Nuclear Norm based Matrix Regression with Applications to Face Recognition with Occlusion and Illumination Changes (1405.1207v1)

Abstract: Recently regression analysis becomes a popular tool for face recognition. The existing regression methods all use the one-dimensional pixel-based error model, which characterizes the representation error pixel by pixel individually and thus neglects the whole structure of the error image. We observe that occlusion and illumination changes generally lead to a low-rank error image. To make use of this low-rank structural information, this paper presents a two-dimensional image matrix based error model, i.e. matrix regression, for face representation and classification. Our model uses the minimal nuclear norm of representation error image as a criterion, and the alternating direction method of multipliers method to calculate the regression coefficients. Compared with the current regression methods, the proposed Nuclear Norm based Matrix Regression (NMR) model is more robust for alleviating the effect of illumination, and more intuitive and powerful for removing the structural noise caused by occlusion. We experiment using four popular face image databases, the Extended Yale B database, the AR database, the Multi-PIE and the FRGC database. Experimental results demonstrate the performance advantage of NMR over the state-of-the-art regression based face recognition methods.

• The paper introduces a novel nuclear norm approach that captures the low-rank structure of error images for robust face recognition.
• It demonstrates improved handling of occlusions and illumination changes compared to traditional regression methods through ADMM optimization.
• Experimental evaluations across multiple face databases reveal that the NMR method outperforms state-of-the-art techniques in challenging conditions.

Nuclear Norm Based Matrix Regression for Face Recognition

The paper explores a novel approach to face recognition by leveraging the nuclear norm based matrix regression (NMR) to address challenges related to occlusion and illumination changes. Traditional regression analysis in face recognition has predominantly utilized one-dimensional pixel-based error models, which assess representation errors on a per-pixel basis. This method, however, overlooks the structural information inherent in error images, a limitation that becomes evident in situations involving occlusions or illumination variations. The authors propose a shift towards a more holistic, two-dimensional matrix-based error model to capture and utilize the low-rank structure of error images effectively.

Methodology

The proposed method, NMR, incorporates the minimal nuclear norm of the representation error image as a criterion for face representation and classification. The research utilizes the alternating direction method of multipliers (ADMM) for optimizing regression coefficients. This approach offers distinct advantages over traditional regression techniques such as Ridge regression and Lasso, which rely on the Euclidean norm and sparse representation, respectively. The authors argue that the nuclear norm is less sensitive to extreme illumination changes and more effective at handling the structural noise associated with occlusions.

Experimental Results

The paper reports extensive experiments conducted across four popular face image databases: Extended Yale B, AR, Multi-PIE, and FRGC databases. The results consistently demonstrate that the NMR model outperforms state-of-the-art regression-based face recognition methods under conditions of occlusion and varying illumination. For instance, in experiments with random occlusions, the NMR model maintained superior performance even when half of the image was occluded, underscoring its robustness and efficacy.

Key Findings

1. Robustness to Illumination: The nuclear norm's robustness against illumination changes is highlighted as a key advantage. Traditional regression methods, which measure representation errors using Euclidean distance, often falter under these conditions, whereas NMR maintains accuracy.
2. Handling of Occlusions: The authors demonstrate that occlusions lead to low-rank errors, which are effectively managed by NMR. This approach eliminates the need for extensive dictionaries required by sparse representation methods to handle occlusions.
3. Unified Framework: Unlike previous methods that separate error detection and error support into distinct processes, NMR offers a unified framework that accommodates both within a single model, requiring fewer parameters and simplifying the process.

Implications and Future Directions

The implications of this research are significant, as it suggests a more resilient and efficient way forward for face recognition systems, particularly in uncontrolled environments where occlusion and lighting variation are prevalent. As the authors note, although NMR is faster than many other robust regression techniques, computational efficiency remains a constraint for real-time applications. Future work could focus on enhancing the algorithm's speed through more streamlined optimization techniques or hardware acceleration.

Moreover, while the current model assumes low-rank structural noise, exploring other forms of noise might extend the model's applicability. The potential to incorporate additional constraints or priors into the regression framework could further enhance its robustness and adaptability across diverse recognition tasks.

In summary, the nuclear norm based matrix regression offers a promising advancement in the field of face recognition, particularly in scenarios with significant occlusion and illumination variations. The method's robust performance and theoretical grounding suggest that NMR could be a valuable tool in the development of more reliable and accurate biometric systems.