# A Feature-Based Structural Measure: An Image Similarity Measure for Face Recognition
## 2 Background  
During the last few years, many studies, methods and approaches to similarity and recognition of human faces have been presented to achieve high success rates for accuracy, confidence in identification and authentication in security systems. A significant step in image similarity was presented by [PERSON] and [PERSON] in 2004 [9], when they proposed the SSIM. This measure is based on the statistical similarity between two images. However, SSIM can give ambiguous results for two different poses, and confusing results in certain cases where it indicates a high similarity for two images which are in fact dissimilar [10]. In an attempt to develop the similarity measures and using them for face recognition; [PERSON] et al. proposed a similarity measure based on Hausdorff distance for face recognition. This measure can provide similarity and dissimilarity information of two objects to compare them such as faces with different illumination condition and facial expression. The measure has a better performance than the measures based on conventional Hausdorff distance and the eigenface approaches [11]. [PERSON] et al. [12] proposed two new operators for face recognition; to find the pixel intensity variation information of overlapping blocks resulted from the original face image. Two factors let the proposed operators work better than the conventional interest operator: the first one is that by taking the relative as the feature of an image block. The second one is that the scheme to partition an image into overlapping allows the proposed operators to give more representation information for the face image. In 2011, an improved version of SSIM was proposed by [PERSON] et al. [13]. This measure was called feature similarity index for image quality assessment (FSIM) in an effort to emphasize its use in recognition; this method depends on the low-level features of images. In this measure, the dimensionless and gradient magnitude are the main features, which play complementary roles in characterizing the image. However, FSIM also produces confusing results in certain cases; for example, it may detect a similarity between dissimilar images or a non-trivial amount of similarity between two different poses. [PERSON] et al. [14] presented a new similarity approach and applied it in face recognition; by combining phase information of wavelet moments and use the real and imaginary components of wavelet moments to describe an image and develop a similarity measure which is invariant under image rotation. In 2016 [PERSON] et al. presented a novel approach for solving the problem of automatic face recognition when the human faces are taken from frontal views with varying illumination and disguise. The approach is based on extracting dynamic subspace of images and obtaining the discriminative parts in each individual to represent the characteristics of discriminative components and give a recognition protocol to classify face images [15]. The topic of 3D face recognition is getting attention. In 2008 a novel deformation invariant image for robust 3D face recognition was proposed by [PERSON] et al. [16]. This work is divided into three phases; firstly getting the depth and the intensity of an image from the original 3D facial data. Secondly, geodesic level curves are created by constructing radial geodesic distance image from the depth image. Finally, deformation invariant image is created by evenly sampling points from the selected geodesic level curves in the intensity image. In 2017 [PERSON] et al. presented 105 new geometrical descriptors for 3D face analysis. These descriptors created by composing primary geometrical descriptors (for instance mean and Gaussian) and the coefficients of the fundamental forms, and by applying trigonometric functions (for instance sine and cosine) and logarithm to them [17]. Another approach for 3D feature extraction via geometrical analysis is presented in [18]. To the best of our knowledge, 3D face recognition methods haven't addressed 3D image similarity so far.