Image Processing Reference
In-Depth Information
Fig. 6.10 Closing performed using 7
×
7 box-shaped structuring elements
Fig. 6.11 Opening of the binary image in Fig. 6.4 using S 1
operation described just below or by finding and deleting small objects, which will
be described in the next chapter.
6.3.2 Opening
Opening deals with the problem associated with erosion, namely that the objects
decrease when we use erosion to erase small noisy objects or fractured parts of big-
ger objects. The decreasing object size is a problem in situations where for example
the size of the object (number of pixels) matters. The solution to this problem is
luckily straight forward, we simply enlarge the object by following the erosion by a
dilation. This operation is denoted Opening and is written as
= f(x,y)
SE
g(x,y)
=
f(x,y)
SE
SE
(6.5)
where SE is the same structuring element. This operation is also idempotent as is
the case for the closing operation. In Fig. 6.11 opening is illustrated for the binary
image in Fig. 6.4 . Opening is done with structuring element S 1 . We can see that only
a compact version of the object remains.
In Fig. 6.12 opening is applied to a real image using a 7
7 box-shaped struc-
turing element. We can see that most noisy objects are removed while the object
preserves its original size.
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