基于特征化字典的低秩表示人脸识别

Characterized dictionary-based low-rank representation for face recognition

针对现有低秩表示（LRR）算法中全局与局部人脸特征信息融合不足的问题，提出了一种新的人脸识别算法——基于特征化字典的低秩表示（LRR-CD）。首先，将每张人脸照片表示成一个个特征化字典的集合，然后同时最小化基于训练样本的低秩重构特征系数以及与之相对应的类内特征差异。为了获得高效且具有高判别性的人脸图像的特征块重构系数矩阵，提出了一种新的数学公式模型，通过同时求解训练样本中相对应的特征块以及对应的类内特征差异词典的低秩约束问题，尽可能完整地保留原始高维人脸图像中的全局和局部信息，尤其是局部类内差异特征。另外，由于对特征块中信息的充分挖掘，所提算法对于一般程度上的面部遮挡和光照等噪声影响具有良好的鲁棒性。在AR、CMU-PIE和ExtendedYaleB人脸数据库进行多项对比实验，由实验结果可知LRR-CD相较于对比的稀疏表示（SRC）、协从表示（CRC）、低秩表示正规切（LRR-NCUT）和低秩递归最小二乘（LRR-RLS）算法在平均识别率上有2．58—17．24个百分点的提高。实验结果表明LRR-CD性能优于与之对比的算法，可以更高效地用于人脸全局和局部特征信息的融合，且具有优良的识别率。

The existing Low-rank representation methods for face recognition fuse of local and global feature information of facial images inadequately. In order to solve the problem, a new face recognition method called Characterized Dictionary-based Low-Rank Representation （LRR-CD） was proposed. Firstly, every face image was represented as a set of characterized patches, then the low-rank reconstruction characteristic coefficients based on training samples as well as the corresponding intra-class characteristic variance were minimized. To obtain the efficient and high discriminative reconstruction coefficient matrix of face image patches, a new mathematical formula was presented. This formula could be used to completely preserve both global and local features of original hyper-dimensional face images, especially the local intra-class variance features, by the way of minimizing the low-rank constraint problem of corresponding patches in training samples and correlated intra-class variance dictionary. What＇s more, owing to the adequate mining of patch features, the proposed method obtained good robustness to the general noise such as facial occlusion and luminance variance. Several experiments were carried out on the face databases such as AR, CMU-PIE and Extended Yale B. The experimental results fully illustrate that the LRR-CD outperforms the compared algorithms of Sparse Representation Classification （SRC）, Collaborative Representation Classification （CRC）, LRR with Normalized CUT （LRR-NCUT） and LRR with Recursive Least Square （ LRR-RLS）, with the higher recognition rate of 2.58 - 17.24 percentage points. The proposed method can be effectively used for the global and local information fusion of facial features and obtains a good recognition rate.