Abstract
Families of 2D arrays can be constructed where each array has perfect autocorrelation, and the cross-correlation between any pair of family members is optimally low. We exploit equivalent Hadamard matrices to construct many families of p p × p arrays, where p is any 4k-1 prime. From these families, we assemble extended families of arrays with members that exhibit perfect autocorrelation and next-to-optimally low cross-correlation. Pseudo-Hadamard matrices are used to construct extended families using p = 4k + 1 primes. An optimal family of 31 31 × 31 perfect arrays can provide copyright protection to uniquely stamp a robust, low-visibility watermark within every frame of each second of high-definition, 30 fps video. The extended families permit the embedding of many more perfect watermarks that have next-to-minimal cross-correlations.
Highlights
A digital watermark is a kind of marker covertly embedded in a noise-tolerant signal such as an audio, video or image data
Families of 2D arrays with low off-peak autocorrelation and low crosscorrelation are useful in digital watermarking to identify the owner of an image, or to embed multiple arrays in an image to increase the amount of hidden information in the watermark
We show that a family of arrays with low cross-correlation between matching array projections must be maximally different in the Hadamard sense
Summary
A digital watermark is a kind of marker covertly embedded in a noise-tolerant signal such as an audio, video or image data. The cross-correlation between watermarking arrays embedded in different frames is the lowest possible. This permits the embedding of more arrays in a single frame to increase data payload or to satisfy the watermark duration requirements. We partition a p × p array into p + 1 projections and assign +1 or −1 values to these projections according to rows of a commensurate Hadamard matrix Such arrays are ideally suited to image and video watermarking, and we show how they can be adapted to greyscale and extended to larger families.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
