# A Robust and Efficient Method for Effective Facial Keypoint Detection
## 4 Experimental Results
### Main Results
#### 4.2.2 Regression Combined with Heatmap Results  
To demonstrate the effectiveness of heatmaps in face keypoint detection, we conducted a series of comparative experiments to evaluate the detection performance when using only the regression model and when adding heatmaps. Figure 3 presents the experimental results of facial keypoint detection across various environments.  
In the base regression model, we directly predicted the coordinates of the keypoints and obtained a mean square error (MSE LOSS) of 0.0556. Next, we added heatmaps as an intermediate representation for keypoint detection. By generating a heatmap on the label image, we further captured and utilized the heat value at the location of each keypoint in the  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Method** & **RCPR [33]** & **CDM [50]** & **SDM [36]** & **ERT [51]** & **LBF [37]** & **CFSS [38]** & **CCL [52]** & **Binary-CNN [53]** & **PCD-CNN [32]** \\ \hline
**AFLW** & 5.43 & 3.73 & 4.05 & 4.35 & 4.25 & 3.92 & 2.72 & 2.85 & 2.40 \\ \hline
**Method** & \begin{tabular}{c} TSR [47] \\ \end{tabular} & \begin{tabular}{c} CPM [45] \\ \end{tabular} & \begin{tabular}{c} SAN [30] \\ \end{tabular} & \begin{tabular}{c} PFLD \\ \end{tabular} & \begin{tabular}{c} PFLD \\ \end{tabular} & \begin{tabular}{c} **mobile-** \\ \end{tabular} & \
\begin{tabular}{c} **mobile-** \\ **distill-** \\ **prune-1X** \\ \end{tabular} &
\begin{tabular}{c} **ResNet-** \\ **50** \\ \end{tabular} \\ \hline
**AFLW** & 2.17 & 2.33 & 1.91 & 2.07 & 1.88 & **2.06** & **1.86** & **1.84** \\ \hline \hline \end{tabular}
\end{table}
Table 2: Normalized mean error comparison on the AFLW–full dataset. The bold entries represent the model proposed in this paper.  
Figure 3: Results of facial keypoint detection for face images in various environments. The red dots represent the detected facial keypoints, including the corners of the eyes, the tip of the nose, and the corners of the mouth. These keypoints are used to identify and track specific facial features.  
image. The experimental results are presented in Table 3, which show that the MSE LOSS significantly decreased to 0.0462 after adding the heatmap, representing an improvement of 16.90%. To evaluate the generalization ability of our regression algorithm and the regression combined with the heatmap algorithm, we utilized a three-fold cross-validation method, involving pairwise combinations of three different test sets, thus yielding three validation values and corresponding \(p\)-values for each set of experiments. Performance metrics were collected for each fold to ensure robust evaluation. We applied the \(t\)-values to examine the mean differences in performance metrics across the folds. Additionally, the Levene test was employed to check for homogeneity of variances. Large \(p\)-values from both the \(t\)-values and Levene test were observed, indicating that the mean performance differences were not statistically significant, and the variances were homogeneous.  
The reason for this improvement is that heatmaps provide more detailed local information, making the model more robust and accurate when processing keypoints in specific areas of the image. Heatmaps are particularly effective in capturing the location of keypoints in challenging scenarios involving large angles, occlusion, or complex lighting conditions, thereby improving the overall performance of the model.