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Extra info for Digital Watermarking Algorithms Robust Against Loss of Synchronization
It could contain different symbols values. No restriction exists on the length of . ✠ ✠✞ We start by choosing two keys ✹ and which can be any integer comprised between and ✢ . We will explain below which combinations of keys should not be used. The pattern is filled with the elements of the sequence in such a way that there exists in the pattern a constant relation between elements in adjacent positions. If the position ✄✄✟✏☎✞✠✫✞ in the pattern is filled with the✠ ✍ symbol of the sequence, then we will take the symbol ✹✵✞ in position ✄ ✍✏✎ in the sequence to fill position ✄✄✟ ✎ ☎✞✠✫✞ of the pattern.
It will however have a computational cost. 14 compares ☞ ☞ detection probability for different sizes of . As increases, detection probability progressively shifts toward higher values. However, as this occurs under both ✿ and ✹ conditions, it is not evident that the required increase of decision threshold value to maintain a constant ✁ will lead to an increase of . 14: Detection improvement using informed embedding with increasing Ns. Such an informed embedding approach to improve resistance against loss of spatial synchronization could be extended to more complex transformation than translation.
This is the case for rotations and also for translation using our cyclic watermark pattern construction. In other words, if the detection scheme is designed to survive any rotation, then the embedding process should adapt watermark pattern considering all possible rotation of the cover media. For transformations where the space in which we have to look for synchronization is unlimited, such as scaling, hypothesis should be made on the severity of a plausible geometrical distortion. However in these latter 48 Chapter 3.