# Fusion of Bilateral 2 DPCA Information for Image Reconstruction and Recognition
## 6 Discussion  
### Other Comparisons  
Five algorithms, as listed in Table 9, are fully compared in the experiments. Considering that the mechanisms of PCA- and 2 DPCA-based algorithms are quite different, as discussed in Section 5.1, and that the unilateral algorithms only extract features from a single lateral of images while the bilateral algorithms extract features from both laterals of images, it is not very fair to compare the five feature extraction algorithms directly using the same number of feature vectors. Strictly speaking, fair comparisons can be made only between the two unilateral algorithms, or between the two bilateral algorithms.  
By comparing between the two unilateral algorithms, 2 DPCA generally outperforms A2 DPCA both in image reconstruction and recognition, as shown in Figures 7-9 and Tables 5-7. However, A2 DPCA greatly outperforms 2 DPCA on the reshaped databases, as shown in Figure 10 and Table 8. As we know, 2 DPCA with \(p=c\) approximates to A2 DPCA with \(p=d/c\). The comparison of 2 DPCA and A2 DPCA is directly influenced by the ratio of image height to image width. Since the image height is commonly larger than the image width on the four databases, 2 DPCA can extract more information than A2 DPCA with the same feature number. Therefore, 2 DPCA generally performs better than A2 DPCA. However, in the reshaped databases, the image height might be much smaller than the image width. In these cases, A2 DPCA generally performs better than 2 DPCA.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(\mathbf{\theta}\) & **Variant** & **PCA** & **2 DPCA** & **A2 DPCA** & **(2D)\({}^{2}\)PCA** & **DB2 DPCA** \\ \hline \multirow{3}{*}{0.5} & 0 & 0.0268 & 0.5134 & 0.9003 & 0.0261 & **0.9436** \\  & 1 & 0.0272 & 0.7254 & **0.9726** & 0.4727 & 0.9722 \\  & 2 & 0.0272 & 0.7199 & **0.9736** & 0.4478 & 0.9732 \\  & 0 & 0.0272 & 0.5133 & 0.9003 & 0.0260 & **0.9434** \\
0.6 & 1 & 0.0272 & 0.7755 & **0.9724** & 0.6662 & 0.9709 \\  & 2 & 0.0272 & 0.7694 & **0.9737** & 0.6510 & 0.9717 \\  & 0 & 0.0266 & 0.5562 & 0.9008 & 0.0328 & **0.9498** \\
0.7 & 1 & 0.0265 & 0.8090 & **0.9668** & 0.7635 & 0.9620 \\  & 2 & 0.0263 & 0.8071 & **0.9666** & 0.7598 & 0.9625 \\  & 0 & 0.0438 & 0.7561 & 0.9456 & 0.2027 & **0.9654** \\
0.8 & 1 & 0.0438 & 0.8708 & **0.9576** & 0.8637 & 0.9510 \\  & 2 & 0.0438 & 0.8698 & **0.9579** & 0.8608 & 0.9509 \\ \hline \hline \end{tabular}
\end{table}
Table 8: The average classification accuracies corresponding to four thresholds on the Extended Yale B face database and its reordered and reshaped variants with CRC as the classifier.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Category** & **Bibliography** & **Algorithm** \\ \hline
1D & Turk and Pentland [11] & PCA \\ Unilateral 2D & [PERSON] et al. [13] & 2 DPCA \\ Unilateral 2D & [PERSON] and Zhou [21] & A2 DPCA \\ Bilateral 2D & [PERSON] [21] & (2D)\({}^{2}\)PCA \\ Bilateral 2D & Proposed & DB2 DPCA \\ \hline \hline \end{tabular}
\end{table}
Table 9: Five algorithms compared in the experiments.  
When the image height equals the image width, the performances of 2 DPCA and A2 DPCA are very close.  
By comparing between the two bilateral algorithms, DB2 DPCA significantly outperforms (2D)\({}^{2}\)PCA in all experiments. The main reason is that \((2\)D)\({}^{2}\)PCA projects the rows and columns of images onto two lateral eigenvectors simultaneously, thus mixing bilateral information together and leading to information loss. In contrast, DB2 DPCA projects the rows and columns of images onto two lateral eigenvectors separately, thus extracting more features from images and obtaining a more interpretable reconstruction model. Therefore, DB2 DPCA performs better than \((2\)D)\({}^{2}\)PCA both in image reconstruction and recognition.