Image Fragile Watermarking through Quaternion Linear Transform in Secret Space

Abstract

In this paper, we apply the quaternion framework for color images to a fragile watermarking algorithm with the objective of multimedia integrity protection (Quaternion Karhunen-Loève Transform Fragile Watermarking (QKLT-FW)). The use of quaternions to represent pixels allows to consider the color information in a holistic and integrated fashion. We stress out that, by taking advantage of the host image quaternion representation, we extract complex features that are able to improve the embedding and verification of fragile watermarks. The algorithm, based on the Quaternion Karhunen-Loève Transform (QKLT), embeds a binary watermark into some QKLT coefficients representing a host image in a secret frequency space: the QKLT basis images are computed from a secret color image used as a symmetric key. A computational intelligence technique (i.e., genetic algorithm) is employed to modify the host image pixels in such a way that the watermark is contained in the protected image. The sensitivity to image modifications is then tested, showing very good performance.

Keywords

• data hiding
• fragile watermarking
• image authentication
• color image processing
• quaternions
• genetic algorithm (GA)
• Karhunen-Loève Transform (KLT)