Quaternion Collaborative and Sparse Representation With Application to Color Face Recognition.

Area of Science:

• Computer Vision
• Pattern Recognition
• Signal Processing

Background:

• Collaborative Representation-based Classification (CRC) and Sparse Representation-based Classification (SRC) are successful in grayscale face recognition (FR).
• Existing CRC and SRC methods treat color channels independently, neglecting inter-channel correlations crucial for color image analysis.
• This limitation hinders their performance in color face recognition tasks.

Purpose of the Study:

• To propose novel quaternion-based methods, quaternion CRC (QCRC) and quaternion SRC (QSRC), for improved color face recognition.
• To address the limitations of existing methods by preserving the structural correlation among color channels.
• To provide theoretical guarantees for the effectiveness of the proposed QCRC and QSRC methods.

Main Methods:

• Modeling color images as quaternionic signals to naturally preserve color structures.
• Utilizing quaternion ℓ1 minimization for holistic coding of query channel images.
• Developing theoretical guarantees for the proposed QCRC and QSRC algorithms under mild conditions.

Main Results:

• The proposed QCRC and QSRC methods demonstrate superior performance compared to competing methods on benchmark color face recognition databases.
• The quaternion approach effectively preserves and utilizes the structural information within color channels.
• Consistent superiority was observed in both color face recognition and image reconstruction tasks.

Conclusions:

• Quaternion-based representation methods offer a significant advancement for color face recognition.
• QCRC and QSRC provide a robust framework that accounts for color image structure, leading to enhanced recognition accuracy.
• The theoretical guarantees further validate the effectiveness and reliability of the proposed quaternion methods.