Robust perceptual color image hashing using quaternion singular value decomposition
Lahouari Ghouti · 2014
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.