Soft Computing

, Volume 22, Issue 7, pp 2369–2379 | Cite as

A new image watermarking technique based on periodic plus smooth decomposition (PPSD)

  • N. Aherrahrou
  • H. Tairi
Methodologies and Application


Robustness against geometric distortion is one of the crucial important issues in watermarking. The discrete Fourier transform (DFT)-based watermarking methods have been proposed to address this issue. However, the effect of the well-known “periodization artifact” caused by the DFT transform limits their application. In this paper, a novel watermarking scheme is proposed. This scheme is based on the periodic plus smooth image decomposition (PPSD). The PPSD is a simple and efficient way to deal with periodization artifacts arising from the use of the DFT transform on 2-D images. It consists in the decomposition of the discrete image into a periodic component that gathers most of the image information but avoids periodization artifacts, and a smooth (harmonic) component that presents very slow variations inside the image. The algorithm is evaluated in terms of imperceptibility and robustness. The experiments indicate that our developed PPSD technique can achieve high imperceptibility while showing good robustness to various kinds of attacks, including geometrical distortions.


Watermarking PPSD DFT Periodization artifact Smooth component Periodic component 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no competing interests.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of InformaticsUniversity Sidi Mohamed Ben AbdellahFezMorocco

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