For the last decades, manifold learning has shown its advantage of efficient non-linear dimensionality reduction in data analysis. Based on the assumption that informative and discriminative representation of the data lies on a low-dimensional smooth manifold which implicitly embedded in the original high-dimensional space, manifold learning aims to learn the low-dimensional representation following some geometrical protocols, such as preserving piecewise local structure of the original data. Manifold learning also plays an important role in the applications of computer vision, i.e., face image analysis. According to the observations that many face-related research is benefitted by the head pose estimation, and the continuous variation of head pose can be modelled and interpreted as a low-dimensional smooth manifold, we will focus on the head pose estimation via manifold learning in this chapter. Generally, head pose is hard to directly explore from the high-dimensional space interpreted as face images, which is, however, can be efficiently represented in low-dimensional manifold. Therefore, in this chapter, classical manifold learning algorithms are introduced and the corresponding application on head pose estimation are elaborated. Several extensions of manifold learning algorithms which are developed especially for head pose estimation are also discussed and compared.
Part of the book: Manifolds