesions. These results indicate that a lower ${\tau }_l$ allows the model to explore more potentially valuable low-confidence pseudo labels, which is essential for detecting subtle and small lesions in panoramic X-rays. Overly conservative thresholds (e.g., ${\tau }_l=0.7$) may miss important training signals, leading to inferior performance.

4.4.5. Influence of Promotion Threshold $\Delta q$ in LCPLM

To further analyze the behavior of our LCPLM strategy, we conduct an ablation study on the promotion threshold $\Delta q$, which determines the minimum required score improvement from entropy-guided features for a low-confidence pseudo-label to be accepted. As shown in

Table 9. Ablation study on promotion threshold $\Delta q$ of LCPLM.

$\mathbf{\Delta }\mathit{q}$	AvgBox	${\mathit{AP}}_{50}$	${\mathit{AP}}_{\mathit{S}}$	${\mathit{AP}}_{\mathit{M}}$	${\mathit{AP}}_{\mathit{L}}$
0.0	4.15	54.2	42.4	56.7	68.4
0.1	4.81	55.9	45.3	59.4	70.7
0.2	4.32	55.5	44.7	58.7	70.3

, when $\Delta q=0.0$, no additional pseudo-label selection based on score improvement is performed, resulting in 4.15 average boxes per image and an $A{P}_S$ of 42.4. Setting $\Delta q=0.1$ introduces a moderate quality constraint, increasing the average number of pseudo labels to 4.81 and significantly boosting $A{P}_S$ to 45.3—the highest among all settings. In contrast, when $\Delta q=0.2$, the constraint becomes too strict, reducing the average pseudo labels and slightly degrading performance across all scales. These results confirm that a moderate $\Delta q$ strikes a good balance between precision and recall in pseudo-label selection, especially benefiting the detection of small-scale lesions.

4.5. Qualitative Visualization

Figure 4 compares the visualization results of Soft Teacher, PseCo, and our method on the Dental Disease Dataset. These results demonstrate the impressive capability of our Entropy Teacher, particularly in identifying low-contrast small objects—such as the two lesion regions indicated by white arrows in the first row—which were missed by previous methods like Soft Teacher and PseCo. Purple represents diseases that are difficult to detect.

5. Discussion

Despite recent advances in semi-supervised object detection (SSOD), existing frameworks still face considerable challenges in detecting small-scale dental lesions in panoramic X-rays due to low contrast, high background complexity, and limited annotations. Methods such as Unbiased Teacher [10], Soft Teacher [12], and PseCo [24] have attempted to address these issues by enhancing consistency regularization or improving pseudo-label reliability. However, they rely heavily on high-confidence thresholds, which often discard valuable pseudo labels associated with small and low-contrast lesions. Additionally, their unimodal feature extraction fails to sufficiently capture the fine-grained features needed for accurate detection in complex dental imagery.

To overcome these challenges, we propose Entropy Teacher, a novel SSOD framework tailored to small-scale dental disease detection. Our method introduces an Entropy-Guided Feature Pyramid by integrating entropy-guided representations via an EIA module, which enhances the model’s capacity to focus on lesion areas and improves fine-grained feature extraction. In addition, we design an LCPLM strategy with a class-adaptive threshold mechanism, enabling the model to recover reliable low-confidence pseudo labels that would otherwise be discarded.

Quantitative results on the Dental Disease Dataset demonstrate that Entropy Teacher outperforms existing SSOD approaches. Specifically, it achieves 55.9 $A{P}_{50}$ and 45.3 $A{P}_S$, improving upon the strongest baseline MixTeacher by +1.5 $A{P}_{50}$ and +4.1 $A{P}_S$, respectively. The model also achieves 68.1 $A{R}_S$ and 80.5 $A{R}_L$, confirming its robustness across different lesion scales. These improvements are attributed to the model’s ability to dynamically fuse entropy-guided features and mine informative but uncertain labels, thereby enriching the training signal for small lesions.

Compared to other frameworks, Entropy Teacher provides a unique combination of modality fusion and adaptive label mining. For instance, while PseCo incorporates perturbation consistency, it lacks entropy-based representation enhancement. Unbiased Teacher and Soft Teacher rely solely on confidence-based filtering, which limits supervision for small and ambiguous targets. Our ablation studies show that adding the entropy branch improves $A{P}_{50}$ by +2.7, and the LCPLM strategy contributes another +1.7 gain. The synergy between EIA and LCPLM is especially effective in boosting detection recall and precision for small-scale lesions, a critical need in dental diagnostics.

