Image Processing Reference
In-Depth Information
Fig. 6.8 Erosion with different sized structuring elements
Fig. 6.9 Closing of the binary image in Fig. 6.4 using S 1
6.3.1 Closing
Closing deals with the problem associated with dilation, namely that the objects
increase in size when we use dilation to fill the holes in objects. This is a problem
in situations where, for example, the size of the object (number of pixels) matters.
The solution to this problem is luckily straightforward: we simply shrink the object
by following the Dilation by an Erosion. This operation is denoted Closing and is
written as
= f(x,y)
SE
g(x,y)
=
f(x,y)
SE
SE
(6.4)
where SE is the structuring element. It is essential that the structuring elements
applied are exactly the same in terms of size and shape. The closing operation is
said to be idempotent , meaning that it can only be applied one time (with the same
structuring element). If applied again it has no effect whatsoever except for of course
a reduced size of g(x,y) due to the border problem. In Fig. 6.9 , closing is illustrated
for the binary image in Fig. 6.4 . Closing is done with structuring element S 1 . We can
see that the holes and convex structures are filled, hence the object is more compact.
Moreover, the object preserves its original size.
In Fig. 6.10 the closing operation is applied to a real image. We can see that most
internal holes are filled while the human object preserves its original size. The noisy
objects in the background have not been deleted. This can be done either by the
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