# A Feature-Based Structural Measure: An Image Similarity Measure for Face Recognition
## 1 Introduction  
In view of the current issues of terrorism, security in the western world has been heightened, and is becoming an important and challenging task. Surveillance cameras are now common in airports, hospitals, universities, ATMs, banks and anywhere else with a security system. There is an urgent need to find an accurate and reliable automated system which is able to recognize human faces, in order to identify suspicious persons using cameras [1]. Facial recognition has therefore become the focus of current research, and has received significant attention from academics; many techniques and methods for recognizing human faces have been proposed and applied. However, until now there has been no method which offers the required accuracy in all situations. In other words, existing systems still fall far short of the abilities of a human perception system. This challenge is mainly due to factors that affect the features of an image, such as changes in illumination, background, facial expressionand head pose. The task of automatic face recognition is therefore a very complex problem; see [2; 3; 4] for surveys.  
In general, there are two classes of face recognition methods: structural and statistical approaches. Structural approaches are based on the extraction of the local features of a face, such as the shapes of the eyes, mouth and nose. These methods suffer from the unpredictability in facial appearance and environmental conditions, e.g., head pose, when a profile image is compared with a frontal image [5]. Conversely, in statistical approaches the complete face region is treated as input data; in other words, global features are extracted from the whole image. The region surrounding the face, including the hair, shoulders and background, is considered to be irrelevant data and may adversely affect the recognition results [6]. Statistical approaches for feature extraction which are based on statistical moment have been used for classification and recognition applications due to their invariance properties [7].  
In most facial recognition applications, the similarity between two images is calculated, i.e., using a reference image and a training database image. Several matching algorithms for face and object recognition systems have been designed based on image similarity measurements, such as the structural similarity measure (SSIM), which won an Emmy award for its prediction of the perceived quality of digital images and videos [8].  
The main aim of this work is to design an efficient similarity index to resolve the shortcomings of the existing measures in giving high confidence in recognition. The proposed measure combines the best features of the well-known SSIM and FSIM approaches, striking a balance between performance for similar and dissimilar images of human faces. In addition to the statistical structural properties provided by SSIM, edge detection is incorporated as a distinctive structural feature. In addition to confidence, the proposed measure (FSM) gives a reliable similarity between any two images even under noise, in other words, FSM produces maximal similarity when the images are similar, while giving near-zero similarity when the images are dissimilar. These properties gave the proposed measure high ability to recognize face images under noisy conditions, different facial expressions and pose variations. Such properties are highly needed in security applications while checking the identity of a specific face image in a big database.