# Fusion of Bilateral 2 DPCA Information for Image Reconstruction and Recognition
## 5 Results
### Image Reconstruction  
Figure 6 shows the reconstructed images of the five algorithms, wherein the first ten feature vectors are used for image reconstruction. Note that for the two bilateral algorithms, the first ten projection vectors from both laterals are used. The reconstructed images of PCA and (2D)\({}^{2}\)PCA are very obscure. The reconstructed images of 2 DPCA and A2 DPCA have vertical stripes and horizontal stripes, respectively. The reconstructed images of DB2 DPCA highly approximate the original images. Obviously, the proposed algorithm outperforms the other four algorithms in image reconstruction. Figure 7 shows the average reconstruction errors of the five algorithms with different numbers of extracted features. For the two bilateral algorithms, we select the same number of features for both laterals. By averaging the results in Figure 7 across different feature numbers, we obtain Table 5. With the exception of Figure 7a, the average reconstruction errors of PCA are the largest among the five algorithms, the average reconstruction errors of DB2 DPCA are the smallest and the results of the other three algor \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline \multirow{2}{*}{**Database**} & \multirow{2}{*}{**Algorithm**} & \multicolumn{6}{c}{**Number of Principal Components**} \\  & & **1** & **2** & **3** & **4** & **5** & **6** \\ \hline \multirow{4}{*}{Extended Yale B face} & PCA & 0.3674 & 0.7206 & 0.7705 & 0.7993 & 0.8144 & 0.8288 \\  & 2 DPCA & 0.7734 & 0.8813 & 0.9367 & 0.9560 & 0.9708 & 0.9840 \\  & A2 DPCA & 0.7734 & 0.8813 & 0.9367 & 0.9560 & 0.9708 & 0.9840 \\  & PCA & 0.2545 & 0.3727 & 0.4688 & 0.5393 & 0.5885 & 0.6242 \\ AR face & 2 DPCA & 0.5638 & 0.7618 & 0.8535 & 0.8964 & 0.9175 & 0.9320 \\  & A2 DPCA & 0.5638 & 0.7618 & 0.8535 & 0.8964 & 0.9175 & 0.9320 \\  & PCA & 0.0699 & 0.1378 & 0.1917 & 0.2426 & 0.2909 & 0.3298 \\ Binary Alphadigits & 2 DPCA & 0.3327 & 0.5488 & 0.6705 & 0.7645 & 0.8451 & 0.9119 \\  & A2 DPCA & 0.3327 & 0.5488 & 0.6705 & 0.7645 & 0.8451 & 0.9119 \\  & PCA & 0.8622 & 0.8864 & 0.9052 & 0.9175 & 0.9247 & 0.9298 \\ PolyU 3D palmprint & 2 DPCA & 0.9563 & 0.9788 & 0.9849 & 0.9905 & 0.9932 & 0.9950 \\  & A2 DPCA & 0.9563 & 0.9788 & 0.9849 & 0.9905 & 0.9932 & 0.9950 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The percentages of total variance explained by the first six principal components. Figure 6: The reconstructed images of the five algorithms. In each subfigure, the first column shows the original images while the remaining columns show the reconstructed images of PCA, 2 DPCA, A2 DPCA, (2D)\({}^{2}\)PCA and DB2 DPCA, respectively. (**a**) Extended Yale B face database. (**b**) AR face database. (**c**) Binary Alphadigits database. (**d**) PolyU 3D palmprint databse. of PCA and DB2 DPCA. These results again demonstrate that DB2 DPCA outperforms the other four algorithms in image reconstruction. It is not surprising that the reconstructed images of PCA are very obscure and the average reconstruction errors of PCA are large. The maximal number of principal components that can be extracted by PCA is much larger than those of the two unilateral algorithms, as shown in Table 3, but only the first few feature vectors are used to generate the reconstructed image or calculate the reconstruction errors. The percentages of total variance explained by these feature vectors are relatively small, as shown in Figure 5 and Table 4, and cannot be guaranteed to reconstruct the original image accurately. By comparison, the total number of features that can be extracted by 2 DPCA-based algorithms is small and the percentage of total variance explained by the same number of feature vectors of these algorithms is large. Therefore, 2 DPCA-based algorithms perform much better than PCA with the same number of feature vectors in image reconstruction. The reconstructed images of 2 DPCA and A2 DPCA have vertical stripes and horizontal stripes, respectively.