Robust and Secure Image Hashing via Non-Negative Matrix Factorizations

In this paper, we propose the use of non-negative matrix factorization (NMF) for image hashing. In particular, we view images as matrices and the goal of hashing as a randomized dimensionality reduction that retains the essence of the original image matrix while preventing intentional attacks of guessing and forgery. Our work is motivated by the fact that standard-rank reduction techniques, such as QR and singular value decomposition, produce low-rank bases which do not respect the structure (i.e., non-negativity for images) of the original data. We observe that NMFs have two very desirable properties for secure image hashing applications: 1) The additivity property resulting from the non-negativity constraints results in bases that capture local components of the image, thereby significantly reducing misclassification and 2) the effect of geometric attacks on images in the spatial domain manifests (approximately) as independent identically distributed noise on NMF vectors, allowing the design of detectors that are both computationally simple and, at the same time, optimal in the sense of minimizing error probabilities. Receiver operating characteristics analysis over a large image database reveals that the proposed algorithms significantly outperform existing approaches for image hashing.