Nuclear Norm Based Matrix Regression with Applications to Face Recognition with Occlusion and Illumination Changes

Area of Science:

• Computer Vision
• Machine Learning
• Pattern Recognition

Background:

• Regression analysis is widely used for face recognition.
• Existing methods often use 1D, pixel-based error models, ignoring 2D error structures.
• Occlusion and illumination changes typically result in low-rank error images.

Purpose of the Study:

• Introduce a novel 2D image-matrix-based error model for face recognition.
• Develop Nuclear Norm based Matrix Regression (NMR) to leverage low-rank error information.
• Enhance face representation and classification accuracy under challenging conditions.

Main Methods:

• Proposed Nuclear Norm based Matrix Regression (NMR) using a minimal nuclear norm criterion.
• Employed the Alternating Direction Method of Multipliers (ADMM) to compute regression coefficients.
• Developed a fast ADMM algorithm for the approximate NMR model, demonstrating quadratic convergence.

Main Results:

• NMR effectively utilizes the 2D structure of error images.
• Experimental results on five benchmark datasets (Extended Yale B, AR, EURECOM, Multi-PIE, FRGC) show significant performance gains.
• NMR outperforms state-of-the-art regression-based methods, particularly under occlusion and illumination variations.

Conclusions:

• The proposed NMR method offers a superior approach to face recognition compared to traditional 1D methods.
• NMR's 2D error model is robust to common image degradations like occlusion and illumination changes.
• This work advances regression-based face recognition techniques by incorporating matrix structural information.