Image Secret Sharing - Visual Cryptography and Secret Image Sharing - page 388

Note that each of the steps has to be applied separately for each color
channel. The use of a rational curve has several advantages, such as it does
not have the oscillations phenomenon of polynomials with a high degree; a
rational curve is easy to be controlled and is able to express conic curves. Also
a polynomial curve with a high degree cannot guarantee that the interpolation
values can be constrained to a given range [16]. Thus, when a rational curve is
employed to share a color image, the scheme based on moving lines yields more
shares than that of the one based on the Lagrange interpolating polynomial.
With more shares, the secret color image can be shared in a more secure
manner with greater flexibility. However, this greater flexibility comes at an
increased cost of computation compared to that of the Lagrange interpolations
scheme.

14.3.4 Improved Algorithm
If we carefully examine Figure 14.3, we can see that the profile of the se-
cret image is visible in the constructed image shares. The reason is that the
correlation of the secret image is not broken during the image sharing pro-
cess. So far, we selected only one X-position parameter for the secret image,
thus only one share (i.e., the newly created one) is closely related to the se-
cret image and the other shares are totally independent. Thus, the innocuous
images do not contribute towards image hiding. We now modify the earlier
approach slightly to make all the shares involved in data hiding by utilizing a
block-based approach with multiple parameters:
Steps of block-based image sharing:

1. Divide the secret image into blocks.

2. Designate different parameters (i.e., different innocuous image po-

sition) for each block.

3. Share the secret image using the earlier approach.

4. Write down the parameters and positions embedded in the corre-

sponding shares of each block for secret restoration.

The restoration handling is the inverse procedure of the encoding proce-
dure.
In order to clearly explain the scheme, we illustrate the improved approach
in Figure 14.7. In Figure 14.7, the secret image is divided into four blocks, each
block is embedded into the given innocuous image share at a different spatial
position. The secret image can be reconstructed by applying the scheme block-
wise again. This method effectively breaks the correlation of the original secret
image with the secret image being divided into many blocks and these blocks
being hidden in different shares at different locations. Thus, the secret image
is no longer visible in the shares.