We also validate the generalizability of the Entropy-Guided Feature Pyramid by integrating it into other SSOD frameworks, including Unbiased Teacher, Soft Teacher, and PseCo. All variants exhibit consistent performance gains, particularly on APS. Notably, integrating EGFP into Soft Teacher yields a +4.3 $A{P}_S$ increase, underscoring the universal applicability of our feature enhancement strategy.

Despite its strong performance, Entropy Teacher has certain limitations. First, although entropy maps enhance local information extraction, they are computed externally and may introduce slight overhead during training. Second, while we designed the EIA module to be lightweight, the dual-branch feature pyramid still increases memory usage slightly during training (though it is removed during inference). Third, our current method has only been tested on dental and chest X-rays. Its effectiveness across other modalities (e.g., CT or MRI) or anatomical regions remains to be validated.

Compared with recent learned uncertainty estimators (e.g., Monte Carlo Dropout), entropy maps offer a simpler yet effective alternative. While learned methods provide fine-grained uncertainty modeling, they require additional model complexity and training cost. In contrast, entropy maps are lightweight and rely solely on input image statistics. This is particularly suitable for panoramic X-rays, which exhibit consistent anatomical structures and well-defined boundaries. Therefore, entropy-based representations can effectively highlight lesion-relevant regions without relying on heavy probabilistic modeling.

Furthermore, the proposed Entropy Teacher framework holds promising clinical value. By alleviating the need for extensive manual annotation and improving detection sensitivity for subtle and small-scale lesions, it can assist dental professionals in achieving earlier and more accurate diagnoses. This has the potential to reduce missed diagnoses, improve treatment planning, and ultimately enhance patient outcomes. Future work may focus on integrating learned uncertainty maps instead of pre-computed entropy, further optimizing memory usage via lightweight backbone networks, and expanding the framework to other domains such as endoscopic imagery or histopathology. Moreover, exploring self-distillation or temporal consistency in longitudinal data could further enhance label reliability for small target detection.

6. Conclusions

This study proposes the Entropy Teacher framework, a novel semi-supervised approach tailored for small-scale dental disease detection in panoramic X-rays. By integrating an Entropy-Guided Feature Pyramid with entropy-guided representations and a low-confidence pseudo-label mining strategy, our method significantly enhances detection accuracy for subtle, low-contrast lesions. The experimental results demonstrated the following:

• The Entropy Teacher framework achieved state-of-the-art performance on both the Dental Disease Dataset and ChestX-Det. On the Dental Disease Dataset, it attained 55.9 $A{P}_{50}$ and 45.3 $A{P}_S$, outperforming the baseline Unbiased Teacher by +3.8 $A{P}_{50}$ and +4.5 $A{P}_S$, respectively. This highlights its superior capability in detecting small-scale lesions under complex anatomical backgrounds.
• The proposed Entropy-Guided Feature Pyramid, which fuses entropy maps with raw image features through an EIA module, improved small-scale detection precision by +3.9 $A{P}_S$ compared to the baseline. This demonstrates the effectiveness of entropy-guided attention in enhancing fine-grained feature representation.
• The LCPLM strategy with class-adaptive thresholds dynamically recovered high-quality pseudo labels below conventional confidence thresholds, increasing the average number of retained small-lesion proposals by 15.8% and boosting recall $A{R}_S$ to 68.1. This addresses the critical issue of insufficient supervision for small-scale targets.
• Ablation studies validated the generalizability of our framework. Integrating the Entropy-Guided Feature Pyramid into existing semi-supervised frameworks (e.g., Soft Teacher, PseCo) improved their performance by +2.1 – 4.3 $A{P}_S$, demonstrating its compatibility and robustness across diverse architectures.

The Entropy Teacher framework holds significant clinical value for dental diagnostics. By improving detection sensitivity for small-scale lesions (e.g., low-density shadows, root tip shadows), it reduces missed diagnoses and enables earlier intervention, which is critical for preventing disease progression. For instance, accurate localization of early-stage periapical lesions or subtle caries can guide timely treatment, minimizing invasive procedures and improving patient outcomes. Additionally, its semi-supervised design alleviates reliance on costly expert annotations, making it scalable for deployment in resource-constrained healthcare systems. In future work, we intend to explore the applicability of entropy-guided pseudo-label mining to other medical imaging modalities, such as CT and MRI. These modalities exhibit different noise profiles and structural features, and validating the generalizability of our entropy-based strategy in such contexts will further confirm its robustness and clinical relevance.