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to a distinct member of some waveform set W, where W={w1, w2, â€¦.., wn). Researchers

have devoted significant efforts into defining an optimal set W and function Î¦. Barni and

Bartolini (2004) outline a method for defining W where each value wx , is a pseudo-

randomly generated sequence drawn from a probability density function.

In a direct embedding system, each possible message m is mapped to a unique code bn.

Embedding m into the original work is now simply a matter of adding the workâ€™s vector

and bnâ€™s associated watermark wn. Watermark detection is a matter of comparing the work

to each of the n watermark vectors in W. This comparison produces a value estimating

the probability that mark w has been embedded into the work being examined. The wn

(and thus the message mn mapped to it) that yields the highest detection probability is

deemed to be embedded in the work once this probability falls within a pre-defined

threshold. If all probability values fall below this threshold, it is deemed that no

watermark is in the work.

In informed embedding approaches, the embedding application uses information about

the cover work when devising the mark actually inserted. This allows the system to

create a mark is most suitable for the application in question. Often, obtaining strong

watermark robustness and ensuring that marked works retain perceptual similarity to the

original are contradictory goals. Informed embedding applications can have multiple

watermarks wn associated with a particular code ba. By utilizing the cover workâ€™s

properties, the embedding algorithm can choose the wn that best suits its goals.

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Assigning a unique mark to each message is simple however this technique is impractical

when there are a large number of possible messages. Embedding a small piece of

information such as a postal code or driverâ€™s license number would require generating

thousands of unique watermarks. Large numbers of messages can be represented by

defining each code bn to be a symbol in some alphabet A. Let |A| be equal to the number

of symbols that are contained in A. If the system is defined to support messages which are

represented by sequences of up to x codes, then |A| x messages can be embedded in a

work. For example, this allows a system which supports 4 unique symbols and ten

character sequences to represent 1048576 different messages. Each code bn is assigned a

unique watermark wn as described earlier. A set of watermarks representing a message m

is defined to be {m1, m2, â€¦. ,mx } , where ma, Ð„ W and 0<a<(x+1). In order to perform

the embedding process, the system first divides the original work into n disjoint regions.

This can be done in either the spatial or frequency domain. Each region is designated a

symbol position or index value between one and x. After this process is complete, each

symbol ma is embedded into the region designed to index a. Figure 20 explains this

process. In the previously mentioned direct embedding case, each unique watermark

vector would have to be compared with the work being examined in order to determine

which watermark, if any, has been inserted into it. By using a sequence of symbols to

embed the message as described above, only |A| * n comparisons are needed.

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Figure 20: Division of the Image Space Into Disjointed Blocks For Watermarking Purposes

Symbol 2

Symbol 1 embedded

embedded here

here

Symbol 3 Symbol 4

embedded embedded

here here

Watermarking Techniques

Watermarking techniques differ by the domain in which they embed marks into cover

works. Domains are carefully chosen because they ultimately determine attributes of the

system such as robustness and computational complexity.

Cover works can be marked in the spatial domain. Since most images are natively

represented in this domain, spatial watermarks tend to be computed very quickly. Marks

are embedded into a cover work by slightly modifying the luminance or colour of a

known set of pixels in order to satisfy defined encoding rules. Detectors extract the mark

by observing the set of pixels in question.

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Katzenbeisser and Petitcolas (2000) describe a popular marking technique called Least

Significant Bit substitution, or LSB, in their work. Assuming that the mark can be

represented as a binary sequence of length n, the system selects an ordered set of n pixels

to evaluate. Both embedding and detector processes must be aware of or be able to derive

the selected pixel set. This can be done in some arbitrary manner (i.e. consecutively or

pseudo randomly). In order to embed a mark using this technique, the embedding system

modifies the pixels as follows. The binary representation of luminance for the nth pixel is

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