## 2 Materials and Methods
### Ensemble Voting Methods  
Ensemble Voting Methods allow for more reliable and accurate detection by combining the predictions of different classifiers [31]. In addition to the masks generated through YOLO models, voting-based ensembles were evaluated using three different strategies:  
Figure 3: ROI areas for meniscal segmentation in the sagittal section. (**a**) An image with meniscal injury in the posterior and anterior horn of the medial meniscus in the test set. (**b**) Representation of healthy lateral meniscus in the external set.  
(i) pixel-based voting, (ii) weighted multiple voting, and (iii) dynamic weighted multiple voting with grid search. These strategies aim to achieve better results by combining the diversity and strengths of different models. Empirical results and quantitative data are presented in detail in the findings section. Within the scope of multiple voting methods, prediction masks generated from the models obtained after the training of the YOLO series were created, and these masks were used as input images (\(I_{M\text{m}}\)). These masks consist of black (0) and white (255) pixel values.  
The pixel-based voting method is calculated as shown in Equation (1). In this equation, the input images for each model are \((I_{M1}\), \(I_{M2}\), \(I_{M3}\), \(I_{M4}\), \(I_{M5})\) and \((x,y)\) are the pixel positions. \(W(x,y)\) represents the average of the sum value for the \((x,y)\) pixel position. The thresholding process is shown in Equation (2) and allows \(O(x,y)\) for the assignment of white (255) or black (0) according to a value of 128.  
\[W(x,y)=\frac{I_{M1}(x,y)+I_{M2}(x,y)+I_{M3}(x,y)+I_{M4}\ (x,y)+I_{M5}(x,y)}{5} \tag{1}\]  
\[O(x,y)=\begin{cases}255,&W(x,y)\geq 128\\ 0,&W(x,y)<128\end{cases} \tag{2}\]  
In the weighted multiple voting method, the three most successful models are selected from five models, and each input image is assigned a weight value between [0.1:0.9]. The weighted multiple voting method is shown in Equation (3), where \(w_{i}\) represents the weight coefficient of the input image. The thresholding process for the new mask image is completed as shown in Equation (2). The sample weight values of the input images are (0.5, 0.3, 0.2), respectively. The three highest-performing YOLO models were selected for training.  
\[W(x,y)=w_{1}I_{M1}(x,y)+w_{2}I_{M2}(x,y)+w_{3}I_{M3}(x,y) \tag{3}\]  
Grid search and dynamic weighted multiple voting are used to determine the optimal weight combinations by the pixel-based weighting of the prediction masks generated by different YOLO segmentation models. This method goes beyond static weights and enables a systematic search for dynamic weight values to optimize the prediction performance of each model. For this purpose, the grid search algorithm is used to determine the weights for each mask dynamically. Equation (4) is the equation for calculating the dynamic weighted voting method. The thresholding process for the new mask image was performed as shown in Equation (2). With this method, the segmentation performance of each model is calculated by the dynamic weights (\(w_{i}\)) and by grid search, and a composite prediction mask is created. This method provides a dynamic contribution to the segmentation performance of the models by taking into account their differences, and a significant improvement is realized to increase the segmentation accuracy.  
\[W(x,y)=w_{1}I_{M1}(x,y)+w_{2}I_{M2}(x,y)+w_{3}I_{M3}(x,y)+w_{4}I_{M4}(x,y)+w_{5 }I_{M5}(x,y) \tag{4}\]