Hybrid second-order gradient histogram based global low-rank sparse regression for robust face recognition

TL;DR

The paper tackles robust face recognition under occlusion and illumination by introducing a Hybrid second-order gradient histogram (H2H) descriptor that fuses first- and second-order gradient information. This descriptor is integrated into a Sparse Regression framework with a global low-rank constraint on the residuals (H2H-GLRSR), enabling joint modeling of cross-sample structured noise. An ADMM-based optimization strategy yields a fast solution, with complexity dominated by a single SVD per iteration and a precomputed inverse, resulting in substantial speedups over prior methods. Empirical results on AR, Extended Yale B, and LFW show state-of-the-art accuracy and notable computational efficiency, highlighting practical potential for real-world, occlusion-robust face recognition tasks. The work advances both feature representation for structural cues and global residual regularization, with clear implications for robust recognition in challenging environments.

Abstract

Low-rank sparse regression models have been widely adopted in face recognition due to their robustness against occlusion and illumination variations. However, existing methods often suffer from insufficient feature representation and limited modeling of structured corruption across samples. To address these issues, this paper proposes a Hybrid second-order gradient Histogram based Global Low-Rank Sparse Regression (H2H-GLRSR) model. First, we propose the Histogram of Oriented Hessian (HOH) to capture second-order geometric characteristics such as curvature and ridge patterns. By fusing HOH and first-order gradient histograms, we construct a unified local descriptor, termed the Hybrid second-order gradient Histogram (H2H), which enhances structural discriminability under challenging conditions. Subsequently, the H2H features are incorporated into an extended version of the Sparse Regularized Nuclear Norm based Matrix Regression (SR\_NMR) model, where a global low-rank constraint is imposed on the residual matrix to exploit cross-sample correlations in structured noise. The resulting H2H-GLRSR model achieves superior discrimination and robustness. Experimental results on benchmark datasets demonstrate that the proposed method significantly outperforms state-of-the-art regression-based classifiers in both recognition accuracy and computational efficiency.

Figures (7)

• Figure 1: Flowchart for constructing H2H feature descriptors
• Figure 2: Some sample images of one person from the AR database
• Figure 3: Sample images with illumination changes collected from Subset 4 and Subset 5 of Extended Yale B. First row: Subset 4, Second row: Subset 5.
• Figure 4: Some sample images of one person from the LFW database
• Figure 5: Recognition rates (%) with different parameters on the AR dataset