ANGLE QIM: A NOVEL WATERMARK EMBEDDING SCHEME ROBUST AGAINST AMPLITUDE SCALING DISTORTIONS Fabr´ ıcio Ourique, Vinicius Licks, Ramiro Jordan The University of New Mexico Electrical & Computer Engineering Dept Albuquerque, USA, 87106 fourique,vlicks,rjordan@ece.unm.edu Fernando P´ erez-Gonz´ alez University of Vigo Dept. Teor´ ıa de la Se ˜ nal y Comunicaciones, Vigo, Spain, 36200 fperez@tsc.uvigo.es ABSTRACT Quantization index modulation (QIM) watermarking has re- ceived a great deal of attention ever since the rediscovery of Costa’s result on codes with host-interference rejecting properties. While such embedding scheme exhibit consid- erable improvement in watermark capacity over its earlier predecessors, (e.g. spread-spectrum), their fragility to even the simplest attacks soon became apparent. Among such at- tacks, amplitude scaling has received special attention. In this paper, we introduce a quantization scheme that is prov- ably insensitive to amplitude scaling attacks, named Angle QIM (AQIM). Instead of embedding information by quan- tizing the amplitude of pixel values, AQIM works by quan- tizing the angle formed by the host-signal vector with the origin of a hyperspherical coordinate system. Hence, AQIM’s invariance to amplitude scaling can be shown by construc- tion. Experimental results are presented for the bit error rate performance of AQIM under additive white Gaussian noise attacks. 1. INTRODUCTION The rediscovery of Costa’s original results on dirty paper codes by Chen and Wornell, in 1999, marked the beginning of a new stage in watermarking research [1, 2]. The idea of using host-signal state information at the encoder side in order to guarantee host-interference rejection influenced the creation of embedding schemes based on the quantization of the original image, namely quantization index modula- tion (QIM) methods. In these schemes, the amplitudes of one single pixel or of a vector of pixels are quantized using one of a series of quantization lattices, chosen accordingly to the symbol to be embedded. While such methods ex- hibit a significant gain in terms of watermark capacity over This work has been partially funded by the Brazilian Ministry of Edu- cation under CAPES grant 1423-00/2, and by the Ibero American Science and Technology Education Consortium (ISTEC), under the Los Liberta- dores initiative. known-host statistics schemes such as the spread-spectrum (SS), they were shown in turn to be easily defeated by even the simplest attacks. This limitation of pure quantization based embedding motivated the creation of hybrid schemes (e.g., quantized projection, QP [3]) that merged concepts from both SS and QIM to simultaneously increase robust- ness and capacity. This accounts for quantizing a diversity projection of the host signal, in a much similar way to what is done for spread transform dither modulation (STDM), proposed earlier by Chen and Wornell. While such differ- ent amends to Costa’s original idea helped to mitigate the effects of attacks, at the same time they turned out to be suboptimal in terms of capacity, lying far away from the originally targeted achievable rate for the watermark chan- nel modeled after the AWGN channel. In this paper, we present a novel technique that is shown by construction to be insensitive to amplitude scaling, named Angle QIM (AQIM). Instead of embedding information by quantizing the amplitude of pixel values, AQIM works by quantizing the angle formed by the host-signal vector with respect to the origin of a hyperspherical coordinate system. We present a detailed description of this method by building upon a simple example in two dimensions in order to con- struct angle quantizers in arbitrarily higher dimensions. Fi- nally, we present experimental results that evidence AQIM’s bit error performance under additive white Gaussian noise attacks. 2. PRELIMINARIES In this paper, we follow the usual watermarking notation, where: k is a secret key used during the embedding/decoding process; x are samples taken from the original image, which can be pixels, DCT coefficients, DWT coefficients, or any other transformed domain coefficients used for embedding; m is a message that needs to be transmitted to the receiver end; w is the watermark to be added to the original image samples; y is the watermarked image; n represents an ad- ditive noise source contaminating y and z is the possibly II - 797 0-7803-8874-7/05/$20.00 ©2005 IEEE ICASSP 2005 ➠ ➡