Robust image hashing by downsampling: Between mean and median

The arithmetic mean and the non-linear median operation, provide two slightly different abstractions of any discrete dataset. The differential information contained in these two filtering operations reveal several trends in the processed data. This principle has been applied towards the process of deriving robust binary PINs from gray-scale images by first extracting pseudo-images by random rectangular downsampling of a parent image, fusing them with a median operation and then mean thresholding the filtered set. Robustness against recompression, noise and most importantly geometric operations, stems from two factors: (a) the random sampling which provides elasticity and (b) the process of selecting the PIN-thresholds as the arithmetic mean filtered set.