Digital Watermarking Algorithms Robust Against Loss of by Delannay

By Delannay

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A Random repetition (expansion) ✝✆ Sequence S ~ A A Pattern construction ~ A A ... ✂✁ ☎ ✄ , Pattern W ( ✞✠✟☛✡☞✞✍✌✎✡☞✏ ; ✑✓✒✔✡✖✕✘✗ ; ✙✛✚✜✡☞✢ ; ✙✤✣✥✡✦✕✧✏ ) ~ ~ A A ~ ~ A A A A A A ... ~ ~ A A ~ ~ A A ... A A A A ... ... ... ... 7: Watermark pattern construction parameters should be optimized for each situation. 38 Chapter 3. 12 is motivated by the will to minimize the image degradation while maximizing the detection reliability. This leads to the shaping of the watermark signal to fit image characteristics.

In our scenario, the different detection values ✥ ✼ are derived combining all realizations from the fixed set of✠ realizations in . For this✞ reason, distribution of ✏ ✼ for varying shifts ✞ will not exactly fit the ✔ distribution. The way that it will differ from ✔ distribution is described below. 25) ✞ In our case, distribution ✑ ✒ differs from the ✔ distribution in accordance ☞ ❍ with the values of and . One can show that the first moment will still be but the variance will take values comprised between 0 and ✫✄ ☎✢ ✞ ☞ depending on the ratio .

In order to address more complex transform while maintaining reasonable computational cost, detection can sometimes be performed on smaller regions of the image [29, 30] provided sufficient watermark-to-image power ratio is available. Strong hypotheses can be made on the relative continuity or smoothness of the deformation, further reducing the search space [31]. Another mean to reduce search space is to use periodically structured watermarks [32, 33, 34]. It enables to limit search for synchronization over one repetition period.

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