Simultaneous Facial Landmark Detection, Pose and Deformation Estimation under Facial Occlusion

Facial landmark detection, head pose estimation, and facial deformation analysis are typical facial behavior analysis tasks in computer vision. The existing methods usually perform each task independently and sequentially, ignoring their interactions. To tackle this problem, we propose a unified framework for simultaneous facial landmark detection, head pose estimation, and facial deformation analysis, and the proposed model is robust to facial occlusion. Following a cascade procedure augmented with model-based head pose estimation, we iteratively update the facial landmark locations, facial occlusion, head pose and facial de- formation until convergence. The experimental results on benchmark databases demonstrate the effectiveness of the proposed method for simultaneous facial landmark detection, head pose and facial deformation estimation, even if the images are under facial occlusion.Comment: International Conference on Computer Vision and Pattern Recognition, 201

On the superlinear problem involving the p(x)p(x)-Laplacian

This paper deals with the superlinear elliptic problem without Ambrosetti and Rabinowitz type growth condition of the form: \begin{align*}\left\{ \begin{aligned} &-div(|\nabla u|^{p(x)-2}\nabla u)=\lambda f(x,u) \quad \text{in } \Omega,\\ &u=0 \quad \text{on } \partial \Omega, \end{aligned} \right.\end{align*} where $\Omega\subset R^{N}(N\geq 2)$ is a bounded domain with smooth boundary $\partial \Omega$, $\lambda>0$ is a parameter. Existence of nontrivial solution is established for arbitrary $\lambda>0$. Firstly, by using the mountain pass theorem a nontrivial solution is constructed for almost every parameter $\lambda>0$. Then, it is considered the continuation of the solutions. Our results are a generalization of Miyagaki and Souto

Existence and multiplicity of solutions for the nonlocal p(x)-Laplacian equations in RNR^N

This work deals with the nonlocal $p(x)$-Laplacian equations in $R^{N}$ with non-variational form \begin{align*} \left\{\begin{aligned} &A(u)\big(-\Delta_{p(x)}u+|u|^{p(x)-2}u\big)=B(u)f(x,u) \text{in}R^{N},\\ &u\in W^{1, p(x)}(R^{N}), \end{aligned} \right.\end{align*} and with the variational form \begin{align*} \left\{\begin{aligned} & a\Big(\int_{R^{N}}\frac{\vert \nabla u\vert^{p(x)}+\vert u\vert^{p(x)}}{p(x)}dx\Big)(-\Delta_{p(x)}u+|u|^{p(x)-2}u)&\\ &=B\Big(\int_{R^{N}}F(x, u)dx \Big)f(x, u) \text{in} R^{N},&\\ &u\in W^{1, p(x)}(R^{N}), \end{aligned}\right. \end{align*} where $F(x,t)=\int_{0}^{t}f(x,s)ds$, and $a$ is allowed to be singular at zero. Using $(S_{+})$ mapping theory and the variational method, some results on existence and multiplicity for the problems in $R^{N}$ are obtained