2 Related PCNN Models
2.1 Original PCNN
Any neural network consists of many neurons. These
neurons work together to perform specific function.
Namely, neuron is the basic function unit of a network. For
two-dimensional network, any neuron in the net is denoted
by N(i, j), where i and j represent the position coordinates
of N(i, j). The neuron model of PCNN is described as
iteration by the following equations [4]:
F
i;j
½n¼e
a
F
F
i;j
½n 1þV
F
X
k;l
w
i;j;k;l
Y
i;j
½n 1þS
i;j
ð1Þ
L
i;j
½n¼e
a
L
L
i;j
½n 1þV
L
X
k;l
m
i;j;k;l
Y
i;j
½n 1ð2Þ
U
i;j
½n¼F
i;j
½nð1 þ bL
i;j
½nÞ ð3Þ
Y
i;j
½n¼
1; U
i;j
½n[ T
i;j
½n
0 otherwise
ð4Þ
T
i;j
½n¼e
a
T
T
i;j
½n 1þV
T
Y
i;j
½nð5Þ
In these equations, S
i,j
is the external input stimulus of
N(i, j); F
i,j
[n] is the feedback input of N(i, j), and L
i,j
[n]is
the linking item. U
i,j
[n] is the internal activity of neuron,
and T
i,j
[n] is the dynamic threshold. Y
i,j
[n] stands for the
pulse output of N(i, j) and it gets either the binary value 0
or 1.
The inter-connections m
i,j,k,l
and w
i,j,k,l
reflect the rela-
tionship between the current neuron and the surrounding
neurons. b is the linking strength or linking coefficient. a
F
,
a
L
, and a
T
are the attenuation time constants of F
i,j
[n],
L
i,j
[n], and T
i,j
[n], respectively. V
F
, V
L
, and V
T
denote the
inherent voltage potential of F
i,j
[n], L
i,j
[n], and T
i,j
[n],
respectively.
The input stimulus is received by the feeding element
and the internal activation element combines the feeding
element with the linking element. The value of internal
activation element is compared to a dynamic threshold
which gradually decreases at iteration. The internal acti-
vation element accumulates the signals until it surpasses
the dynamic threshold and then fires the output element and
the dynamic threshold increases simultaneously strongly.
The output of the output neuron is then iteratively fed back
to the element with a delay of one iteration.
When PCNN is applied into the field of image pro-
cessing, the size of PCNN is equal to the size of two-
dimensional image. In this case, one pixel point corre-
sponds to one neuron. The value of pixel I(i, j) is the
external stimulus of N(i, j). W and M are the constant
synaptic weight matrices for the feeding and the linking
inputs respectively, which depend on the distance between
neurons. Gen erally, M and W (normally W = M) refer to
the Gaussian weight functions with the distance.
2.2 Modified PCNN Models
Above mentioned PCNN model is original model proposed
by Johnson et al. [4]. In fact, based on this original model,
mangy modified PCNN mode ls are presented by
researchers for different purpos es. We cannot intend to list
all existing modified models about image fusion. Instead,
some approaches of modifying the PCNN model are
summarized in this Sect.
1. Most researchers are apt to simplify the feedback input
in the Eq. (1). Usually, the simplified result is
F
ij
n½¼S
ij
n½: ð6Þ
Anyhow, this approach can reduce the complexity and
computation of original PCNN.
2. Alternately, the linking input also can be simplified.
For example, some researchers simplify the Eq. (2)as
L
i;j
¼
1; f
P
ðk;lÞ2Nði;jÞ
Y
k;l
[ 0
0; otherwise
; ð7Þ
where N(i, j) refers to the neighbor field of neuron (i , j).
Obviously, this approach also reduce the computation
time because the complicated convolution operation is
replaced by the operation of summing.
3. For the application of image fusion, the linking
strength b in Eq. (3) is usually set as adaptive local
value instead of globe value, because adaptive local
linking strength can fuse the data well and also
enhance the robustness of image fusion.
4. Seen from the existing literature, dynamic threshold in
Eq. (5) and pulse output in Eq. (4) do not modified.
2.3 Multi-channel PCNN
Besides, extending the multi -channel PCNN for image
fusion is also paid great attention by many researchers. In
1997, Kinser [5] proposed the multichannel PCNN struc-
ture for the first time. This multichannel structure can
realize interaction among the channels, but this structure
also remains the form of original PCNN.
F
e
ij
½n¼e
a
F
dn
F
e
ij
½n 1þS
e
ij
þ V
F
X
kl
M
e
ijkl
Y
e
kl
½n 1ð8Þ
L
e
ij
½n¼e
a
L
dn
L
e
ij
½n 1þS
e
ij
þ V
L
X
kl
W
e
ijkl
Y
e
kl
½n 1ð9Þ
U
e
ij
½n¼F
e
ij
½nð1 þ bL
e
ij
½nÞ ð10Þ
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