# Fusion of Bilateral 2 DPCA Information for Image Reconstruction and Recognition
###### Abstract  
Being an efficient image reconstruction and recognition algorithm, two-dimensional PCA (2 DPCA) has an obvious disadvantage in that it treats the rows and columns of images unequally. To exploit the other lateral information of images, alternative 2 DPCA (A2 DPCA) and a series of bilateral 2 DPCA algorithms have been proposed. This paper proposes a new algorithm named direct bilateral 2 DPCA (DB2 DPCA) by fusing bilateral information from images directly--that is, we concatenate the projection results of 2 DPCA and A2 DPCA together as the projection result of DB2 DPCA and we average between the reconstruction results of 2 DPCA and A2 DPCA as the reconstruction result of DB2 DPCA. The relationships between DB2 DPCA and related algorithms are discussed under some extreme conditions when images are reshaped. To test the proposed algorithm, we conduct experiments of image reconstruction and recognition on two face databases, a handwritten character database and a palmprint database. The performances of different algorithms are evaluated by reconstruction errors and classification accuracies. Experimental results show that DB2 DPCA generally outperforms competing algorithms both in image reconstruction and recognition. Additional experiments on reordered and reshaped databases further demonstrate the superiority of the proposed algorithm. In conclusion, DB2 DPCA is a rather simple but highly effective algorithm for image reconstruction and recognition. Keywords:DB2 DPCA; bilateral 2 DPCA; image reconstruction; image recognition; face recognition +
Footnote †: journal:  
_Applied_  
_Acticle_  
Fusion of Bilateral 2 DPCA Information for Image Reconstruction and Recognition  
**Citation:** [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Fusion of Bilateral  
to handle. Moreover, 2 DPCA generally outperforms PCA in image reconstruction and recognition [13]. Due to its simple formulation and superior performance, 2 DPCA has been successfully applied in various fields such as image retrieval [14; 15], fault detection [16], iris recognition [17], target recognition based on synthetic aperture radar images [18], bearing fault diagnosis [19], brain tumor diagnosis [20], etc. Despite having many advantages, 2 DPCA treats the rows and columns of images unequally, thus lacking symmetry in its theory. Specifically, to extract features from an image by 2 DPCA, rows rather than columns of the image are projected onto the principal components. In order to project the other direction, i.e., columns of the image, the alternative 2 DPCA (A2 DPCA) [21] was proposed. Then, it is natural to combine the two kinds of unilateral 2 DPCA. Following this idea, (2D)\({}^{2}\)PCA [21], generalized 2 DPCA (G2 DPCA) [22] and sequential row-column 2 DPCA (RC2 DPCA) [23] were proposed in order to fuse the bilateral information of images. (2D)\({}^{2}\)PCA calculates bilateral eigenvectors by directly taking the projection matrices from 2 DPCA and A2 DPCA. Generalized 2 DPCA calculates bilateral eigenvectors by iteratively solving a minimization problem. RC2 DPCA calculates bilateral eigenvectors in two stages, i.e., first performing 2 DPCA in the row direction on the original data and then performing A2 DPCA in the column direction on the projected results of the first stage. All of these algorithms project an image onto the two lateral eigenvectors simultaneously in order to compute the final projection results. In this paper, we propose a novel bilateral 2 DPCA by fusing 2 DPCA and A2 DPCA in a direct fashion, called Direct Bilateral 2 DPCA (DB2 DPCA). Unlike the previously proposed bilateral 2 DPCA algorithms, we concatenate the projection results of 2 DPCA and A2 DPCA together for projection, and we take the average reconstruction results of 2 DPCA and A2 DPCA for reconstruction. The proposed method has three advantages. First, it has a symmetric property in the sense that it treats the rows and columns of images equally. Second, for projection, it concatenates the bilateral information rather than mixing them together.