Robust perceptual color image hashing using randomized hypercomplex matrix factorizations

Compact representations of color image and video content allow efficient search, retrieval and storage of this content over the Internet and online repositories. However, most of these representations neither take into account the inherent correlation nor the perceptual redundancy of the color information. In this paper, we propose a perceptual hash representation for color images using robust image features. These features, most dominant singular vectors extracted using the quaternion singular value decomposition (QSVD) of pseudorandomly selected overlapping image blocks, are efficiently used for color image search and retrieval applications. Their robustness is guaranteed by the underlying singular vectors. The motivation behind our work is twofold: 1) the ability of the QSVD algorithm to provide the best low-rank approximation of color images in the Frobenius norm sense and 2) compact representations to handle the color components as a single entity. The QSVD algorithm leads to proper modeling of possible geometric attacks as an independent and identically-distributed (i.i.d) quaternionic random noise on the singular vectors. Such modeling simplifies the hash code detector design. Hash code robustness against geometric attacks is evaluated over a large set of test color images where the proposed scheme outperforms existing factorization-based hashing algorithms in terms of lower miss and false alarm probabilities by orders of magnitude. Finally, the improved robustness and performance does not come at the expense of increased computational complexity which is another salient feature of the proposed hashing scheme.