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Chapter 3 ■ Digital Morphology 101

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This file will be called elise_se.pbm. To perform the dilation seen in
Figure 3.9, the call to BinErode would be:

BinErode
Enter input image file name: elise.pbm
Enter structuring element file name: elise_SE.pbm
Enter output filename: out1.pbm

where the elise.pbm file contains the image 3.8a, and out1.pbm will be the
file into which the dilated image will be written (Figure 3.9c). The C function
bin_erode is implemented in a very similar manner to bin_dilate,and
appears in Figure 3.10.

3.3.5 Opening and Closing
The application of an erosion immediately followed by a dilation using the
same structuring element is referred to as an opening operation. The name
opening is a descriptive one, describing the observation that the operation
tends to ‘‘open’’ small gaps or spaces between touching objects in an image.
This effect is most easily observed when using the simple structuring element.
Figure 3.11 shows an image having a collection of small objects, some of them
touching each other. After an opening using simple, the objects are better
isolated and might now be counted or classified.
Figure 3.11 also illustrates another, and quite common, use of opening: the
removal of noise. When a noisy grey-level image is thresholded some of the
noise pixels are above the threshold, and result in isolated pixels in random
locations. The erosion step in an opening will remove isolated pixels as well as
boundaries of objects, and the dilation step will restore most of the boundary
pixels without restoring the noise. This process seems to be successful at
removing spurious black pixels, but does not remove the white ones.
The example in Figure 3.9 is actually an example of opening, albeit with
a more complex structuring element. The image was eroded, leaving only a
horizontal line, and then dilated by the same structuring element, which is
certainly an opening. What is being eroded in this case is all portions of the
image that are not staff lines, which the dilation subsequently restores. The
same description of the process applies to Figure 3.11; what is being eroded is
all parts of the image that are not small black squares, which are restored by
the dilation thus removing everything except that in which we are interested.