Orthogonal tucker decomposition using factor priors for 2D+3D facial expression recognition

Abstract

Abstract 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.

Keywords

• emotion recognition
• face recognition
• graph theory
• matrix decomposition
• tensors