Soft Computing

, Volume 22, Issue 12, pp 4083–4098 | Cite as

A predictive model-based image watermarking scheme using Regression Tree and Firefly algorithm

  • Behnam Kazemivash
  • Mohsen Ebrahimi MoghaddamEmail author
Methodologies and Application


Digital image watermarking has a great importance in the image security nowadays. In this paper, we have proposed a novel robust image watermarking scheme based on combining Regression Tree as a predictive model and Firefly algorithm as a flexible optimization algorithm. In the proposed scheme, Lifting Wavelet Transform as a strong transform domain is employed to separate the host image into four sub-bands and the low frequency sub-band is used to produce non-overlapping blocks. Then, we sort the blocks in ascending order due to the block’s standard derivation. Primary required blocks (owing to the size of watermark image) are used for embedding process, and others used for making Regression Tree. Firefly algorithm is used to optimize multi-scaling factor according to its significant influence in imperceptibility and robustness. For satisfying security aspects, Fibonacci-Q transform is applied to watermark and the bits of resulted scrambled image participated in embedding process. To evaluate the proposed method, it has been investigated by various image processing operations and due to standard metrics, the experimental results are satisfactory.


Image watermarking Regression Tree Firefly algorithm Lifting wavelet transform Fibonacci-Q transform 


Compliance with Ethical Standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Faculty of Computer Science and EngineeringShahid Beheshti UniversityTehranIran

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