Data-Driven Bilateral Generalized Two-Dimensional Quaternion Principal Component Analysis with Application to Color Face Recognition

TL;DR

This paper introduces BiG2DQPCA, a novel method for extracting features from color images directly in 2D, enhancing face recognition and image reconstruction by preserving spatial and color information.

Contribution

It proposes a new data-driven bilateral quaternion PCA framework with an efficient optimization algorithm, directly working on 2D color images without vectorization.

Findings

Outperforms state-of-the-art methods in recognition accuracy

Achieves higher image reconstruction quality

Demonstrates effectiveness on real-world color face databases

Abstract

A new data-driven bilateral generalized two-dimensional quaternion principal component analysis (BiG2DQPCA) is presented to extract the features of matrix samples from both row and column directions. This general framework directly works on the 2D color images without vectorizing and well preserves the spatial and color information, which makes it flexible to fit various real-world applications. A generalized ridge regression model of BiG2DQPCA is firstly proposed with orthogonality constrains on aimed features. Applying the deflation technique and the framework of minorization-maximization, a new quaternion optimization algorithm is proposed to compute the optimal features of BiG2DQPCA and a closed-form solution is obtained at each iteration. A new approach based on BiG2DQPCA is presented for color face recognition and image reconstruction with a new data-driven weighting technique. Sufficient numerical experiments are implemented on practical color face databases and indicate the superiority of BiG2DQPCA over the state-of-the-art methods in terms of recognition accuracies and rates of image reconstruction.