基于块的二维核四元数主成分分析
|
摘要
核四元数主成分分析(KQPCA)被成功应用于处理非线性四元数信号,然而,核矩阵维数太高使其对角化非常耗时,目前二维形式的KQPCA(2DKQPCA)并没有成功实现.对此,采用基于块处理和并行计算的思想,提出基于块的2DKQPCA(B2DKQPCA),实现真正意义上的2DKQPCA.基于时间复杂度、应用性能和分块矩阵应为四元数Hermitian矩阵的综合考虑,B2DKQPCA重点处理主对角线、反对角线和主对角线旁3个方向的小块.然后,结合B2DKQPCA与RGB-D图像四元数表示方法,将B2DKQPCA应用于RGB-D目标识别领域.在2个公开库上的实验结果表明,提出的基于列向B2DKQPCA的RGB-D识别算法优于现有基于主成分分析算法和基于卷积神经网络的一些算法.
Currently,kernel quaternion principal component analysis( KQPCA) has been proposed and successfully applied to process linear quaternion signals. However,two dimensional version of KQPCA( 2 DKQPCA) 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 2 DKQPCA( B2 DKQPCA) is proposed to implement 2 DKQPCA really. After the overall consideration of computational complexity,application performance and quaternion Hermitian block,B2 DKQPCA mainly processes the blocks of three directions: main-diagonal direction,anti-diagonal direction and side-diagonal direction. Then,B2 DKQPCA is applied into RGB-D object recognition by combining B2 DKQPCA 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 B2 DKQPCA outperforms some existing algorithms using principal component analysisand some existing algorithms using convolutional neural network.
Currently,kernel quaternion principal component analysis( KQPCA) has been proposed and successfully applied to process linear quaternion signals. However,two dimensional version of KQPCA( 2 DKQPCA) 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 2 DKQPCA( B2 DKQPCA) is proposed to implement 2 DKQPCA really. After the overall consideration of computational complexity,application performance and quaternion Hermitian block,B2 DKQPCA mainly processes the blocks of three directions: main-diagonal direction,anti-diagonal direction and side-diagonal direction. Then,B2 DKQPCA is applied into RGB-D object recognition by combining B2 DKQPCA 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 B2 DKQPCA outperforms some existing algorithms using principal component analysisand some existing algorithms using convolutional neural network.
引文
[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 10thIEEE 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 RGBD 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]Sch9lkopf 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 algorithm 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]∥2011IEEE 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]∥13thInternational 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. Co De4D: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.
[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 10thIEEE 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 RGBD 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]Sch9lkopf 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 algorithm 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]∥2011IEEE 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]∥13thInternational 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. Co De4D: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.