Robust Perceptual Color Image Hashing Using Quaternion Singular Value Decomposition

Perceptual hashing provides compact and efficient representations for image retrieval, authentication and tamper detection applications. However, most of existing perceptual hashing algorithms are designed for gray-level images and, therefore, color correlation and interaction are simply ignored. In this paper, we propose a novel perceptual hashing for color images using the quaternion singular value decomposition (Q-SVD). In this algorithm, color images are processed through randomized dimensionality reduction which results in secure and robust hashing codes. The motivation behind our work is twofold: 1) a compact representation of color images where the red, green and blue (RGB) components are handled as a single entity using hypercomplex representations and 2) the ability of Q-SVD decomposition to provide the best low-rank approximation of quaternion matrices in the sense of Frobenius norm. Possible geometric attacks are properly modeled as an independent and identically-distributed hypercomplex noise on the singular vectors. Such modeling simplifies the hash code detector design. Finally, the hashing robustness against geometric attacks is evaluated over a large set of standard test images using the receiver operating characteristics analysis. The proposed scheme outperforms SVD-based hashing algorithms in terms of lower miss and false alarm probabilities by orders of magnitude.