A ROBUST IMAGE WATERMARKING SCHEME BASED ON THE ALPHA-BETA SPACEP. Martins and P. CarvalhoCentre for Informatics and Systems, University of CoimbraP´olo II, Pinhal de Marrocos, 3030-290 Coimbra, Portugal{pjmm,carvalho}@dei.uc.ptABSTRACTA robust image watermarking scheme relying on an affine in-variant embedding domain is presented. The invariant spaceis obtained by triangulating the image using affine invariantinterest points as vertices and performing an invariant trian-gle representation with respect to affine transformations basedon the barycentric coordinates system. The watermark is en-coded via quantization index modulation with an adaptive quan-tization step.1. INTRODUCTIONThe robustness with respect to geometric transformations hasbeen a widely studied topic in digital image watermarking,leading to the introduction of several solutions trying to over-come the effects carried out by these distortions, speciallythe de-synchronization effect, since most of the watermark-ing schemes perform a detection based on a correlation mea-sure; thus, if a marked image is geometrically distorted, thedetector will correlate wrong image components [1]. Robustschemes can be be grouped into four categories: invariant do-main based methods, template based methods, self-synchro-nization based methods and content based methods. The firstcategory includes methods which exploit invariant or partiallyinvariant domains for watermark insertion, e.g., applying theFourier-Mellin transform [2] or the Radon transform [3]. Themain drawback of invariant based methods is that they usuallyrequire interpolation in order to obtain the invariant domain;at least two interpolation stages are present in an invariant-based scheme (one to obtain the invariant space and embedthe watermark into it and another one to perform the inversemapping). Because of the inaccuracy of interpolation meth-ods, the performance of these solutions is highly affected.Methods from the second category provide robustness to ge-ometric distortions by retrieving artificially embedded refer-ences which are used as a mean of identification of geometrictransformations [4]. Template-based methods tend to affectseverely the image fidelity due to the addition of the referencesignal. Moreover, templates can be easily removed. Self-synchronization-based methods are similar to template-basedmethods in the sense that they achieve robustness by meansof the identification of geometric distortions, but in this case,the watermark itself can be used to identify the transformation[5]. These approaches are quite sensitive to filtering. Featurebased methods make use of perceptually significant portionsof data to embed the information. For example, Bas et al.[6] exploited strategies based on feature points. The featureswere utilized to construct a Delaunay tesselation that later wasapplied to embed the watermark. In [7], Hang and Tang pro-posed a scheme based on the detection of feature points re-trieved by the Mexican Hat wavelet scale interaction method.These feature points were used as references to embed the wa-termark into a normalized representation of the points neigh-borhood. The main disadvantages exhibited by feature-basedschemes are the fact that the effectiveness of t he watermark-ing depends on the effectiveness, i.e. robustness, of the fea-ture detector/extractor, and they are usually computationallyexpensive.In this paper, we present a content-based image water-marking scheme providing resilience to affine transformations,relying on the (α, β) space, an affine invariant embedding do-main. The mapping is achieved without any interpolation,avoiding the inaccuracy carried out by this operation. The wa-termark embedding is performed via quantization index mod-ulation [8], adjusting t he quantization step in order to have thebest trade-off between the robustness and imperceptibility ofthe watermark.The remainder of this paper is organized as follows: Sec-tion 2 provides a description of the steps required to achievethe (α, β) domain; in Section 3, we describe a quantization-based technique which adopts the suggested space as the em-bedding domain; simulation results concerning the resilienceof the watermarking scheme are given in Section 4; finally, inSection 5, concluding remarks are presented.2. THE (α, β)SPACEThe main steps required to obtain the (α,β) space, an affineinvariant domain, are outlined in Fig. 1. The first step in-cludes an affine invariant interest point detection by meansof a modified version of the detector introduced by Mikola-jczyk and Schmid [9], a method based on an iterative pro-cess that converges to affine invariant key points by modify-15811424403677/06/$20.00 ©2006 IEEE ICME 2006AdaptiveLUM filteringImageAffine invariantinterestpoint detectionPartial imagetriangulationAffine invariantdomain(Alpha,Beta)mappingFig. 1. Achieving the (α, β) space, an affine invariant domain.ing the location, scale and shape of the initial points givenby the Harris method [10], which are already translation androtation invariant. Completely invariant points to any kindof affine transformation are obtained by introducing a scale-space representation for the Harris operator with pre-selectedscales. Locations at which the Laplacian attains a maximumover scales are chosen (this procedure provides scale invari-ance). Invariance to other affine transformations is providedby estimating the affine shape of a pixel derived from the sec-ond moment matrix. In the affine scale-space, at pixel x,thesecond moment matrix is defined byM(x, ΣI, ΣD) = det(ΣD)g(ΣI)∗L2x(x, ΣD) LyLx(x, ΣD)LxLy(x, ΣD) L2y(x, ΣD), (1)where ΣIand ΣDare the covariance matrices which deter-mine the size of the integration and differentiation Gaussiankernels, respectively; Lxand Lyare the image derivatives inthe x and y direction, respectively, computed with a Gaussiankernel whose size was determined by ΣD; and g is a Gaus-sian kernel determined by ΣI. The aforementioned methodis modified by performing an adaptive LUM filtering [11]over the image before the detection in order to improve therepeatability of the detector across a wide range of transfor-mations over an image by setting adaptively the filter parame-ters which define the levels of s harpening and smoothing car-ried out by the filter (Fig. 2 illustrates the effects of this pre-filtering on the interest point detection). These parameterssettings take