## 3 Experiments and Results
### Evaluation Metrics  
Model performance was primarily assessed using mean average precision (mAP), which is computed as the area under the precision-recall (PR) curve, providing a unified measure of both classification accuracy and localization precision. All reported mAP \begin{table}
\begin{tabular}{c c} \hline
**Software Environment** & **Hardware Environment** \\ \hline Operating system: Windows 11 & CPU: AMD R5-7500f \\ Programming language: Python 3.10 & GPU:RTX 40/70 Ti Super(16 GB) \(\times\) 1 \\ Deep learning framework: PyTorch 2.3.0 & Accelerated environment: CUDA 12.1 \\ \hline \end{tabular}
\end{table} 
Table 1: The experimental environment. \begin{table}
\begin{tabular}{c c} \hline
**Parameters** & **Values** \\ \hline lr0 & 0.01 \\ lrf & 0.01 \\ Momentum & 0.937 \\ Weight decay & 0.0005 \\ Warmup epochs & 3 \\ Warmup momentum & 0.8 \\ Batch size & 8 \\ Epochs & 300 \\ Workers & 4 \\ \hline \end{tabular}
\end{table} 
Table 2: Hyperparameter setting. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Model** & **Optimizer** & \begin{tabular}{c} **Initial** \\ **Learning** \\ **Rate** \\ \end{tabular} & \begin{tabular}{c} **Final** \\ **Learning** \\ **Rate** \\ \end{tabular} & \
\begin{tabular}{c} **Batch** \\ **Size** \\ \end{tabular} &
\begin{tabular}{c} **Epoch** \\ **Number** \\ \end{tabular} \\ \hline YOLOv8n & SGD & 0.01 & 0.01 & 8 & 300 \\ YOLOv10n & SGD & 0.01 & 0.01 & 8 & 300 \\ YOLOv11n & SGD & 0.01 & 0.01 & 8 & 300 \\ YOLOv12n & SGD & 0.01 & 0.01 & 8 & 300 \\ Faster R-CNN & Adam & 0.0001 & 0.01 & 8 & 300 \\ RTDETR-r18 & AdamW & 0.0001 & 1.0 & 8 & 300 \\ Ours & SGD & 0.01 & 0.01 & 8 & 300 \\ \hline \end{tabular}
\end{table} 
Table 3: Model parameters. values use an IoU threshold of 0.50 ([EMAIL_ADDRESS]). The corresponding calculation formula is detailed below. \[P=\frac{TP}{TP+FP}\times 100\% \tag{5}\]  
\[R=\frac{TP}{TP+FN}\times 100\% \tag{6}\]  
\[AP=\sum_{i=1}^{N}p_{i}\Delta r_{i} \tag{7}\]  
\[mAP=\frac{1}{n}\sum_{i=1}^{n}AP_{i} \tag{8}\]  
where _TP_ (true positive) is the count of correctly detected targets; _FP_ (false positive) refers to cases where the model erroneously identifies a region of one organoid class as another; _FN_ (false negative) denotes instances where the model fails to detect an actual organoid; _AP_ (average precision) quantifies the accuracy for a specific category; \(N\) denotes the number of targets within the same category; _p_\({}_{i}\) is a function of precision; _r_\({}_{i}\) is a function of recall; and \(n\) represents the total number of target categories. To comprehensively evaluate detection performance on medium and small targets, this study incorporates the COCO evaluation metrics [43], which categorize objects into three size classes: large (area > 96 \(\times\) 96 pixels), medium (32 \(\times\) 32 < area \(\leq\) 96 \(\times\) 96 pixels), and small (area \(\leq\) 32 \(\times\) 32 pixels). Average Precision (AP) is computed as the mean over 10 IoU thresholds ranging from 0.5 to 0.95 in steps of 0.05, providing increased sensitivity to localization precision. Additionally, we introduce task-independent diagnostic evaluation (TIDE) [44], an error diagnostic framework that overcomes the aggregation limitations of the conventional mAP metric. TIDE applies a decoupled error decomposition approach, incorporating a dynamic IoU threshold strategy: it defines both a foreground determination threshold \(t_{f}\) and a background exclusion threshold \(t_{b}\), then quantifies the spatial correlation between false-positive (FP) detection boxes and ground truth (GT) annotations using the maximum IoU overlap (\(IoU^{\text{max}}\)). This enables systematic decomposition of detection errors into six core categories:  
1. Classification Error (Cls): The predicted box overlaps correctly with GT (\(IoU^{\text{max}}\geq t_{f}\)) but is assigned an incorrect class label. 2. Localization Error (Loc): The class label is correct, but the box lacks sufficient spatial alignment with the GT (\(t_{b}\leq IoU^{\text{max}}\leq t_{f}\)). 3.