IEEE Trans Pattern Anal Mach Intell. 2017 Jan;39(1):156-171. doi: 10.1109/TPAMI.2016.2535218. Epub 2016 Feb 26.
Recently, regression analysis has become a popular tool for face recognition. Most existing regression methods use the one-dimensional, pixel-based error model, which characterizes the representation error individually, pixel by pixel, and thus neglects the two-dimensional structure of the error image. We observe that occlusion and illumination changes generally lead, approximately, to a low-rank error image. In order to make use of this low-rank structural information, this paper presents a two-dimensional image-matrix-based error model, namely, nuclear norm based matrix regression (NMR), for face representation and classification. NMR uses the minimal nuclear norm of representation error image as a criterion, and the alternating direction method of multipliers (ADMM) to calculate the regression coefficients. We further develop a fast ADMM algorithm to solve the approximate NMR model and show it has a quadratic rate of convergence. We experiment using five popular face image databases: the Extended Yale B, AR, EURECOM, Multi-PIE and FRGC. Experimental results demonstrate the performance advantage of NMR over the state-of-the-art regression-based methods for face recognition in the presence of occlusion and illumination variations.
最近，回归分析已成为人脸识别的一种流行工具。大多数现有的回归方法都使用基于一维像素的误差模型，该模型逐像素地描述表示误差，因此忽略了误差图像的二维结构。我们观察到遮挡和光照变化通常会导致低秩误差图像。为了利用这种低秩结构信息，本文提出了一种基于二维图像矩阵的误差模型，即基于核范数的矩阵回归（NMR），用于人脸表示和分类。NMR 使用表示误差图像的最小核范数作为准则，并使用增广拉格朗日乘子法（ADMM）计算回归系数。我们进一步开发了一种快速 ADMM 算法来求解近似 NMR 模型，并表明它具有二次收敛速度。我们在五个流行的人脸图像数据库上进行实验：Extended Yale B、AR、EURECOM、Multi-PIE 和 FRGC。实验结果表明，在存在遮挡和光照变化的情况下，NMR 比基于回归的最新方法在人脸识别方面具有性能优势。
