Geometrically invariant image watermarking using Polar Harmonic Transforms Leida Li a,⇑ , Shushang Li a , Ajith Abraham b , Jeng-Shyang Pan c a School of Information and Electrical Engineering, China University of Mining and Technology, Xuzhou 221116, China b Machine Intelligence Research Labs, Scientific Network for Innovation and Research Excellence, Auburn, WA 98071-2259, USA c Department of Electronic Engineering, National Kaohsiung University of Applied Sciences, Kaohsiung 807, Taiwan article info Article history: Received 31 January 2011 Received in revised form 24 December 2011 Accepted 26 February 2012 Available online 8 March 2012 Keywords: Digital watermark Invariant moment Polar Harmonic Transform abstract This paper presents an invariant image watermarking scheme by introducing the Polar Harmonic Transform (PHT), which is a recently developed orthogonal moment method. Similar to Zernike moment (ZM) and pseudo-Zernike moment (PZM) approaches, PHT is defined on a circular domain. The magnitudes of PHTs are invariant to image rotation and scaling. Furthermore, the PHTs are free of numerical instability, so they are more suit- able for watermarking. In this paper, the invariant properties of PHTs are investigated. Dur- ing embedding, a subset of the accurate PHTs are modified according to the binary watermark sequence. Then a compensation image is formatted by reconstructing the mod- ified PHT vector. The final watermarked image is obtained by adding the compensation image to the original image. In the decoder, the watermark can be retrieved from the mag- nitudes of the PHTs directly. Experimental results illustrate that the proposed scheme out- performs ZM/PZM based schemes in terms of embedding capacity and watermark robustness and is also robust to both geometric and signal processing based attacks. Ó 2012 Elsevier Inc. All rights reserved. 1. Introduction Information hiding plays an important role in multimedia content protection. During the past few years, several informa- tion hiding techniques have been investigated extensively and great achievements have been obtained, including robust watermarking [15,22], fragile watermarking [6], reversible watermarking [7,34] and steganography [19,33]. This paper fo- cuses on robust watermarking. A good watermarking scheme should be able to retrieve the watermark even when the image is attacked by geometric distortions, such as image rotation and scaling. In order to achieve this goal, extensive research has been done, which can be grouped into the following three categories [24,40]: (1) Inverse transform. The idea is to transform the distorted image into a form, which has the same size and orientation with the original image. The watermark is then detected from the aligned image. Extensive search and template based methods belong to this category [23,27]. In practice, extensive search based methods are computationally expensive, and template based embedding is subject to template re- moval attacks. (2) Feature based embedding. The basic principle is to associate the watermark signal with image features. While the salient image features are invariant to geometric distortions, invariance of the watermark is achieved. This method has been addressed extensively these years [18,22,29]. The robustness of this kind of method depends on the invariance of the image features. Watermark capacity is often limited, because the watermark is embedded into the feature based on local regions. (3) Invariant domain embedding. The image is first processed to form a representation invariant to the general 0020-0255/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.ins.2012.02.062 ⇑ Corresponding author. Tel.: +86 150 0520 3739. E-mail address: reader1104@hotmail.com (L. Li). Information Sciences 199 (2012) 1–19 Contents lists available at SciVerse ScienceDirect Information Sciences journal homepage: www.elsevier.com/locate/ins