Facial analysis with a Lie group kernel

To efficiently deal with the complex nonlinear variations of face images, a novel Lie group kernel is proposed in this work to address the facial analysis problems. Firstly, we present a linear dynamic model (LDM) based face representation to capture both the appearance and spatial information of the face image. Secondly, the derived linear dynamic model can be parameterized as a specially-structured upper triangular matrix, the space of which is proved to constitute a Lie group. A Lie group (LG) kernel is then designed to characterize the similarity between the linear dynamic models for any two face images and the kernel can be fed into classical kernel-based classifiers for different types of facial analysis. Finally, experimental evaluations on face recognition and head pose estimation are conducted on several challenging datasets and the results show that the proposed algorithm outperforms other facial analysis methods.