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Two Binary Number Coding Systems

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PBC and CGC are related by Exclusive OR operation as follows.

                  

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The following pictures illustrate the difference of the views of one single bmp picture. The left side is in PBC, and the right in CGC.

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PBC CGC

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In BPCS-Steganography embedding operation is executed after the vessel image has been transformed from PBC to CGC. This is because CGC is better than PBC in producing a "better looking (or, blocking-less)" stego image. The reason is as follows.

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Let  an "n-th least plane" be the n-th Least Significant bit-plane. (For example, the 3rd least plane in PBC as above is the b2 bit-plane.)

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"Embedding a file-block in an n-th least PBC plane" actually means "changing the colors of several pixels in that block by the value 2n-1 "uniformly." In this case the "blocking effect" likely to emerge on the stego image.

  <Example>

If a bit in the 3rd least plane is changed from "0" to "1", it actually changes 0 (=0000) ->4 (=0100),  1 (=0001) ->5 (=0101),  2 (=0010) ->6 (=0110),  3 (=0011) ->7 (=0111), and 8 (=1000) ->12 (=1100), ... . The amount of the change is always 4, and will cause a blocking effect.

 

While in the CGC embedding, the color change "differs pixel by pixel" in the block ranging from 1 to 2n-1. The average change in the block is 2n-1.

  <Example>

The change occurs like, 0 (=0000) ->7 (=0100),  1 (=0001) ->6 (=0101),  2 (=0011) ->5 (=0111),  3 (=0010) ->4 (=0110), and 12 (=1010)->11 (=1110), ... . The amount of the change in this case differs case by case, but the average is 4. This will not produce a blocking effect remarkably.

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Consequently, we conclude that CGC is better than PBC.

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(Updated on Jun. 18, 2015, by Eiji Kawaguchi)

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