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The extraction of facial features is the key to micro-expression recognition. This paper puts forward a micro-expression recognition algorithm through multi-feature fusion. In this algorithm, the change of local binary pattern (LBP) feature distribution is correlated with projection error. For fast and accurate detection, the research data were all extracted from professional facial expression databases, the images had basically the same positions in each expression library, and the pure face image was acquired through manual segmentation from the selected expression library. Through comparison and its application in an intelligent classroom environment, it is proved that the proposed algorithm clearly outperforms the original LBP algorithm. The proposed method can be extended to other image recognition and classification problems.

Basis functions play important roles in computational electromagnetics (GEM). It is interesting to investigate the errors in the projection of the equivalent current of a plane wave using various basis functions. In this work, the projection error of various basis functions is studied. The basis functions involved are the pulse basis function, the triangular basis function, higher-order versions of these basis functions, and the divergence-conforming basis function on rectangular and triangular elements. The projection errors are derived in closed form. The asymptotic expression of the closed form is given. The analytical results are verified by numerical results. The projection error of the pth order one-dimensional (ID) basis is asymptotically inversely proportional to the (p+1)th power of the density of unknowns. Based on the closed-form projection errors in the one- dimensional case, it is found that when the expansion basis is fixed, the application of different testing functions only affects the coefficient of the projection error, rather than the order. Generally, the error of the divergence-conforming basis in the projection of curl-free vectors is less than that of divergence-free vectors. [ABSTRACT FROM AUTHOR]