# Facial Expression Recognition Based on Discrete Separable Shearlet Transform and Feature Selection
## 1 Introduction  
Facial expression recognition (FER) is attracting a lot of research attention because of its prospective applications in human-computer interactions and intelligent transportation systems [1; 2; 3; 4]. Researchers have found that facial expressions can be analyzed to identify emotions, behavioral information, and psychological activities. In the field of multimedia, if an effective FER system can recognize users' facial expressions in real time, it can feedback the changes of customers' facial expressions to the multimedia system, and the multimedia system can provide different multimedia contents for the customers [5; 6; 7; 8]. Therefore, facial expressions not only reflect the inner thoughts of human beings but are also an indispensable part of interpersonal communication [9]. FER usually involves three steps: preprocessing the image, extracting the facial expression features, and training and recognizing the expression feature model. Facial expression feature extraction is the most important part of an FER system. An effective expression feature extraction greatly improves the recognition performance. Many algorithms have been developed for this purpose. The study addressed in [10] employed biorthogonal wavelet entropy to extract multiscale features, and used a fuzzy multiclass support vector machine to be the classifier; experimental results demonstrate the effectiveness of the proposed algorithm. The study in [11] proposed a novel facial emotion recognition method based on discrete wavelet transform, principal component analysis, and cat swarm optimization. They used discrete wavelet transform to extract wavelet coefficients and principal component analysis was utilized to reduce the features. Finally, a single-hidden-layer neural network was used as the classifier. Experimental results demonstrate the feasibility of theproposed algorithm. Gabor is widely used in the pattern recognition fields, such as image processing and feature extraction [12]. Gabor wavelet transform is an important feature extraction tool because of its multiresolution analysis. After the original image is decomposed by Gabor wavelets at different decomposition scales, we can obtain the approximated and detailed information of the target image at different levels. Unfortunately, for FER, the Gabor wavelet transform still has defects. Because the two-dimensional (2D) separable wavelet formed by the one-dimensional (1D) wavelet transform has limited directions, it cannot best represent the high-dimensional features with line or surface singularities. In fact, the features with line or surface singularities are very common in facial expression images, such as the outline of the mouth and the eyes. These are remarkable and precise features of human facial expressions. To overcome this limitation, multiscale geometric analysis tools have been developed, such as curvelet transform [13] and shearlet transform [14]. Although curvelet basis functions are advantageous for approximating linear singularities, the edge of a facial expression image is usually a curve rather than a straight-line, so curvelet transform has limitations in expression recognition. The discrete separable shearlet transform (DSST) is a multiscale geometric framework for image analysis [15]. It can better detect the edge and detail information because it has characteristics like multidirectional, multiscale, localization, and anisotropy. However, the coefficients of the image after DSST are large, so it is not desirable to use all the transformation coefficients as the expression feature set. Therefore, it is necessary to find the optimal feature subset of the original feature set so as to retain the key classification information of the original data and improve the identification efficiency of the system. In this paper, a novel approach to facial expression recognition based on DSST and normalized mutual information feature selection is proposed.