366
9 Memristor Cellular Neural Networks Computing in the Flux-charge Domain
9.4.2 Hole Filling
Consider now a 2D M-SCNN for solving the task “hole filling” of a 2D image. Let
us choose the 3 × 3 feedback cloning template as in [20, p. 44]
A =
⎛
⎝
0 1 0
1 3 1
0 1 0
⎞
⎠
from which we obtain a symmetric interconnection matrix G. Moreover, let the 3×3
control template be given by
B =
⎛
⎝
0 0 0
0 4 0
0 0 0
⎞
⎠ .
According to the design procedure in [20, p. 44] let
Q 0 = BI + z
where I is the initial image and z is a biasing vector with all elements equal to 1.
Moreover, choose the initial conditions q i (0) = q i 0 = −1.1 for all i = 1, 2, . . . , n.
Note that in this case the image to be processed is provided via Q 0 . As discussed
before, the initial conditions for the state variables in the (v, i)-domain are chosen
according to (9.15) as
q M (0) = k q q 0
and
v C (0) =
k q
C
[BI + z − q 0 + G ˆ
Φ(q 0 )].
It can be checked that (9.16) is satisfied. It is seen from Figs. 9.14 and 9.15
that the M-SCNN is able to correctly solve the task in real time via the transient
evolution of memristor charges and that, as predicted by the theory, all capacitor
voltages vanish in steady state.
9.5 Discussion
A number of remarks on the M-SCNNs introduced in this chapter are in order.
9 Memristor Cellular Neural Networks Computing in the Flux-charge Domain
9.4.2 Hole Filling
Consider now a 2D M-SCNN for solving the task “hole filling” of a 2D image. Let
us choose the 3 × 3 feedback cloning template as in [20, p. 44]
A =
⎛
⎝
0 1 0
1 3 1
0 1 0
⎞
⎠
from which we obtain a symmetric interconnection matrix G. Moreover, let the 3×3
control template be given by
B =
⎛
⎝
0 0 0
0 4 0
0 0 0
⎞
⎠ .
According to the design procedure in [20, p. 44] let
Q 0 = BI + z
where I is the initial image and z is a biasing vector with all elements equal to 1.
Moreover, choose the initial conditions q i (0) = q i 0 = −1.1 for all i = 1, 2, . . . , n.
Note that in this case the image to be processed is provided via Q 0 . As discussed
before, the initial conditions for the state variables in the (v, i)-domain are chosen
according to (9.15) as
q M (0) = k q q 0
and
v C (0) =
k q
C
[BI + z − q 0 + G ˆ
Φ(q 0 )].
It can be checked that (9.16) is satisfied. It is seen from Figs. 9.14 and 9.15
that the M-SCNN is able to correctly solve the task in real time via the transient
evolution of memristor charges and that, as predicted by the theory, all capacitor
voltages vanish in steady state.
9.5 Discussion
A number of remarks on the M-SCNNs introduced in this chapter are in order.