Kernel quaternion principal component analysis and its application in RGB-D object recognition

While the existing quaternion principal component analysis (QPCA) is a linear tool developed mainly for processing linear quaternion signals, the quaternion representation (QR) used in QPCA creates redundancy when representing a color image signal of three components by a quaternion matrix having four components. In this paper, the kernel technique is used to improve the QPCA as kernel QPCA (KQPCA) for processing nonlinear quaternion signals; in addition, both RGB information and depth information are considered to improve QR for representing RGB-D images. The improved QR fully utilizes the four-dimensional quaternion domain. We first provide the basic idea of three types of our KQPCA and then propose an algorithm for RGB-D object recognition based on bidirectional two-dimensional KQPCA (BD2DKQPCA) and the improved QR. Experimental results on four public datasets demonstrate that the proposed BD2DKQPCA-based algorithm achieves the best performance among seventeen compared algorithms including other existing PCA-based algorithms, irrespective of RGB object recognition or RGB-D object recognition. Moreover, for all compared algorithms, consideration of both RGB and depth information is shown to achieve better performance in object recognition than considering only RGB information. (C) 2017 Elsevier B.V. All rights reserved.