Robust image hashing based on radial variance of pixels

Robust image hashing defines a feature vector that characterizes the image, independently of non-significant distortions of its content. As a consequence, the comparison between robust image hash vectors is able to indicate whether the corresponding images are equivalent or not, independently of visually non-significant distortions due for example to compression or re-sampling. We define a robust image hash based on radial projections of the image pixels. Specifically, our proposed radial hASH (RASH) considers moments of different orders to describe the luminance pdf of the pixels encountered on a set of lines articulated around the center of the image. In short, each RASH component is defined based on the moment of the pixels belonging to a specific line. Our paper provides a careful analysis of the robustness and discriminating capabilities of the RASH vectors computed based on different moment orders. As a first contribution, it demonstrates that the second order moment, i.e. the variance of the pixels on a line, allows for optimal trade-offs between the robustness and the discriminating capabilities of the resulting RASH vector. As a second contribution, extensive simulations prove that a decision engine based on RASH vectors cross-correlations is able to successfully identify pairs of equivalent or distinct images. Bottom line, the RASH assets are a low computational complexity, a strong robustness to both filtering and geometrical distortions, and a risk of collision that is estimated to less than 10 per million of images.