Subspace-based approaches

Subspace-based methods, also known as appearance-based approaches, have been suggested to consider a palmprint image as a high-dimensional vector and hence mapping it into a lower dimensional vector. Principal Component Analysis (PCA), Fisher Discriminant Analysis (FDA), independent component analysis (ICA) and linear discriminant analysis (LDA) were initially used in face recognition. The coefficients acquired in the subspace are employed as features and a distance metric and some other classifiers are implemented for matching purposes. Rather than subsequently employing the subspace algorithms, researchers can employ DCT, Gabor filters and wavelets. Subspace feature extraction techniques provide a powerful representation, low computational cost, ease of implementation and reliable splitting, and are extensively used in various areas such as face and palmprint recognition. PCA is one of the most commonly used techniques applied to extract feature vectors.

Figure 2.7: Sample of palmprint features [71]: (a) subpalmprint samples in the training set; (b) eigenpalms derived from the above samples.

Lu et al. [71] were among the first to propose the use of PCA in palmprint recognition. In their approach, the original palm images are transformed into a small feature space set, named ”eigenpalms”, which are the eigenvectors of the training set and can describe the principal components of the palm images. Notwithstanding the success of PCA, some challenges still remain which require further research.

Two-dimensional PCA (2DPCA) have been introduced effectively in palmprint recogni- tion [90]. This particular process is reliant on a 2D image matrix rather than a 1D vector, and an image covariance matrix is created by employing the original palm image matrices. Unlike the palm covariance matrix related to PCA, the size of the palm covariance matrix applied in 2DPCA is significantly smaller. Thus, the advantages of 2DPCA include a precise assessment of the covariance matrix which is much more straightforward to determine the corresponding eigenvectors takes less time.

Zuo et al., [136] presented a new projection which relies on a bilateral directional PCA (BD-PCA) provided with an Assembled Matrix Distance (AMD) metric for image recog- nition. BD-PCA is employed to extract features by decreasing dimensionality in both the column and row directions in order to avoid the problem of overfitting. Finally, an AMD metric is presented to determine how far apart the two feature matrices are; subsequently, nearest neighbour and nearest feature line classifiers are applied to improve recognition performance.

Pan et al., [85] suggested an approach using a Gabor feature-based (2D)2PCA for palm- print recognition. Gabor features of five levels and six orientations are extracted through the convolution of the Gabor filter bank and the original image. Then (2D)2PCA is used to reduce the dimensions of the feature space in two directions, which results in fewer coeffi- cients being needed to represent an image. Finally, Euclidean distance is employed together with the nearest neighbour classifier for classification. The outcomes from experiments have revealed the usefulness of the suggested GB(2D)2PCA regarding both speed and accuracy. PCA focuses on how the images are represented rather than discrimination, whereas LDA is used to find the optimal projection matrix and then its ratio of scatter between-

class and within-class can be maximized in a feature subspace with a lower dimensionality (Fisher criterion). This is more suitable than PCA for classifying palmprints. Wu et al. [108] suggested a new Fisher palm recognition technique dependent on PCA-LDA. The PCA is employed to decrease the size of the dimensions of the initial palmprint, and then LDA is applied to carry out the projection of the image. For classification, Euclidean distance is used as a matching function.

Wang at al. [102] suggested a Kernel Linear Discriminant Analysis (KFDA) algorithm to extract features of palmprints for the recognition task. A tool with no fixed peg is conceived to capture the palm images. However, it has been observed that the features taken from these palmprints bear some nonlinearity because of the uncontrollability of the rotation and the stretching of hands. KFDA is employed to detect higher order relations among images of palmprints in order to accomplish the recognition task. The outcomes acquired from Wang et al.’s experiments indicated that KFDA performs better than eigenpalms and Fisher palms, principally with regard to using only a few training samples.

Du et al. [23] used both horizontal 2DLDA and vertical 2DLDA to extract the Gabor features of palmprints, and moreover applied a distance-based adaptive strategy to fuse these two features together. In order to perform palmprint recognition, the nearest neighbour classifier is used and this technique reduces the time required for the process.

Locality Preserving Projection (LPP) is a linear subspace technique for manifold learn- ing, with various characteristics that are nonlinear. The aim of LPP is to preserve the local structure of the palmprint image space by taking account of different structures with much detail, and this can effectively address a generalized eigenvalue issue. The technique seems to be less affected by noise than PCA and LDA [110].

Hu et al. [39] developed a two-dimensional LPP (2DLPP) which extracts the appropriate features from the palm image according to a locality preserving criterion. The principal advantage of 2DLPP over LPP is that it offers a more accurate approximation of the original palmprints and therefore can directly solve the singularity problem. Thus, this can help to avoid losses of important information in recognition. Although it is argued that 2DLPP is more powerful than LPP, it does suffer from the limitation that it de-emphasizes discriminant information, which is essential in connection with the recognition problem. Figure 2.7 presents an example of finding useful palmprint representations in the subspace.