Fresnel transform of images for application to watermarking

Abstract

AbstractThe Fresnel transform describes the diffraction phenomena of the waves and is used for simulation of diffraction phenomena. From the relationship to simulation of wave diffraction, it is found necessary to investigate various conditions when Fresnel transform is carried out numerically to apply to electronic watermarking. Difference in the numerical Fresnel transformation between the simulation of the wave diffraction phenomena and the application to electronic watermarking is studied by using the numerical simulation results of Fresnel transformation by the convolution method and the spectrum method. Further, an example is presented for an application of Fresnel transform to electronic watermarking by the convolution method. Characteristics of the electronic watermarking using Fresnel transform are discussed. It is discussed how the image compression of the wavelet transform can affect the electronic watermarking by Fresnel transform. Quantitative evaluation of the image quality of noted images extracted with PSNR is carried out. Further, it is studied when Fresnel transform method is effective for the cropping attack extracting a portion of the image. © 2001 Scripta Technica, Electron Comm Jpn Pt 3, 84(12): 48–58, 2001