Tensor Representation And Decomposition Algorithm And Theory Research On 3D Facial Expression Recognition

Expression is the main way to express emotions in people's daily communication.With the increasing popularity of Internet and the continuous development of artificial intelligence,facial expression recognition technology has drawn much more attention.This paper takes 3D facial expressions as research objects,aiming at extracting features and descending dimension based on tensor representation,manifold learning and tensor decomposition technique.The main work of this paper includes:(1)According to the geometric characteristics of 3D surface,we not only extract the depth information which is commonly used in the 3D domain,but also calculate the normal vector and curvature at each point by local surface fitting.Five kinds of features are obtained after mapping them into the 2D space.Experimental results show that these geometric features can effectively improve the recognition results.(2)Combined with the characteristics of tensor and manifold learning method,Orthogonal Tensor Marginal Fisher Analysis based on Tensor Distance is proposed.First,the nearest neighbors are searched based on the tensor distance,and the optimization model is formed according to the graph-preserving criterion.Then,a set of base tensors are learned to get the low dimensional representation of samples.Compared with the traditional Euclidean distance,tensor distance can better reflect the difference of high-order data.It not only considers the relationship between the corresponding elements among samples,but also gives full consideration to the spatial structure of their own,making the manifold learned from data set more close to the real manifold of expressions.Experimental results show that the algorithm can improve the recognition rate of expression.(3)Considering the locomotion of the muscle movement when expression occurs,a novel approach called Orthogonal Tensor Marginal Fisher Analysis based on Weighted Tensor Distance is proposed for expression recognition.First,feature images are divided into blocks.Combined with the entropy weighting idea,each sub-block is given a different weight.And the distances among samples are measured by the weighted sum of the tensor distances of the corresponding sub-blocks.It is beneficial to construct the graph model that accurately reflects the intrinsic structure of expressions,improving the discrimination ability of the algorithm.Experimental results show the effectiveness of the algorithm.(4)In view of the proposed algorithms,a 3D facial expression recognition system is constructed,which can visually show the recognition result of each algorithm.The system includes four parts,namely,preprocessing,training,testing and displaying.