Nuclear Norm based Matrix Regression with Applications to Face Recognition with Occlusion and Illumination Changes

摘要

Recently regression analysis becomes a popular tool for face recognition. Theexisting regression methods all use the one-dimensional pixel-based errormodel, which characterizes the representation error pixel by pixel individuallyand thus neglects the whole structure of the error image. We observe thatocclusion and illumination changes generally lead to a low-rank error image. Tomake use of this low-rank structural information, this paper presents atwo-dimensional image matrix based error model, i.e. matrix regression, forface representation and classification. Our model uses the minimal nuclear normof representation error image as a criterion, and the alternating directionmethod of multipliers method to calculate the regression coefficients. Comparedwith the current regression methods, the proposed Nuclear Norm based MatrixRegression (NMR) model is more robust for alleviating the effect ofillumination, and more intuitive and powerful for removing the structural noisecaused by occlusion. We experiment using four popular face image databases, theExtended Yale B database, the AR database, the Multi-PIE and the FRGC database.Experimental results demonstrate the performance advantage of NMR over thestate-of-the-art regression based face recognition methods.