Image Processing Reference
In-Depth Information
The goal of this chapter is to introduce such a framework, to propose cellular
automata for implementing image forgery detection system and to give experimen-
tal results. In this chapter we proposed two active methods to detect digital image
forgery in a reliable manner. The aim of this work is to develop a framework to active
image forgery detection using cellular automata. The proposed methods take a dig-
ital image as input and compute some statistical information from its Lower Upper
(LU) and Singular Value Decomposition (SVD). We use singular value decompo-
sition and also lower upper decomposition plus one dimensional cellular automata
to generate a cipher key. This key has the image features and completely related to
digital image that every small change in the content of digital image will change the
key value without any exception.
The rest of the chapter is arranged as follows. In Sections 7.2 and 7.3 we develop
two different scenarios to image forgery detection based on a cellular automata.
Section 7.4 introduces our sample dataset and describes the experimental results.
Section 7.5 discusses limitations of the proposed models. Conclusion and areas for
future development is considered in Section 7.6.
7.2
Scenario 1: Using Cellular Automata and LU
Decomposition
LU decomposition is a kind of matrix decomposition which composes a matrix by
the product of a lower and an upper triangular matrix [6]. Let
A
be a square matrix.
An LU decomposition is a matrix decomposition of the form
A
LU
,where
L
and
U
are lower and top triangular matrices of the same dimensions. This means that
L
has
just zeros overhead the diagonal and
U
has only zeros underneath the diagonal [6].
For a 3
=
×
3 matrix, this becomes:
⊡
⊣
⊤
⊦
=
⊡
⊣
⊤
⊦
⊡
⊣
⊤
⊦
a
11
a
12
a
13
a
21
a
22
a
23
a
31
a
32
a
33
l
11
00
l
21
l
22
0
l
31
l
32
l
33
u
11
u
12
u
13
0
u
22
u
23
00
u
33
Section 7.2.1 describes the usage of LU decomposition for the proposed active
forgery detection algorithm. Let's a little describing one dimensional cellular au-
tomata we want to use in our proposed model. In this topic, there are some chapters
with details descriptions on cellular automata, so we just give a really brief overview
which is necessary for the proposed model. Figure 7.1 shows a simple two state and
one dimensional cellular automata with a line of cells. The state of
X
at the time
t
1 will be determined by the states of the cells within its neighborhood at the time
t
[10, 17, 18].
We can define and set our own local rule for each cellular automata. You can see
just two example of how we may define a local rule and how does it work. Let us to
consider two following rules to estimate the value of cell
X
at time
t
+
+
1 based on
the value of cell
X
at the time
t
:
Search WWH ::
Custom Search