Color Image Processing Using Reduced Biquaternions with Application to Face Recognition in a PCA Framework

Semi‐supervised uncorrelated dictionary learning for colour face recognition

“…We compare our SUDL approach with eight representative colour face recognition methods including QSRC [20], 2DBPCA [24], CMR‐DF [27], CMR‐FF [27], DMDCA [41], DFDE [44], TC [47] and YWPM [48]. In AR‐ours and FRGC‐ours datasets, we run all compared methods 20 times with random training and testing sample selection.…”

“…Based on the theory of reduced biquaternion algebra and the framework of principal component analysis (PCA) [51], 1D reduced biquaternion PCA [24] uses reduced biquaternions to represent colour images in the typical PCA framework, which can make full use of the face colour cues, and 2DBPCA [24] further combines the face spatial and colour information. We use 2DBPCA as the compared method in the following experiment section.…”

“…To deal with this problem, many colour face recognition methods have been designed, which can be divided into following three categories: (i) Data level fusion methods : These methods may reduce the similarity between the data of colour component images by selecting an existing colour space (or an existing colour scheme) or designing a new colour scheme, and then fuse the data of all components. They include uncorrelated colour space [8], independent colour space [8], discriminating colour space [8], extended general colour image discriminant [9], ICA colour space [10], discriminant colour space with double‐zero‐sum characteristic [11], colour space normalisation [12], tensor discriminant colour space [13], sparse tensor discriminant colour space [14], multilinear colour tensor discriminant model [15], compact colour image representation [16], quaternion‐based improved locality preserving projection [17], sparse tensor canonical correlation analysis [18], colour two‐dimensional principal component analysis [19], quaternion collaborative representation‐based classification [20], quaternion sparse representation‐based classification (QSRC) [20], adaptive singular value decomposition in the two‐dimensional discrete Fourier domain [21], collaborative facial colour feature learning of multiple colour spaces [22], quaternion based maximum margin criterion [23], 1D reduced biquaternion principal component analysis [24], 2D reduced biquaternion principal component analysis (2DBPCA) [24], colour two‐dimensional principal component analysis‐convolutional neural network [25], colour‐flow values and colour‐flow eigenspace manifold [26] and covariance matrix regularisation (CMR) [27]. (ii) Feature level fusion methods : These methods may reduce the similarity between the features of colour component images, and then fuse the features of all components, including discrete cosine features [28], holistically orthogonal analysis [29], boosting colour‐component feature selection framework [30], statistically orthogonal analysis [31], colour local Gabor wavelets [32], colour local binary pattern [32], two‐dimensional colour uncorrelated discriminant analysis [33], DeepFace [34], within‐component and between‐component discriminant analysis […”