# Fusion of Bilateral 2 DPCA Information for Image Reconstruction and Recognition
## 5 Results
### The Effect of Reshaping Images  
Figure 10 shows the average classification accuracies with different image heights and different thresholds \(\theta\) on the Extended Yale B face database and its reordered and reshaped variants. Specifically, the three columns show the results corresponding to the three series of modified databases, i.e., variants 0-2 in order, and the four rows show the results corresponding to the four thresholds in order. The classifier is chosen to be CRC for illustration. By averaging the results in Figure 10 across different image heights, we obtain Table 8.  
The experiments corresponding to the three columns in Figure 10 differ in the way of reordering pixels in images. It again demonstrates that reordering pixels in images will affect the classification performances of the four 2D algorithms. The results on variants 1-2 (column 2-3) are much better than the results on variant 0 (column 1). The reason might be that the features extracted from the original images contain more redundant information than the features extracted from the randomly reordered and reshaped images. In other words, by randomly reordering the pixels in images and reshaping the image size, we can extract more valuable information that can improve the classification performance. In the first column of Figure 10, the accuracy of 2 DPCA generally increases with image height and the accuracy of A2 DPCA generally decreases with image height. The reason is that 2 DPCA projects the rows of images onto its projection matrix while A2 DPCA projects the columns of images onto its projection matrix. As a result, the number of features extracted by 2 DPCA increases with image height and the number of features extracted by A2 DPCA decreases with image height. More features generally indicate higher classification accuracies, especially when the percentage of total variance explained by these features is small. Therefore, the accuracy of 2 DPCA generally increases with image height and the accuracy of A2 DPCA generally decreases with image height in the first column of Figure 10. This is not the case in the last two columns since the reordering and reshaping effect dominates these results. The accuracies of DB2 DPCA are rather stable with different image heights in all cases in Figure 10; this is because that DB2 DPCA can extract features from both literals of images. In this way, it inherits the advantages of 2 DPCA and A2 DPCA, and can achieve high classification accuracies with different image heights. From Table 8, DB2 DPCA greatly outperforms competing algorithms except A2 DPCA on all of the three variants. To be specific, DB2 DPCA is significantly better than A2 DPCA on variant 0 and slightly worse than A2 DPCA on variants 1-2. The reason why DB2 DPCA is slightly worse than A2 DPCA on variants 1-2 might be that the features extracted from the randomly reordered and reshaped images by A2 DPCA are sufficient for image classification, and extracting more features by DB2 DPCA introduces redundant information that deteriorates the classification performances. Generally speaking, DB2 DPCA achieves the best classification performances among the five competing algorithms on the reordered and reshaped images. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Variant** & **PCA** & **2 DPCA** & **A2 DPCA** & **(2D)\({}^{2}\)PCA** & **DB2 DPCA** \\ \hline
0 & 0.0267 & 0.9013 & 0.8415 & 0.0336 & 0.9379 \\
1 & 0.0264 & 0.9013 & 0.8431 & 0.0335 & 0.9394 \\
2 & 0.0265 & 0.9018 & 0.8405 & 0.0338 & 0.9372 \\
3 & 0.0264 & 0.9018 & 0.8405 & 0.0338 & 0.9372 \\
4 & 0.0265 & 0.9018 & 0.8405 & 0.0338 & 0.9372 \\
5 & 0.0265 & 0.9189 & 0.9051 & 0.0419 & 0.9607 \\
6 & 0.0265 & 0.9260 & 0.9040 & 0.0562 & 0.9588 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The average classification accuracies on the Extended Yale B face database and its six reordered databases with CRC as the classifier when only the first two features are used to perform classification.