Robust perceptual image hashing via matrix invariants

In this paper we suggest viewing images (as well as attacks oil them) as a sequence of linear operators and propose novel hashing algorithms employing transforms that are based oil matrix invariants. To derive this sequence. we simply cover a two dimensional representation of an image by a Sequence of (possibly overlapping) rectangles R-i whose sizes and locations are chosen randomly(1) from a Suitable distribution. The restriction of the image (representation) to each R-i gives rise to a matrix A(i). The fact that A(i)'s will overlap and are random. makes the sequence (respectively) a redundant and non-standard representation of images, but is crucial for our purposes. Our algorithms first construct a secondary image, derived from input image by pseudo-randomly extracting features that approximately capture semi-global geometric characteristics. From the secondary image (which does not perceptually resemble the input), we further extract the final features which call be used as a hash value (and call be further Suitably quantized). In this paper, We use spectral matrix invariants as embodied by Singular Value Decomposition. Surprisingly. formation of the secondary image turns Out he quite important since it not only introduces further robustness (i.e. resistance against standard signal processing transformations), but also enhances the Security properties (i.e. resistance against intentional attacks). Indeed, Our experiments reveal that our hashing algorithms extract most of the geometric information from the images and hence are robust to severe perturbations (e.g. up to %50 cropping by area with 20 degree rotations) on images while avoiding misclassification. Our methods are general enough to yield a watermark embedding scheme, which will be studied in another paper.