Journal of Software - Academy Publisher

852 JOURNAL OF SOFTWARE, VOL. 6, NO. 5, MAY 2011
'
LL
CF
i, j, s, t
'
i, j, s, t
M M
⎧ α1
⎪LLi,
jst , , + 2 ∑∑LLi,
jst , , if wst
, = 1
⎪ M s= 1 t=
1
= ⎨ M M
⎪ α1
LLi, jst , , − LL 2
i, jst , , if wst
, = 0
⎪ ∑∑
⎩ M s= 1 t=
1
(2)
M M
⎧ α2
⎪CFi,
jst , , + 2 ∑∑ CFi, jst , , if wst
, = 1
⎪ M s= 1 t=
1
= ⎨ M M
⎪ α2
CFi, jst , , − CF 2
i, jst , , if wst
, = 0
⎪⎩
∑∑ M s= 1 t=
1
(3)
The parameter α 1 and α 2 are the embedding
intensities and CF maybe one of HL and LH . Do
inverse discrete wavelet transform after modifying the
'
'
wavelet coefficients and get I i, j.
All of I i, j are united
' '
to a watermarked image I = [ I ( i, j)]
(1 ≤i, j ≤ N ).
5) Define the fitness function using peak
signal-to-noise ratio (PSNR) between I = [ I( i, j)]
and
' '
I = [ I ( i, j)]
.
2 2
N × max( I ( i, j))
N N
' 2
PSNR = 10× log 10(
)
( Iij ( , ) − I( i, j))
∑∑
i= 1 j=
1
6) Create some random chromosomes into an original
colony and give the values of s P and P m . Evaluate the
fitness values of chromosomes and do the genetic
operation until the process of GA stops and the optimal
watermarked image I� is gotten.
The final chromosome of GA and parameters
( µ 1, µ 2, γ, x0, y0, P)
of the two-dimensional chaotic
Logistic map system can be looked upon the key of this
watermarking scheme used in watermark extraction.
IV. WATERMARK IDENTIFICATION
To an encrypted meaningful watermark extracted from
watermarked image, people maybe not distinguish its
decrypted form through technical indexes, such as BCR,
NC, and eyes, because of some interferential causations
to watermarked image in the communication and usage.
The SNN can effectively identify the extracted watermark
in our former research[15] so that it is used in this scheme
too.
A. Synergetic Neural Networks
The SNN model is a top-down network constructed by
synergetic different from traditional network constructed
by the method researched in single neuron’s characteristic,
configuration and connection[16].
© 2011 ACADEMY PUBLISHER
(4)
Dynamical system can be described by state vector in
Synergetic. Let a state vector be q= ( q1, q2, � , q ' ) .
M
A synergetic associative pattern recognition system can
be described by dynamical evolutionary process, in which
the system evolves by neural network learning to fill
incomplete data set and form pattern. Furthermore, let
'
prototype pattern number be M and prototype pattern
'
' '
vector’s dimension be N , where satisfies M ≤ N .
A dynamical equation can be described by (5).
.
∑ ∑ (5)
q= λ v ( v q) −B ( v q) ( v qv ) −Cq
( qq )
+ + 2 + +
k
k k k
'
k≠k '
k k k
where q as recognizable pattern vector with original
input value q0 = q(0)
can be decomposed into
prototype v k and remnant vector w , having
'
M
∑ ξk
k = 1
k and
+
w = 0
q= v + w
vk . Attention parameter
λ k is positive. B and C are appointed coefficients
and must be more than zero. Prototype pattern vector k v
is expressed as vk = ( vk1, vk2, � v ' ) ′ and
kN
+
v k is an
adjoint vector of v k , which satisfies an orthogonal
⎧ ′
+
1,
k = k
condition vk vk
= δ kk′
= ⎨ . All v k will be
⎩0,
k ≠ k′
normalized as
'
N
∑ vkl
= 0 and centered as
l = 1
'
N
2 1/2
k = ( ) 1
2 ∑ kl =
l=
1
v v
.
Order parameter ξ k is defined as k k vq ξ
+
= . The
dynamical equation can be rewritten by order parameter.
k = k k − B∑ 2
k′ '
M
k − C ( ∑
2
k′ ) k
k′ ≠ k k′
= 1
ξ� λξ ξ ξ ξ ξ (6)
D= ( B+ C) ∑ ξ , (6) is simplified to (7).
k
2
Used '
'
k
� (7)
ξ ξ λ ξ
2
k = k( − D+ B k )
So the SNN model is constructed with three layers.
The top layer is the input layer. All order parameter
neurons form the middle layer. The down layer is the
output layer.
B. Watermark Extracting
The watermark extracting is the contrary producer of
watermark embedding. The DWT transforms of the
received watermarked image I � and host image I
could be done according to the rule of watermark
embedding and the final chromosome of GA need be