# AutoStageMix: Fully Automated Stage Cross-Editing System Utilizing Facial Features
## 4 Experimental Results
### Quantitative Evaluations
#### 4.1.2 Normalized Mean Error (NME)  
At the FBT point, an alignment operation is performed to match the size and position of the faces of the main figures appearing in different frames. The more accurately the shapes of the two faces are aligned, the greater the visual satisfaction derived from the FBT. In our work, we compared our proposed method for identifying similar faces across frames with those of [PERSON] et al. [1] and [PERSON] et al. [2]. The morphological congruence of the detected face pairs was evaluated using the NME, a commonly used metric for assessing the accuracy of facial landmark alignment, as shown in previous studies by [PERSON] and [PERSON] [30] and [PERSON] et al. [31]. Specifically, 68 landmarks were extracted using SPIGA [12], and the two sets of landmarks were aligned using Procrustes analysis [32], after which the NME was computed. Let the two landmark sets be denoted as \(A\) and \(B\). After applying Procrustes analysis, we obtain aligned landmark sets \(A^{\prime}\) and \(B^{\prime}\), from which the Euclidean distance \(d_{i}\) between corresponding landmarks is calculated. The Mean Error (ME) is defined as the average of these Euclidean distances. The NME is then computed by normalizing the ME by \(d_{e}\), the inter-ocular distance, defined as the distance between the centers of the two eyes. The distance \(d_{e}\) is calculated from the coordinates of the left eye center \((l_{x},l_{y})\) and the right eye center \((r_{x},r_{y})\). \[(A^{\prime},B^{\prime})=\mathit{procrustes}(A,B), \tag{16}\]  
\[d_{i}=\sqrt{\left(a^{\prime}_{ix}-b^{\prime}_{ix}\right)^{2}-\left(a^{\prime} _{iy}-b^{\prime}_{iy}\right)^{2}}, \tag{17}\]  
\[\mathrm{ME}=\frac{1}{N}\sum_{i=1}^{N}d_{i}, \tag{18}\]  
\[d_{e}=\sqrt{\left(l_{x}-r_{x}\right)^{2}+\left(l_{y}-r_{y}\right)^{2}}, \tag{19}\]  
\[\mathrm{NME}=\frac{\mathrm{ME}}{d_{e}}. \tag{20}\]  
For the NME comparison, we used three videos of Seventeen's \"Darl+ing\" [28] (4384 frames), two videos of \"Ready to love\" [29] (5676 frames), and three videos of \"God of \begin{table}
\begin{tabular}{c c c c c c c} \hline  & **Video \#1** & **Video \#2** & **Video \#3** & **Video \#4** & **Video \#5** & **Mean** \\ \hline Precision & 1 & 1 & 0.828 & 0.624 & 1 & 0.890 \\ \hline Recall & 0.857 & 0.935 & 0.828 & 0.869 & 0.679 & 0.834 \\ \hline F1-Score & 0.923 & 0.967 & 0.828 & 0.726 & 0.808 & 0.850 \\ \hline \end{tabular}
\end{table} 
Table 1: Shot detection results for five videos. Music\" [33] (6078 frames), all with a resolution of 1920 \(\times\) 1080. Analogous face pairs suitable for FBT were detected according to the procedures described by [PERSON] et al. [1] and [PERSON] et al. [2], as well as our proposed method. The number of similar face pairs identified using each method for the three 'Darl+ing' videos is presented in Table 2.  
As shown in Table 2, the number of potential FBT frame pairs detected varies by method. [PERSON] et al. 's method identified the fewest frame pairs, as it only allowed transitions when the angle between the line connecting the eyes and the horizontal axis was 7 degrees or less [1]. In contrast, [PERSON] et al. 's method identified the most frame pairs due to its looser constraints [2]. For each detected frame pair, 68 facial landmarks were extracted and aligned using Procrustes analysis, after which the NME was computed. To determine whether significant differences existed in morphological consistency among the three methods, a non-parametric Kruskal-Wallis H tests [34] was first performed. If the global test was significant, indicating at least one group differed, we conducted pairwise post hoc comparisons using the Mann-Whitney U test [35]. To control for the increased risk of Type I error due to multiple comparisons, Bonferroni correction [36] was applied to the resulting _p_-values. The detailed results are presented in Tables 3 and 4. The NME reflects subtle positional differences between facial landmarks, with lower values indicating greater morphological similarity between faces. As shown in Table 3, across all the