中文摘要：

针对人脸表情数据的非线性分布特性，提出一种基于非线性联合学习的三维人脸表情合成方法．首先提出非线性联合学习理论，通过无监督回归将具有相同属性的三维人脸映射到相同的低维表达；其次，基于三维人脸的低维表达对低维表达进行重建操作，为给定的三维人脸合成表情，或基于样例表情进行表情的重定向．另外，非线性联合学习方法还能有效地处理带噪声及不完整的人脸数据，获得完整的表情人脸．实验结果表明，文中方法的表情重定向合成结果及合成效率优于已有方法．

英文摘要：

3D facial expression synthesis has been an important and challenging task in the field computer animation. Inspired by the fact that facial expressions distribute on a nonlinear manifold, propose an approach for 3D facial expression synthesis based on nonlinear co-learning. Firstly, facial expressions with the same attribute are projected onto an identical low dimensional representat according to the theory of nonlinear co-learning, by means of unsupervised regression. Second based on the low dimensional representations of 3D faces, reconstruction operations are needed of we aD ion ly, to synthesize expressions for given 3D faces, and to retarget expressions based on given expression samples. The proposed approach is able to handle noisy/incomplete input faces, and generate intact expressional faces. Experimental results show that the proposed 3D facial expression synthesis outperforms the existing methods both in quality and in efficiency.