Active Image Forgery Detection Using Cellular Automata - Cellular Automata in Image Processing and Geometry - page 129

This scenario is applied on grayscale images and it is definitely extendable to
apply on color images.

7.3 Scenario 2: Using Cellular Automata and Singular Value

Decomposition

Here, we define our second algorithm for digital image forgery detection. This part
continues by providing a very brief description of Singular Value Decomposition
(SVD), followed by our proposed model. Experiments for the second scenario will
be also described in detail in Section 7.4.
SVD [6, 11] is very important in many areas of science. It is a way to very com-
pactly represent what a matrix does to space. SVD can be seen as a generalization
of eigenvalues and eigenvectors to a non-square matrix. It is very useful for solving
linear algebraic problems like matrix inversion, linear least square estimation and
fix-ranked approximation.

7.3.1 Proposed Model

The proposed method here is again based on the active approaches. Two set of dom-
inant attributes that achieve from SVD (eigenvalues and eigenvectors) and one di-
mensional cellular automata could provide and generate the secret key. Here and in
contrast to scenario 1, we prefer to work on RGB digital images to design such a
scalable and flexible algorithm. We firstly achieve the eigenvalues and eigenvectors
of the Red matrix (Red layer of the RGB image) of the input image and perform the
same task for the Green matrix (Green layer of the RGB image). We calculate the
eigenvalues and eigenvectors of the image, implementing one dimensional and sin-
gle iteration cellular automata with a XOR local rule to create the secret key, based
on those values. Next, we embed the bit sequence of the secret key into the LSB
of the first eight pixels of the Blue layer (Blue Matrix) in the original image. The
reason of using XOR logical operation and first eight pixels for embedding purpose
was illustrated in previous section. We need to use a real to binary conversion same
as the scenario 1.
Table 7.4 shows the main idea of our proposed cellular automata. Only eight
number of values of the original image have been used to generate this key. These
values consist of sum of eigenvalues, sum of eigenvectors, mean of eigenvalues and
mean of eigenvectors.
All of these values are easy to calculate and also exclusive for a particular matrix.
Figure 7.4 shows the block diagram of the proposed method and Figure 7.5 illus-
trates the diagram of the proposed cellular automata to create a secret key, based on
these attributes of an image. You see a .png format as an input image in this figure,
but our proposed model is suitable and applicable for any format of RGB digital
images.