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Chapter 3 ■ Digital Morphology 93

simple.pbm contains the data for the structuring element.
xx.pbm is the name of the file that will be created to hold the resulting
dilated image.
Both the input file and the output file will be in PBM image file format.
The structuring element file has its own special format, because the location
of the origin is needed. Because dilation is commutative, though, the struc-
turing element should also be a PBM image. It was decided to add a small
‘‘feature’’ to the definition of a PBM file — if a comment begins with the string
#origin, then the coordinates of the origin of the image will follow, first the
column and then the row. Such a file is still a PBM image file, and can still
be read in and displayed as such because the new specification occurs in a
comment. If no origin is explicitly given, it is assumed to be at (0,0).
Thus, the PBM file for the structuring element B 1 of Figure 3.4 would be:

P1
#origin 1 0
31
10 1
This file will be called B1.pbm. To perform the dilation seen in Figure 3.4, the
call to BinDil would be:

BinDil
Enter input image filename: A1.pbm
Enter structuring element filename: B1.pbm
Enter output filename: A1dil.pbm
where the file A1.pbm contains the image A 1 ,and A1dil.pbm will be the file
into which the dilated image will be written.
The program BinDil really does not do very much. It merely reads in the
images and passes them to the function that does the work: the C function
bin_dilate, defined as

int bin_dilate (IMAGE im, SE p);
This function implements a dilation by the structuring element pointed to by
p by moving the origin of p to each of the black pixel positions in the image im,
and then copying the black pixels from p to the corresponding positions in the
output image. Figure 3.5 shows this process, which is basically that specified
in Equation 3.9, and which has a strong resemblance to a convolution.
As shown in Figure 3.6, the function bin_dilate looks through the data
image for black pixels, calling dil_apply when it finds one; this function
performs the actual copy from the current position of the structuring element
to the output (dilated) image. A temporary image is used for the result, which
is copied over the input image after the dilation is complete.