Image Processing Reference
In-Depth Information
Fig. 5.6
Three different kernels
value beneath
f(
2
,
1
)
, etc. The final value which will be written into the output
image as
g(
2
,
2
)
is found as
g(
2
,
2
)
=
h(
−
1
,
−
1
)
·
f(
1
,
1
)
+
h(
0
,
−
1
)
·
f(
2
,
1
)
+
h(
1
,
−
1
)
·
f(
3
,
1
)
+
h(
−
1
,
0
)
·
f(
1
,
2
)
+
h(
0
,
0
)
·
f(
2
,
2
)
+
h(
1
,
0
)
·
f(
3
,
2
)
+
h(
−
1
,
1
)
·
f(
1
,
3
)
+
h(
0
,
1
)
·
f(
2
,
3
)
+
h(
1
,
1
)
·
f(
3
,
3
)
(5.3)
The principle is illustrated in Fig.
5.7
. We say that we correlate the input image
f(x,y)
with the kernel
h(x,y)
and the result is
g(x,y)
. Mathematically this is
expressed as
g(x,y)
=
f(x,y)
◦
h(x,y)
and written as
R
R
g(x,y)
=
h(i, j)
·
f(x
+
i, y
+
j)
(5.4)
j
=−
R
i
=−
R
where
R
is the radius of the kernel.
3
Below, a C-code example of how to implement
correlation is shown:
for
(y =
Radius ;
y <
(M
−
Radius );
y = y +
1)
{
for
(x =
Radius ;
x <
(N
−
Radius );
x = x +
1)
{
temp
=
0;
for
(j =
−
Radius ;
j
<
( Radius
+
1);
j
=
j
+
1)
{
for
(i =
−
Radius ;
i
<
( Radius +1);
i
=
i
+
1)
{
temp
=
temp
+ h ( i , j )
∗
GetPixel ( input , x+i , y+j );
}
3
The reader is encouraged to play around with this equation in order to fully comprehend it.
