Image Processing Reference

In-Depth Information

Fig. 5.5
An illustration of the border problem, which occurs when using neighborhood processing

algorithms. If a kernel with a size of 3

3 is used, then the border illustrated in
f(x,y)
cannot be

processed. One solution to this is to apply kernels with special sizes on the borders, like the ones

showed to the
right

×

5.1.1 Rank Filters

The Median Filter belongs to a group of filters known as
Rank Filters
. The only

difference between them is the value which is picked after the pixels have been

sorted:

The minimum value
This filter will make the image darker.

The maximum value
This filter will make the image brighter.

The difference
This filter outputs the difference between the maximum and min-

imum value and the result is an image where the transitions between light and

dark (and opposite) are enhanced. Such a transition is often denoted an edge in an

image. More on this in Sect.
5.2.2
.

5.2

Correlation

Correlation
is an operation which also works by scanning through the image and

applying a filter to each pixel. In correlation, however, the filter is denoted a
kernel

and plays a more active role. First of all the kernel is filled by numbers—denoted

kernel coefficients
. These coefficients weight the pixel value they are covering and

the output of the correlation is a sum of weighted pixel values. In Fig.
5.6
some

different kernels are shown.

Similar to the median filter the kernel is centered above the pixel position whose

value we are calculating. We denote this center
(
0
,
0
)
in the kernel coordinate system

and the kernel as
h(x,y)
, see Fig.
5.7
. To calculate the output value we take the

value of
h(

1
)
and multiply it by the pixel value beneath. Let us say that we

are calculating the output value of the pixel at position
(
2
,
2
)
. Then
h(

−

1
,

−

1
)
will

be above the pixel
f(
1
,
1
)
and the value of these two pixels are multiplied together.

The result is added to the product of the next kernel element
h(
0
,

−

1
,

−

−

1
)
and the pixel