“…Usually, given L labeled 2D landmarks and corresponding predefined 3D landmarks on its 3D face mesh, the pose matrix { R , t }, identity coefficients u , expression coefficients e , and displacements D = { d k } can be solved by minimizing the Huber loss function applied to re‐projected error between 2D landmarks and 3D landmarks: where P ={ R , t , u , e , D } and d k is computed on the basis of the definition above: In the case that 2D landmarks has been detected, a nonlinear trust region optimization method like a sparse variant of the Levenberg–Marquardt algorithm can be used to solve pose and bilinear parameters, as Shuang et al do. It is obvious that a reliable landmark detector is necessary, but popular detectors are usually 2D‐based and cannot capture large variations of pose and expression out of plane.…”