Image Processing Reference
In-Depth Information
Fig. 17.2. (
Left
) The result of applying the dilation,
F
⊕
G
and (
right
) the erosion
F
G
operators when using the image
F
and the filter
G
shown in Fig. 17.1.
Red
and
blue
represent
1 and 0, respectively. The
light red
and the
light blue
represent 1 and 0, respectively, but they
are chosen so to mark points that have changed their values as compared to the original
4. If there is a dominant filter direction, then erosion has a directional preference
too, e.g., a horizontal filter erodes edges with horizontal direction.
5. If the background pixels are called 1 and the object pixels 0, then the roles of
dilation and erosion are reversed.
Hit-Miss Transform
To detect binary objects of a specific shape and size, the
hit-miss transform
can
be utilized. It exploits the fact that erosion removes only objects “smaller” than the
“target”. To fix the ideas we illustrate it by:
G
=(1
,
1
,
1)
T
(17.6)
so that our goal is to erase every object that does not equal
G
. The center pixel is
marked as boldface for convenience to mark that it is the point that represents the
position of the object.The hit-miss transform is implemented as follows.
1. Delete all objects smaller than the target. This is achieved by
H
=
F
G
(17.7)
where
G
is the target. This step is illustrated by Fig. 17.2 (right).
2. Delete all “objects” larger than the target. This is achieved by
R
=
F
G
(17.8)
where
F
, having the effect that all
ones become zeros and zeros become ones. For the filter this is true too, but it
would result in trivial filters if certain rules were not observed. To avoid this, the
filter is assumed to be limited by a thin boundary of zeros that has no effect on
·
represents the conjugate operation
F
=1
−
