Robust zero-watermarking algorithm based on polar complex exponential transform and logistic mapping

Abstract

This paper introduces a new zero-watermarking algorithm based on polar complex exponential transform (PCET) and logistic mapping. This algorithm takes advantage of the geometric invariance of PCET to improve the robustness of the algorithm against geometric attacks, and the logistic mapping’s sensitivity to initial values to improve the security of the algorithm. First, the algorithm computes the PCET of the original grayscale image. Then it randomly selects PCET coefficients based on logistic mapping, and computes their magnitudes to obtain a binary feature image. Finally, it performs an exclusive-or operation between the binary feature image and the scrambled logo image to obtain the zero-watermark image. At the stage of copyright verification, the image copyright can be determined by performing the exclusive-or operation between the feature image and the verification image and comparing the resulting image to the original logo image. Experimental results show that this algorithm has excellent robustness against geometric attacks and common image processing attacks and better performance compared to other zero-watermarking algorithms.