Contents lists available at ScienceDirect Optik journal homepage: www.elsevier.com/locate/ijleo Original research article A robust blind color image watermarking based on Fourier transform domain Kahlessenane Fares, Khaldi Amine*, Euschi Salah Computer Science Department, Faculty of Sciences and Technology, Artificial Intelligence and Information Technology Laboratory (LINATI), University of Kasdi Merbah, 30000, Ouargla, Algeria ARTICLE INFO Keywords: Digital watermarking Color image watermarking Discrete Fourier transform Fractional Fourier transform Fractal dimension Quaternion discrete Fourier transform ABSTRACT In this work, we propose a new substitution scheme for color images watermarking based on the Fourier transform. This scheme will be declined into two variants in which the image will be divided into three components R, G and B, and then to each component a transform is applied. The parity of the resulting coefficients will then be combined to hide the watermark in the medium frequency band. In our experiments several variants of the Fourier transform are used (Discrete Fourier Transform, a Fractional Fourier Transform as well as a Quaternion Discrete Fourier Transform). For each transform, both variants of our watermarking scheme are applied. The obtained results show that our approach offers good imperceptibility and generates water- marking images robust against various attacks with a high-quality watermark. 1. Introduction Digital watermarking has become a significant discipline in the information processing community. Digital watermarking tech- niques have evolved to offer very sophisticated methods [1]. Many industry sectors have seen this new field as an innovative solution for securing digital documents. Digital watermarking consists of inserting an imperceptible mark into a document. This mark is a random sequence of bits, a binary logo, or a message, depending on the targeted application [2]. An effective watermarking system must guarantee the imperceptibility of the inserted data. The insertion of the watermark must not affect the visual quality of the image [3]. A watermarking system is also evaluated for its robustness. This criterion represents the resistance or not of the watermark after modifications undergone by attacks. Capacity is also an important measure to evaluate the effectiveness of a watermarking system [4], it represents the amount of information that can be inserted into the image, however, the larger the size of the watermark the greater the degradation. Depending on the area of insertion, the watermarking techniques proposed in the literature can be grouped into two classes [5]: those that operate in the spatial domain or those that operate in the transformed domain. In spatial domain technique, the mark is inserted by a direct modification of the pixels. Spatial methods allow inserting the mark directly into the image without any transformation [6]. The insertion will consist in working directly on the image by modifying the intensity of the pixels which will contain the mark [7]. These remain simple and inexpensive methods in computing time since they do not require a prior transformation. They are dedicated to real-time markings needed in environments of low computing power [8]. Many works have been proposed in the spatial domain image watermarking. Xiong proposed a two-stage watermarking scheme [9], vertical integration and then horizontal integration. In the horizontal direction, hiding is done by increasing the pixel values of the even lines https://doi.org/10.1016/j.ijleo.2020.164562 Received 6 February 2020; Received in revised form 9 March 2020; Accepted 12 March 2020 ⁎ Corresponding author. E-mail addresses: Kahlessnane.Fares@univ-ouargla.dz (K. Fares), Khaldi.amine@univ-ouargla.dz (K. Amine), Euchi.Salah@univ-ouargla.dz (E. Salah). Optik - International Journal for Light and Electron Optics 208 (2020) 164562 0030-4026/ © 2020 Elsevier GmbH. All rights reserved. T