# An Efficient Multiscale Scheme Using Local Zernike Moments for Face Recognition
## 1 Introduction
In this method, the second-order pattern is encoded in four different directions (0, \(\pi/2\), \(\pi\), and \(3\pi/4\)). Gabor wavelets [22] are another local method commonly used to construct local descriptors for face images. In the majority of studies, 40 complex images are obtained by applying 40 Gabor filters to face images in 8 different orientations and 5 different frequencies [14]. Apart from Gabor and LBP-like methods, histograms of oriented gradients (HOGs) [23], scale invariant feature transform (SIFT), [24], patterns of oriented edge magnitudes (POEM) [25] and local quantized patterns (LQP) [26] are also used to generate the descriptors. In this study, the descriptors for face images are generated using Zernike moments (ZMs) [27]. In addition to face recognition, there are many other studies that use ZMs for different recognition problems--for instance, fingerprint [28], character [29], and iris [30]. Studies on face recognition can be summarized as follows: Foon et al. [31] introduced a face verification method which combines ZMs with wavelet transforms [32]. Ouanan et al. [33] use Gabor filters to extract texture features, and ZMs to compute facial shape features. In [34], a global feature descriptor is proposed using Gabor filters and ZMs. First, they generate multi-scale Gabor maps and then compute ZMs of these maps. In [35], the face images are divided into sub-regions and for each sub-region, and local and global features are calculated using LBP and ZMs, respectively. A similar approach is proposed by Singh et al. [36]. Along with the global ZMs, they use the local features obtained with SIFT keypoints. Huang et al. [37] modified the ZMs calculations and obtained the spatially-weighted ZMs to enhance the effect of distinctive regions on the face. In [38], the ZMs are calculated separately for the non-overlapping sub-regions of the face images, and the moments are weighted adaptively according to the regions. It is known that powerful descriptors can be constructed with ZMs for images which have explicit shapes, such as fingerprint and optical characters [28; 29]. However, for face recognition, local structures are more distinctive and prominent than global shape information. For this reason, as mentioned above, along with the local feature extraction operators, ZMs are used for general shape characteristics of face images in most of the previous studies. To expose local patterns from face images using ZMs in a robust way, in our previous work we developed a method called the local Zernike moments (LZM) transformation [39]. In contrast to ZMs calculated from the entire image, LZM representation is obtainedby applying the ZM transform at each pixel using its neighborhood to capture the micro-structure around this pixel. By using the complex ZMs calculated for each pixel, a different number of complex images are generated according to the moment degree. Different studies have been carried out on face recognition with LZM transformation. In [40], using a scale-space representation, a face identification method for low-resolution images is proposed. Kahraman et al. [41] have developed a face verification method with metric learning techniques on the feature vectors generated from LZM maps. In some studies, complex images obtained by LZM transformation have been encoded using different operators, and then descriptors have been created for face images. Basaran et al. [42] use local Zernike xor patterns (LZXP) obtained by encoding LZM images with the xor operator. In [43], real and imaginary LZM components are encoded with a local phase quantization method. In addition to face recognition, there are also some studies on facial expression recognition using LZM transformation. Sariyanidi et al. [44] proposed quantized local ZMs encoding complex ZMs with binary quantization. In [45], LZM features are used with LZXP features and global ZMs. A face recognition scheme developed using complex LZM components is proposed in this work, named multi-scale local Zernike moments (MS-LZM).