The optimal scaling factor based on Secant Method for image watermarking using the hybrid DTCWT-DCT domain

Abstract

This paper proposes an implementation of the secant optimization method on the watermark embedding in DTCWT domain. An objective function combining PSNR and NC (The Normalized Correlation) values calculated for a set of common attacks is used in the optimization process. The aim is to enhance the tradeoff between robustness and imperceptibility against the various image processing attacks via an automatic and careful selection of the scaling factor using optimization. The watermark is inserted in the high energy bands of DCT-transformed sub-vectors, which were generated from the DTCWT coefficient decomposition of the host image. Experimental results performed on a set of 512×512 greyscale images, show better results than the existing schemes for most common image attacks such as compression, low-pass filtering and noise addition.

Keywords

• Watermarking
• DTCWT
• DCT
• Differential Method
• Newton’s Method
• Secant Method