KEYWORDS: Digital watermarking, Quantization, Computer programming, RGB color model, Binary data, Image processing, Data hiding, Signal processing, Digital filtering, Image compression
In this paper, we present a non-linear method of embedding a signature in colour and monochrome images and demonstrate its recovery. The embedding process can be viewed as pseudo-random perturbations to angles between vector elements. The derived angles are dithered by the addition of a watermark, and encoded as a pseudo-noise sequence of dither angle offsets. This is followed by a re-quantisation for storage or transmission. The dither angles are recovered by scaling according to the pre-determined angle quantisation intervals. These intervals may be fixed according to some pattern, or they could be obtained adaptively from the local image. Performing a complex correlation with the known sequence enables recovery of sub-degree dither angles embedded in 8-bit data. This occurs without recourse to the original image. This embedding process is additive in the angular domain and therefore multiplicative in the signal domain. Since the magnitude of the image vector is conserved, the image energy is largely unaltered by the embedding process. Colour watermarks can be treated as sets of ordered triples (RGB), as pixel pairs in spatial or YIQ/YCbCr colour domain, or in a transform domain.
KEYWORDS: Digital watermarking, Digital signal processing, Binary data, Composites, Phase shifts, Steganography, Information security, Fourier transforms, Optical correlators, Image registration
Watermark recovery is often based on cross-correlating images with pseudo-noise sequences, as access to un-watermarked originals is not required. Successful recovery of these watermarks is determined by the (periodic or aperiodic) sequence auto- and cross-correlation properties. This paper presents several methods of extending the dimensionality of 1D sequences in order to utilize the advantages that this offers. A new type of 2D array construction is described, which meets the above requirements. They are constructed from 1D sequences that have good auto-correlation properties by appending rows of cyclic shifts of the original sequence. The sequence values, formed from the roots of unity, offer additional diversity and security over binary arrays. A family of such arrays is described which have low cross-correlation and can be folded and unfolded, rendering them robust to cryptographic attack. Row and column products of 1D Legendre sequences can also produce equally useful 2D arrays (with interesting properties resulting from the Fourier invariance of Legendre sequences). A metric to characterize all these 2D correlation based watermarks is proposed.
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