Generalized Two-Dimensional Quaternion Principal Component Analysis with Weighting for Color Image Recognition

TL;DR

This paper introduces a generalized weighted 2D quaternion PCA method that enhances color image recognition by extracting geometric and color features, improving robustness to noise and outperforming existing algorithms.

Contribution

It proposes a flexible 2DQPCA framework with $L_{p}$ norms and weighting, enabling adaptive feature extraction and improved recognition accuracy.

Findings

Robustness to noise demonstrated on real face databases.

Outperforms state-of-the-art 2DQPCA algorithms.

Surpasses four prominent deep learning methods in recognition tasks.

Abstract

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.