# An Efficient Multiscale Scheme Using Local Zernike Moments for Face Recognition
## 1 Introduction  
Face recognition is actively used in many applications, such as entertainment, social media, security, and law enforcement. Despite the great deal of progress in the last two decades, face recognition systems have not fully met expectations [1]. In particular, for real-world security-related problems, powerful systems are needed that can work on images with different quality and resolutions recorded in different spectra and obtained from controlled and uncontrolled environments. In previous studies, the face recognition problem has been tackled in different ways according to the type of data used. Among them, the number of studies on 2D still images in the visible spectrum is quite high [2]. The main reason for this is the need for methods that can be used on 2D still images for many real-world problems. On the other hand, since video recording is now performed in many environments with surveillance cameras, methods developed for use on 2D video data also have an important place in the field of face recognition [3]. In addition to illuminated environments, to also enable recognition in dark environments, heterogeneous methods are developed to compare the images in infrared and visible spectra [4]. Another example of heterogeneous face recognition is sketch-photo matching [4], which is often used to detect suspects in forensic cases. In addition to 2D data, with the easy access to sensors used to acquire 3D data in recent years, 3D face images have become widely used for facial recognition [5] and facial analysis [6] for different purposes. In this work, we propose a face recognition scheme for 2D still images in visible and infrared spectra. The face recognition problem is generally addressed in two different ways; identification and verification. In the identification problem, the aim is to find the identity of a person from a face image. In the verification problem, it is desired to verify if two (or more) different facial images belong to the same person. The face recognition systems for both problems have two important parts: extraction of face descriptors and classification of these descriptors. The performance of these systems depends largely on the quality of the descriptors used. Therefore, there are many studies in the literature about how to construct descriptors that will maintain intra-class similarities and inter-class differences. Face descriptors are generally divided into three parts: deep learning-based, learning-based, and hand-crafted descriptors. Significant achievements have been obtained with deep learning-based methods, especially in recent years [7; 8; 9]. Among these methods, convolutional neural networks (CNNs) are the most-studied method, and the highest face recognition performances are typically obtained with CNNs [10]. In the literature, many learning-based and hand-crafted representations have been proposed to construct descriptors from face images. Principal component analysis (PCA) [11], linear discriminant analysis (LDA) [12], and independent component analysis (ICA) [13] are well-known examples of the former group. In these methods, the descriptors are constructed by projecting the face images into a subspace. Because the construction of the descriptors using these methods is performed globally on the images, these descriptors are quite sensitive to variations in illumination and facial expression [14]. In most of the recent hand-crafted methods, descriptors are computed locally on face images. Local binary patterns (LBP) [15] is one of the best known local methods used in face recognition. Following its successful results, many other LBP-like methods with local encodings have been developed in the literature [16; 17; 18; 19]. Tan et al. [20] use ternary codes (\(-\)1, 0 and 1) instead of binary codes. Zhang et al. [21] encode high-order local differences in different directions with local derivative patterns. Another recent study makes use of dual cross patterns [2].