One of the most powerful methods of color image recognition is the two-dimensional principle component analysis (2DQPCA) approach, which is based on quaternion representation and preserves color information very well. However, the current versions of 2DQPCA are still not feasible to extract different geometric properties of color images according to practical data analysis requirements and they are vulnerable to strong noise. In this paper, a generalized 2DQPCA approach with weighting is presented with imposing $L_{p}$ norms on both constraint and objective functions. As a unit 2DQPCA framework, this new version makes it possible to choose adaptive regularizations and constraints according to actual applications and can extract both geometric properties and color information of color images. The projection vectors generated by the deflating scheme are required to be orthogonal to each other. A weighting matrix is defined to magnify the effect of main features. This overcomes the shortcomings of traditional 2DQPCA that the recognition rate decreases as the number of principal components increases. The numerical results based on the real face databases validate that the newly proposed method is robust to noise and performs better than the state-of-the-art 2DQPCA-based algorithms and four prominent deep learning methods.

翻译：彩色图像识别最有效的方法之一是基于四元数表示的二维主成分分析（2DQPCA）方法，该方法能够很好地保留颜色信息。然而，当前版本的2DQPCA仍无法根据实际数据分析需求提取彩色图像的不同几何特征，且易受强噪声干扰。本文提出一种带加权的广义二维四元数主成分分析方法，通过对约束函数和目标函数施加$L_{p}$范数。作为统一的2DQPCA框架，该新版本可根据实际应用选择自适应正则化项和约束条件，能够同时提取彩色图像的几何特征和颜色信息。通过紧缩方案生成的投影向量需相互正交。本文定义了加权矩阵以放大主要特征的影响，克服了传统2DQPCA方法中识别率随主成分数量增加而下降的缺陷。基于真实人脸数据库的数值结果表明，所提方法对噪声具有鲁棒性，其性能优于当前最先进的基于2DQPCA的算法及四种主流深度学习方法。