## 4 Experimental Results and Analyses
### Analysis of the Results  
Through the comparison of the results in Table 6, it can be seen that our Tibia-YOLO model provided relatively good improvements in comparison with other models. In Figure 7, an example of the detection in some tests is shown, except for the Tibia-YOLO and YOLOv8 models, which produced results that were skewed and did not include the complete tibia in the image. Some of them produced false detection boxes and missing detection boxes, and it turned out that our Tibia-YOLO model performed well in detecting tibas. To test the generalization of the model, we used two public datasets, VOC2012 and COCO2016. As shown by the comparison of the baseline model with YOLOv8 before the improvement and the baseline model with Tibia-YOLO after the improvement--see the test results on the three datasets in Table 7--the detection accuracy improved for each dataset. As can be seen in Figure 8, our Tibia-YOLO model also performed well in the detection of small targets. Our proposed Tibia-YOLO model was able to achieve an average accuracy of 90.8% in the task of broiler tibia detection; it had improved performance in tests of its generalization to other datasets, and it had excellent small-target detection abilities. However, the blurring of the boundaries between muscle tissue and skeletal tissue caused by the activity of broilers during DR image collection will lead to a reduction in the robustness of the application in real-life scenarios. The limitation of the current method is that it only applies to broiler chickens, and its effectiveness for other poultry animals such as ducks and rabbits has not been confirmed. Additional validation and adjustment will be required when generalizing the model to other poultry species.  
In Figure 9, a scatter plot is used to depict the predicted results and true values for nine regression models. It was observed that the prediction results of LASSO Regression, ElasticNet, and Ridge Regression were evenly distributed on a straight line. Although this situation demonstrated a better fitting effect on the scatter plot, to ensure the robustness and generalization ability of the models a comprehensive evaluation of model performance using indicators such as the mean square error and mean absolute error was still necessary. By comparing the MAE and RMSE in Table 8, it was found that their results were very similar, differing only by a few decimal places. The main differences among LASSO, ElasticNet, and Ridge Regression were their regularization terms. However, if the same features were chosen for these models to fit a given problem, their predictions could also have been very similar. Through the analysis of the results presented in Table 8, it was determined that SVR was more practical for complex nonlinear problems, and for large high-dimensional data such as pixels, the SVR regression method performed better. Among the 22 sets of test data that were not used for training at all, the mean absolute error (MAE) and root mean square error (RMSE) were 2.77 mm and 3.37 mm, respectively. As shown by the combination of the scatter point distribution and the comparison of the MAE, MSE, and RMSE, SVR performed well in all aspects. It was also proven that the system could accurately measure the tibia length and could be used to detect leg diseases in broiler chickens for breeding.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **MAE (mm)** & **MSE (mm\({}^{2}\))** & **RMSE (mm)** \\ \hline Decision Tree & 3.10 & 16.14 & 4.35 \\ XGBoost & 3.36 & 18.34 & 4.28 \\ Gradient Boosting & 3.17 & 16.25 & 4.03 \\ KNeighbors & 3.20 & 15.34 & 3.91 \\ RandomForest & 3.16 & 15.06 & 3.88 \\ LASSO Regression & 3.02 & 13.31 & 3.65 \\ Ridge Regression & 3.02 & 13.31 & 3.65 \\ ElasticNet & 3.02 & 13.31 & 3.65 \\
**SVR** & **2.77** & **11.39** & **3.37** \\ \hline \hline \end{tabular}
\end{table}
Table 8: Comparison of the errors of different regression models.