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In this article, an effective approach is proposed to recognise the 2D+3D facial expression automatically based on orthogonal Tucker decomposition using factor priors (OTDFPFER). As a powerful technique, Tucker decomposition on the basis of the low rank approximation is often used to extract the useful information from the constructed 4D tensor composed of 3D face scans and 2D images aiming to maintain correlations and their structural information. Finding a set of projected factor matrices is our ultimate goal. During the 4D tensor modelling process, high similarities among samples will emerge because of the information missed partially. Based on the tensor orthogonal Tucker decomposition, the involved core tensor with the structured sparsity, and a graph regularisation term via the graph Laplacian matrix together with the fourth factor matrix are employed for better characterisation of the generated similarities and for keeping the consistency of low dimensional space. To recover the missing information, a framework for tensor completion (TC) will be embedded naturally. Finally, an alternating direction method coupled with the majorisation‐minimisation scheme is designed to solve the resulting tensor completion problem. The numerical experiments are conducted on the Bosphorus and the BU‐3DFE databases with promising recognition accuracies.

In this paper, a 4D tensor model is firstly constructed to explore efficient structural information and correlations from multi-modal data (both 2D and 3D face data). As the dimensionality of the generated 4D tensor is high, a tensor dimensionality reduction technique is in need. Since many real-world high-order data often reside in a low dimensional subspace, Tucker decomposition as a powerful technique is utilized to capture multilinear low-rank structure and to extract useful information from the generated 4D tensor data. Our goal is to use Tucker decomposition to obtain a set of core tensors with smaller sizes and factor matrices which are projected into the 4D tensor data for classification prediction. To characterize the involved similarities of the 4D tensor, the low-rank and sparse representation is built in terms of the low-rank structure of factor matrices and the sparsity of the core tensor in the Tucker decomposition of the generated 4D tensor. A tensor completion (TC) framework is embedded to recover the missing information in the 4D tensor modeling process. Thus, a novel tensor dimensionality reduction approach for 2D+3D facial expression recognition via low-rank tensor completion (FERLrTC) is proposed to solve the factor matrices in a majorization–minimization manner by using a rank reduction strategy. Numerical experiments are conducted with a full implementation on the BU-3DFE and Bosphorus databases and synthetic data to illustrate the effectiveness of the proposed approach.

In this paper, we propose a sparse multi-feature tensor-based representation (SMFTR) for 3D facial expression recognition. Overcome the defects of vector-based and matrix- based models, our method develops a tensor model which mix 2D and 3D information and then obtained the sparse tensor feature under Tucker decomposition framework. In details, a high-order tensor model is constructed by multi-feature images that extracted from 2D and 3D facial expression data. The tensor model joints various useful infromation from multiple aspects, including geometric properties, texture information and surface deformation, etc. Then, in order to reduce the redundancy and extract discriminative feature, 3D method of optimal directions (MOD) dictionary learning algorithm is used to learn sparse dictionaries and N-way block orthogonal matching pursuit (OMP) is used to calculate the sparse coefficient tensor which is used as the tensor feature for classification. Finally, the performance of our method is demonstrated on BU-3DFE database by the non-linear support vector machine (SVM) classifier. The experimental results illustrated that the proposed method achieves a competitive accurate rate for 3D facial expression recognition.

In this paper, a novel sparse and low-rank Tucker decomposition approach is proposed and is applied into 2D+3D facial expression recognition (FER). Firstly, a 4D tensor model is bulit to explore the efficient structural and complemental information between 2D and 3D data. Secondly, the information is missed partly in the process of the 4D tensor modeling, and high simirarities among samples are then generated, in which the low-rankness of the generated 4D tensor is used to characterize the involved sample simirarities. At the same time, a tensor completion is then embedded to recover the missed information. Thirdly, under orthogonal Tucker decomposition of the generated 4D tensor, the tensor optimization model is utilized by imposing sparse constraint on the involved core tensor and the invoved factor matrices that are employed finally for classification prediction. Finally, the alternating direction method of multipliers is adopted to solve the proposed optimization problem effectively. Numerical experiments verify the effectiveness of the proposed approach on the BU-3DFE database.

Multimodal facial expression recognition (FER) has been becoming a promising research hotspot in recent years. In this paper, we propose a novel sparse orthogonal Tucker decomposition for 2D+3D facial expression recognition (FER). Firstly, we construct a 4D tensor model to explore the efficient structure and complement information between 2D and 3D data. Secondly, based on orthogonal Tucker decomposition, the tensor optimization model, which impose sparse constraint on the involved core tensor and factor matrices, are utilized to find strong interactions between the core tensor and factor matrices for better classification prediction. Finally, a alternating direction method is employed to effectively solve the proposed optimization problem. Numerical experiments are implemented on the BU-3DFE database to indicate the effectiveness of the proposed approach.

In this paper, we utilize 4D tensor structure to explore efficient structure information for 3D facial expression recognition. As a powerful tool to analyze multidimensional nonnegative tensor data, nonnegative tensor factorization (NTF) aims to obtain a partly localized representation of high-dimensional tensors. However, the NTF algorithms often suffer from both high computational complexity and memory requirements for high-order tensor data. To overcome these disadvantages, we present a low-rank approximation method to decrease the computation complexity. Meanwhile, we extract local geometric and discriminant information to improve facial recognition. Therefore, we propose fast nonnegative tensor factorization based on graph-preserving (FNTFGP) algorithm for 3D facial expression recognition (FER). It is a trial to explore and apply the proposed method into 3D FER. Experiments are conducted on the BU-3DFE database. The result of experiments shows the validity and efficiency of the proposed approaches. The proposed algorithm opens a promising direction for the higher performance of 3D facial expression recognition.