27 January 2010 Reverse-engineering a watermark detector based on a more precise model
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Detection results obtained from an oracle can be used to reverse-engineer the underlying detector structure, or parameters thereof. In particular, if a detector uses a common structure like correlation or normalized correlation, detection results can be used to estimate feature space dimensionality, watermark strength, and detector threshold values. Previous estimation techniques used a simplistic but tractable model for a watermarked image in the detection cone of a normalized correlation detector; in particular a watermarked image is assumed to lie along the axis of the detection cone, essentially corresponding to an image of zero magnitude. This produced useful results for feature spaces of fewer dimensions, but increasingly imprecise estimates for larger feature spaces. In this paper we model the watermarked image properly as a sum of a cover vector and approximately orthogonal watermark vector, offsetting the image within the cone, which is the geometry of a detector using normalized correlation. This symmetry breaking produces a far more complex model which boils down to a quartic equation. Although it is infeasible to find its symbolic solution even with the aid of computer, our numerical analysis results show certain critical behavior which reveals the relationship between the attacking noise strength and the detector parameters. The critical behavior predicted by our model extends our reverse-engineering capability to the case of detectors with large feature space dimensions, which is not uncommon in multimedia watermarking algorithms.
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Jun Yu, Jun Yu, Scott Craver, Scott Craver, "Reverse-engineering a watermark detector based on a more precise model", Proc. SPIE 7542, Multimedia on Mobile Devices 2010, 75420C (27 January 2010); doi: 10.1117/12.839161; https://doi.org/10.1117/12.839161

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