Image Processing Reference
In-Depth Information
One important branch of neighborhood processing is mathematical morphology
or simply morphology . It is applicable to both gray-scale images as well as binary
images, but in this text only operations related to binary images are covered. Mor-
phology on binary images has a number of applications and in Fig. 6.1 three typical
ones are illustrated. The first two illustrate how to remove the noise that very of-
ten is a side effect of thresholding. It is next to impossible to achieve a perfect
binary image using thresholding. We are very likely to under-segmentation in some
regions and over-segmentation in other regions. The leftmost figure illustrates over-
segmentation in the form of the small objects in the image. Under-segmentation is
illustrated in the middle figure as holes inside the object. The problems associated
with thresholding were also mentioned in Chap. 4 where it could be seen as the
problematic histogram in Fig. 4.17.
The rightmost example in Fig. 6.1 illustrates a problem which is related to the
next chapter, where we will start to analyze individual objects. To this end we need
to ensure that the objects are separated from each other.
Morphology operates like the other neighborhood processing methods by ap-
plying a kernel to each pixel in the input. In morphology, the kernel is denoted a
structuring element and contains '0's and '1's. You can design the structuring ele-
ment as you please, but normally the pattern of '1's form a box or a disk. In Fig. 6.2
different sized structuring elements are visualized. Which type and size to use is up
to the designer, but in general a box-shaped structuring element tends to preserve
sharp object corners, whereas a disk-shaped structuring element tends to round the
corners of the objects.
A structuring element is not applied in the same way as we saw in the previous
chapter for the kernels. Instead of using multiplications and additions in the calcula-
tions, a structuring element is applied using either a Hit or a Fit operation. Applying
one of these operations to each pixel in an image is denoted Dilation and Erosion ,
respectively. Combining these two methods can result in powerful image processing
tools known as Compound Operations . We can say that there exist three levels of
operation, see Fig. 6.3 , and in the following, these three levels will be described one
at a time. Note that for simplicity, we will in this chapter represent white as 1 instead
of 255.
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