Block-Wise Two Dimensional Kernel Quaternion Principal Component Analysis

doi:10.13190/j.jbupt.2018-045

JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM ›› 2019, Vol. 42 ›› Issue (1): 53-60.doi: 10.13190/j.jbupt.2018-045

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Block-Wise Two Dimensional Kernel Quaternion Principal Component Analysis

CHEN Bei-jing^1,2,3, YANG Jian-hao³, FAN Chun-nian^1,3, SU Qing-tang⁴, WANG Ding-cheng^1,3

1. Jiangsu Engineering Center of Network Monitoring, Nanjing University of Information Science and Technology, Nanjing 210044, China;
2. Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology, Nanjing University of Information Science and Technology, Nanjing 210044, China;
3. School of Computer and Software, Nanjing University of Information Science and Technology, Nanjing 210044, China;
4. School of Information and Electrical Engineering, Ludong University, Yantai 264025, China

Received:2018-03-20 Online:2019-02-28 Published:2019-03-08

Abstract

Abstract: Currently, kernel quaternion principal component analysis (KQPCA) has been proposed and successfully applied to process linear quaternion signals. However, two dimensional version of KQPCA (2DKQPCA) has not been successfully implemented due to the quite time-consuming problem for diagonalizing the high dimensional kernel matrix. So, using the block-based idea and the parallel computing idea, the block-wise 2DKQPCA (B2DKQPCA) is proposed to implement 2DKQPCA really. After the overall consideration of computational complexity, application performance and quaternion Hermitian block, B2DKQPCA mainly processes the blocks of three directions:main-diagonal direction, anti-diagonal direction and side-diagonal direction. Then, B2DKQPCA is applied into RGB-D object recognition by combining B2DKQPCA and quaternion representation of RGB-D images. Experimental results on two publicly available datasets demonstrate that the proposed RGB-D object recognition algorithm based on the column direction B2DKQPCA outperforms some existing algorithms using principal component analysis and some existing algorithms using convolutional neural network.

Key words: kernel principal component analysis, quaternion, color image, RGB-D object recognition

CLC Number:

TN911.22

CHEN Bei-jing, YANG Jian-hao, FAN Chun-nian, SU Qing-tang, WANG Ding-cheng. Block-Wise Two Dimensional Kernel Quaternion Principal Component Analysis[J]. JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM, 2019, 42(1): 53-60.

References

[1] Subakan O N, Vemuri B C. A quaternion framework for color image smoothing and segmentation[J]. International Journal of Computer Vision, 2011, 91(3):233-250.
[2] Ell T A, Sangwine S J. Hypercomplex Fourier transforms of color images[J]. IEEE Transactions on Image Processing, 2007, 16(1):22-35.
[3] Gai S. New banknote defect detection algorithm using quaternion wavelet transform[J]. Neurocomputing, 2016, 196:133-139.
[4] Bihan N L, Sangwine S J. Quaternion principal component analysis of color images[C]//2003 10^th IEEE International Conference on Image Processing (ICIP 2003). Barcelona:[s.n.], 2003:809-812.
[5] 郎方年, 周激流, 闫斌, 等. 四元数矩阵正交特征向量系的求解方法及其在彩色人脸识别中的应用[J]. 自动化学报, 2008, 34(2):121-129. Lang Fangnian, Zhou Jiliu, Yan Bin, et al. Obtain method of quaternion matrix orthogonal eigenvector set and its application in color face recognition[J]. Acta Automatica Sinica, 2008, 34(2):121-129.
[6] Sun Y F, Chen S Y, Yin B C. Color face recognition based on quaternion matrix representation[J]. Pattern Recognition Letters, 2011, 32(4):597-605.
[7] Chen B J, Yang J H, Jeon B, et al. Kernel quaternion principal component analysis and its application in RGB-D object recognition[J]. Neurocomputing, 2017(266):293-303.
[8] Saoud L S, Ghorbani R, Rahmoume F. Cognitive quaternion valued neural network and some applications[J]. Neurocomputing, 2017(221):85-93.
[9] 王金伟, 周春飞, 王水平, 等. 基于分数阶四元数傅里叶变换的彩色图像自适应水印算法[J]. 电子与信息学报, 2016, 38(11):2832-2839. Wang Jingwei, Zhou Chunfei, Wang Shuiping, et al. Color image adaptive watermarking algorithm using fractional quaternion Fourier transform[J]. Journal of Electronics and Information Technology, 2016, 38(11):2832-2839.
[10] Yang H Y, Liang L L, Li Y W, et al. Quaternion exponent moments and their invariants for color image[J]. Fundamenta Informaticae, 2016, 145(2):189-205.
[11] Chen B J, Qi X M, Sun X M, et al. Quaternion pseudo-Zernike moments combining both of RGB information and depth information for color image splicing detection[J]. Journal of Visual Communication and Image Representation, 2017(49):283-290.
[12] Assefa D, Mansinha L, Tiampo K F, et al. The trinion Fourier transform of color images[J]. Signal Processing, 2011, 91(8):1887-1900.
[13] Schölkopf B, Smola A, Muller K R. Nonlinear component analysis as a kernel eigenvalue problem[J]. Neural Computation, 1998, 10(5):1299-1319.
[14] Eftekhari A, Forouzanfar M, Moghaddam H A, et al. Block-wise 2D kernel PCA/LDA for face recognition[J]. Information Processing Letters, 2010, 110(17):761-766.
[15] Sun N, Wang H X, Ji Z H, et al. An efficient algo-rithm for kernel two-dimensional principal component analysis[J]. Neural Computing Applications, 2008, 17(1):59-64.
[16] Goswami G, Vatsa M, Singh R. RGB-D face recognition with texture and attribute features[J]. IEEE Transactions on Information Forensic and Security, 2014, 9(10):1629-1640.
[17] Browatzki B, Fischer J, Graf B, et al. Going into depth:evaluating 2D and 3D cues for object classification on a new, large-scale object dataset[C]//2011 IEEE International Conference on Computer Vision Workshops (ICCV2011). Barcelona:[s.n.], 2011:1189-1195.
[18] Tang J H, Jin L, Li Z C, et al. RGB-D object recognition via incorporating latent data structure and prior knowledge[J]. IEEE Transactions on Multimedia, 2015, 17(11):1899-1908.
[19] Cheng Y, Zhao X, Huang K, et al. Semi-supervised learning and feature evaluation for RGB-D object recognition[J]. Computer Vision and Image Understanding, 2015, 139:149-160.
[20] Bo L F, Ren X F, Fox D. Unsupervised feature learning for RGB-D based object recognition[C]//13^th International Symposium on Experimental Robotics. Québec City:[s.n.], 2013:387-402.
[21] Wang A R, Lu J W, Cai J F, et al. Large-margin multi-modal deep learning for RGB-D object recognition[J]. IEEE Transactions on Multimedia, 2015, 17(11):1887-1898.
[22] Zhang H, Parker L E. CoDe4D:color-depth local spatio-temporal features for human activity recognition from RGB-D videos[J]. IEEE Transactions on Circuits and Systems for Video Technology, 2016, 26(3):541-555.

Block-Wise Two Dimensional Kernel Quaternion Principal Component Analysis

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