Head Pose Estimation via Manifold Learning

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

Thermal entanglement and teleportation in a two-qubit Heisenberg chain with Dzyaloshinski-Moriya anisotropic antisymmetric interaction

Thermal entanglement of a two-qubit Heisenberg chain in presence of the Dzyaloshinski-Moriya (DM) anisotropic antisymmetric interaction and entanglement teleportation when using two independent Heisenberg chains as quantum channel are investigated. It is found that the DM interaction can excite the entanglement and teleportation fidelity. The output entanglement increases linearly with increasing value of input one, its dependences on the temperature, DM interaction and spin coupling constant are given in detail. Entanglement teleportation will be better realized via antiferromagnetic spin chain when the DM interaction is turned off and the temperature is low. However, the introduction of DM interaction can cause the ferromagnetic spin chain to be a better quantum channel for teleportation. A minimal entanglement of the thermal state in the model is needed to realize the entanglement teleportation regardless of antiferromagnetic or ferromagnetic spin chains.Comment: 1 tex;5eps. accepted by Physical Review