四元数
数学
人工智能
主成分分析
规范(哲学)
标量(数学)
模式识别(心理学)
彩色图像
面部识别系统
算法
计算机视觉
计算机科学
图像处理
应用数学
图像(数学)
几何学
政治学
法学
作者
Wankai Liu,Kit Ian Kou,Jifei Miao,Zhenning Cai
出处
期刊:IEEE transactions on image processing
[Institute of Electrical and Electronics Engineers]
日期:2023-01-01
卷期号:32: 446-457
被引量:3
标识
DOI:10.1109/tip.2022.3229616
摘要
This paper proposes a decomposition called quaternion scalar and vector norm decomposition (QSVND) for approximation problems in color image processing. Different from traditional quaternion norm approximations that are always the single objective models (SOM), QSVND is adopted to transform the SOM into the bi-objective model (BOM). Furthermore, regularization is used to solve the BOM problem as a common scalarization method, which converts the BOM into a more reasonable SOM. This can handle over-fitting or under-fitting problems neglected in this kind of research for quaternion representation (QR) in color image processing. That is how to treat redundancy caused by the extra scalar part when the vector part of a quaternion is used to represent a color pixel. We apply QSVND to quaternion principal component analysis (QPCA) for color face recognition (FR), which can deal with the phenomenon of under-fitting of vector part norm approximation. Comparisons with the competing approaches on AR, FERET, FEI, and KDEF&AKDEF databases consistently show the superiority of the proposed approach for color FR.
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