## 1 Introduction
[PERSON] and [PERSON] [11] studied the cranio-facial changes in feature-position ratios and skin wrinkles as features for three age groups; baby, young adult, and senior adult. The ratios between the features and different face regions were computed. [PERSON] [12] presented a mathematical model to estimate the growth of the head from infancy to adulthood. [PERSON] and [PERSON] [13] computed eight ratios of distance measures for modeling age progression. They proposed a craniofacial growth model by illustrating how the age-based anthropometric constraints on facial proportions translate into linear and non-linear constraints on facial growth parameters. The active appearance model (AAM) was proposed by [PERSON] et al. [14]. This model is a statistical shape model to represent the face in the image by capturing the shape and the grey-level information. [PERSON] et al. [15,16] studied the aging effects on face images and described the effects of aging on facial appearance. They built a statistical-based face model. By their proposed shape intensity face model and automatic age simulation, statistically significant improvement was reported in the performance of the age classification system. [PERSON] et al. [17] proposed an AAM with 68 facial land marks for age estimation. A variation of the AAM model, called the Contourlet Appearance Model (CAM), was proposed in [18] to calculate the landmarks. [PERSON] et al. [19,20] defined an ageing pattern subspace (AGES) model for representing the ageing process as the sequence of an individual's face images sorted in time order by constructing a representative subspace. The images, which were not available for some age groups, are synthesized by using an expectation-maximization (EM) -like iterative learning algorithm. The AGES model builds an aging pattern for different age stages. On the other hand, the manifold model, as proposed by [PERSON] et al. [21; 22], was used to handle the ageing process in [23; 24]. This model is more flexible than the AGES model, since images of different persons can be used for unavailable images of some ages. The manifold models use several linear regression functions to learn the low-dimensional aging trend from a group of face images for each age. The appearance model (AM) is an alternative way to represent the age-related features. It focuses on texture, pattern analysis, and wrinkles. [PERSON] et al. [25; 26] extracted local and global facial features. Texture and shape features were calculated by using a semantic-level description of the face. [PERSON] and [PERSON] [27] used effective texture descriptor for appearance feature extraction and utilized local binary patterns (LBP). [PERSON] and [PERSON] [28] used the Gabor features with fuzzy-LDA. Their work showed that Gabor features are more effective than the LBP. [PERSON] et al. [29; 30] employed spatial flexible patches (SFP) as a feature descriptor in order to handle images with small undesirable defects such as occlusions and head pose. [PERSON] et al. [31] proposed bio-inspired features (BIF) that have the ability to handle small rotations and scale changes effectively. [PERSON] [32] exploited the LBP and Gabor features. Adaboost was used to learn the discriminative LBP-Histogram bins for age estimation. [PERSON] et al. [33] proposed a cost sensitive local binary feature learning by using facial images. They extracted low-dimensional binary codes face patches from the raw pixels while using several hashing functions. Recently CNNs and DNNs have been started to be used for feature extraction and classification for the facial age estimation due to their success in several computer vision fields. [PERSON] and [PERSON] [5] used CNNs in age estimation for the first time. A simple CNN architecture was used as a feature extractor and a classifier to avoid overfitting problem. [PERSON] et al. [34] proposed a cascaded classification and regression system based on a coarse age classifier. They introduced an age regressor for each age group based on the features extracted from the coarse age classifier.