Two Binary Number Coding Systems

PBC and CGC are related by the following Exclusive OR operation.

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.

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.)

"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 2^n-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 (=000) -> 4 (=100), 1 (=001) -> 5 (=101), 2 (=010) -> 6 (=110), and 3 (=011) -> 7 (=111). The amount of the change is always 4, and it 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 2^n-1.

  <Example>

The change occurs like, 0 (000) -> 7 (100), 1 (001) -> 6 (101), 2 (011) -> 5 (111), and 3 (010) -> 4 (110). 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.

Consequently, we conclude that CGC is better than PBC.

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(Updated on June 3 by Eiji Kawaguchi)