# Visual Cryptography and Bit-Plane Complexity Segmentation

### Modified BPCS Steganography

It is still possible that an embedded block will not have a complexity above the threshold value. In this case, the conjugate of the block must be taken. The conjugate of a binary image is obtained by XORing the image with the checkerboard pattern. Obviously, the original data can be remade by XORing the new image with the checkerboard pattern again. If necessary, the conjugate is calculated,and you need a "flag pixel" to mark the region as "conjugated."

In the decryption process (as in a puzzle), you have to detect any piece of embedded data and put it back in place. To properly identify every square, I mark each with a sequence number. The sequence number is an integer number binary representation.

Because the proposed embedding scheme is "blind" (that is, no prior knowledge of the image or other information is needed to extract the embedded message), the additional information consisting of the conjugate flag and sequence number has to be written back into the image, together with the embedding data.

To win space for the supplementary information that mustaccompany every 8x8 square, you can border any square with a row and a column; the information could be organized as in Figure 3.

[Click image to view at full size]

Figure 3: Organizing the information in an extended 959 pixel matrix.

The algorithm doesn't work if you embed more squares than can be marked with a sequence number. That is, the total number of embedded squares the model permits is of 216=65,536 squares. From this perspective, the maximum amount of information that can be embedded is 524,228 bytes, or 512 KB of data.

My steganography scheme writes data from the MSB to the LSB in a spiral from the middle of the image. This is because the lossy compression algorithms are likely to discard the LSB and the most important details are usually in the middle of the image.

A 24-bit true-color image consists of red, green, and blue (RGB). The human visual system seems sensitive to green variations and less sensitive to blue ones. Therefore, I adopt the following order in embedding data: I start with the MSB of every constituent color, then move to the next plane until all the embedding information is written. The order of the color components is blue, red, green.

Though the embedding scheme is known for all images, it does not have to be communicated to the receiving party. The receiver only has to divide the image into color components, then bit-planes and regions. Afterwards, all regions having a complexity above the predefined threshold are checked for data.

If a region has errors and is not identified by its complexity (or if the sequence number was altered), the receiver misses the block. But it is possible to guess which region should contain data (see Listing Seven, available at http://www.ddj.com/code/).

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