Color image watermarking using quaternion Fourier transform

Abstract

This paper presents a digital color image watermarking scheme using the hypercomplex numbers representation and the Quaternion Fourier Transform (QFT). Previous color image watermarking methods are first presented and the quaternion representation is then described. In this framework RGB pixel values are associated with an unique quaternion number having three imaginary parts. The QFT is presented, this transform depends on an arbitrary unit pure quaternion. The value of is selected to provide embedding spaces having robustness and/or perceptual properties. In the presented approach is function of the mean color value of a block and a perceptual component. A watermarking scheme based on the QFT and the Quantization Index Modulation scheme is afterwards presented. This scheme is finally evaluated for different color image filtering process (JPEG, blur) and the fact that perceptive QFT embedding can offer robustness to luminance filtering techniques is outlined.

Robust watermarking scheme based on the JPEG2000 standard

“…[22] extends the Lab space to the S-CIELAB decomposition which includes the spatial structure of the image. A more recent result can be found in [23], where a quaternion (hypercomplex) representation is used to model the RGB space, and then the quaternion Fourier transform is applied to embed the mark in the transformed domain.…”

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“…Watermarks have been used on postage stamps, currency, and other government documents to discourage counterfeiting. The process of hiding digital information in a carrier signal is known as "Watermarking" [9] . Traditional watermarks may be applied to visible media (like images or video), whereas in digital watermarking, the signal may be audio, pictures, video, texts or 3D models.…”

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“…Quaternions have found applications in computer graphics, for the modelling of three-dimensional (3-D) rotations [6], in robotics [7], molecular modelling [8], processing colour images [9], hyper-complex digital filters [10], texture segmentation [11], source separation [12], watermarking [13], spectrum estimation [14] quaternion singular value decomposition and in the MUSIC algorithm to process polarized waves [15], [16], quaternion least squares [8], [17], and quaternion singular spectrum analysis [18]. In [4] the formulation for a quaternion LMS adaptive filtering has also been provided and used for the processing of quaternion valued signals.…”