# Fusion of Bilateral 2 DPCA Information for Image Reconstruction and Recognition
## 5 Results
### Image Recognition  
Figure 8 shows the average classification accuracies of the five algorithms followed by three different classifiers on four databases. By averaging the results in Figure 8 across different feature numbers, we obtain Table 6. PCA underperforms compared with 2 DPCA-based algorithms in most cases. The reason is similar to that discussed in Section 5.2. With the exceptions of Figure 8a,d,i, DB2 DPCA obtains the highest classification accuracies among the five algorithms.  
Two exceptions where 2 DPCA outperforms DB2 DPCA exist in Figure 8a,d, in which cases the classifier is chosen to be NN. The accuracies of NN in both cases are much lower than corresponding results of SVM and CRC in Figure 8b,c,e,f where DB2 DPCA outperforms 2 DPCA. Therefore, we conclude that NN cannot make the most of the information extracted by DB2 DPCA in the two cases.  
Comparing between the two bilateral 2D algorithms, DB2 DPCA outperforms (2D)\({}^{2}\)PCA in most cases. The only exception occurs on the Binary Alphadigits database in Figure 8i, when CRC is applied as the classifier and the feature number is larger than four. The reason might be that the image size of the Binary Alphadigits database is much smaller than the other three databases. With the exception of Figure 8i, DB2 DPCA greatly outperforms (2D)\({}^{2}\)PCA in image recognition. It is also due to the fact that (2D)\({}^{2}\)PCA projects the rows and columns of images onto the corresponding projection matrices simultaneously, thus mixing bilateral information together and leading to information loss. On the other side, DB2 DPCA concatenates bilateral information directly and extracts more features that can improve the image recognition performance.  
The curves of the four 2D algorithms on the Binary Alphadigits database in Figure 8g-i are different from the corresponding curves in other figures in that they do not monotonically increase with feature number; this is because the image size of the Binary Alphadigits database (20 \(\times\) 16) is much smaller than those of the other three databases. Since we extract at most 16 features for this database, there exist redundant features when the feature number is large. The redundant features deteriorate the classification performances. For the other three databases, the maximal feature number is much smaller than the image size of the databases; so, their classification accuracies tend to increase with feature number. If we focus on the results when the feature number is small and no redundant features are extracted, DB2 DPCA has obvious advantages over competing algorithms.  
Since DB2 DPCA can make the most of bilateral information from images, it is natural that DB2 DPCA generally outperforms the other four algorithms in image classification.  
Based on the results in Table 6, it is straightforward to compare classification performances among the three classifiers. CRC greatly outperforms the other two classifiers on the Extended Yale B face database; SVM greatly outperforms the other two classifiers on the AR face database; SVM slightly outperforms NN on the Binary Alphadigits database; NN greatly outperforms the other two classifiers on the PolyU 3D palmprint database. Therefore, no classifier has an absolute advantage over the others.  
Figure 8: The average classification accuracies on four databases by three different classifiers. The subfigures in the four rows are results of the Extended Yale B face database, AR face database, Binary Alphadigits database and PolyU 3D palmprint database, respectively. The subfigures (**a–**l**) in three columns are results of NN, linear SVM and CRC, respectively. In each subfigure, there are five accuracy curves corresponding to the five feature extraction algorithms, i.e., PCA, 2 DPCA, 2 DPCA, (2D)\({}^{2}\)PCA and DB2 DPCA.