Research On Three-dimensional Facial Expression Recognition Based On Tensor Decomposition Theory

Facial expression is naturally preeminent way and the most cogent for humans,and it is often used to regulate interactions with the environment or other people and to communicate emotions.Nowadays,the facial expression recognition(FER)has received enormous attention and played an important role in computer vision,affective computing and multimedia research.The traditional algorithms of facial expression recognition use the data representation based on vector representation to describe all kinds of expression features,resulting in the space structure information loss of facial expression data sample and the problem of small sample and dimension disaster because of high dimensions.To solve this problem,we introduce the data structure of the high-order tensor,and propose3 D face expression recognition algorithms based on the theory of tensor decomposition.On the one hand,with the help of high order tensor structure,the space structure of 3D face expression information can be retained fully;on the other hand,with the help of tensor sparse low-rank decomposition,the similarities of facial expression features can be characterized and the data dimension reduction is implemented effectively.Finally,sparse and low-rank tensor optimization model is established by using the current popular large-scale optimization theory and method,and efficient and stable 3D face expression recognition algorithm is then designed.The main contribution of the paper is as follows:1.A 3D facial expression recognition framework based on sparse and low-rank tensor decomposition theory is proposed.This idea of tensor modeling and sparse lowrank tensor decomposition is a novel technology in 3D facial expression recognition methodology.To efficiently solve this sparse low-rank tensor optimization model,designing a fast robust optimization algorithm requires indepth analysis of the corresponding high-order tensor optimization theory,in which the research results will enrich the optimization theory,especially the research content of large-scale optimization theory in 3D facial expression recognition;2.A tensor decomposition algorithm based on low-rank tensors completion(FERLr TC)is proposed.To solve the problem of small sample and dimension disaster caused by high dimensions caused by feature extraction based on vector representation,2D+3D face data are used to construct 4D tensor,and through Tucker decomposition of it,log-sum penalty function of the core tensor and low rank constraint of factor matrices are utilized to maintain the discriminability of tensor projection space.Finally,we use a rank reduction strategy in a majorization–minimization manner to solve the factor matrices.The proposed algorithm is verified by the complete numerical experiments,which also shows that Tucker decomposition,as a powerful dimension reduction technique,can capture the low-rank structure of 4D tensor,and the low-dimensional features generated can better reflect the essence of the original 4D tensor data in the tensor subspace;3.An orthogonal tensor completion algorithm based on factor prior(OTDFPFER)is proposed.To solve the problem that low-dimensional features extracted by the decomposition of the 4D tensor are similar in the tensor subspace,Laplacians graph derived from the similarity matrix of the fourth mode of 4D tensor is taken as factor prior,the factor matrix is introduced into the graph embedding regularization for keeping the consistency of low dimensional space.Then,alternating direction method(ADM)and optimization minimization(MM)schemes are designed to solve the resulting tensor completion problem.The experimental results show that OTDFPFER achieves good results for facial expression recognition,which also shows that the graph embedding framework related to factor matrices can better represent the similarity among samples than that using the low-rank structure of factor matrices;4.A model of 3D facial expression recognition FERMROTD based on orthogonal tensors is proposed,manifold structure constraints are used to maintain the local structure(geometric information)of 3D tensor samples in the low-dimensional tensors space.The block coordinate descending algorithm(BCD)is used to optimize the solution of the model,and the convergence and complexity of the model are analyzed.At the same time,the first order optimality condition based on the stability point is established.The validity of the model is verified by BU-3DFE and Bosphorus databases,and the experimental results also show that the use of manifold regularization term can better extract the lowdimensional features of the real 3D tensor manifold in the low-dimensional tensor subspace compared with introducing the graph embedding regularization into the factor matrix.