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Chapter 3 ■ Digital Morphology 107

00 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0
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00 0 1 1 1 2 2 2 1 1 1 0 0 0 00 0 1 1 1 2 2 2 1 1 1 0 0 0 00 0 3 3 3 3 3 0 0 0
00 1 1 2 2 2 2 2 2 2 1 1 0 0 00 1 1 2 2 2 . 2 2 2 1 1 0 0 00 3 3 . 3 3 0 0
00 1 2 2 3 3 3 3 3 2 2 1 0 0 00 1 2 2 3 3 3 3 3 2 2 1 0 0 00 3 3 3 3 3 0 0
01 1 2 3 3 4 4 4 3 3 2 1 1 0 01 1 2 3 3 4 4 4 3 3 2 1 1 0 03 3 3 3 3 3 3 3 3 3 3 3 3 0
01 2 2 3 4 4 5 4 4 3 2 2 1 0 01 2 2 3 4 4 . 4 4 3 2 2 1 0 03 3 3 3 3 3 . 3 3 3 3 3 3 0
01 2 3 3 4 5 5 5 4 3 3 2 1 0 01 2 . 3 4 . . . 4 3 . 2 1 0 03 3 . 3 3 . . . 3 3 . 3 3 0
01 2 2 3 4 4 5 4 4 3 2 2 1 0 01 2 2 3 4 4 . 4 4 3 2 2 1 0 03 3 3 3 3 3 . 3 3 3 3 3 3 0
01 1 2 3 3 4 4 4 3 3 2 1 1 0 01 1 2 3 3 4 4 4 3 3 2 1 1 0 03 3 3 3 3 3 3 3 3 3 3 3 3 0
00 1 2 2 3 3 3 3 3 3 2 2 0 0 00 1 2 2 3 3 3 3 3 3 2 2 0 0 00 3 3 3 3 3 0 0
00 1 1 2 2 2 3 2 2 2 1 1 0 0 00 1 1 2 2 2 . 2 2 2 1 1 0 0 00 3 3 . 3 3 0 0
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(a) (b) (c)
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00 5 5 5 5 5 . 5 5 5 5 5 0 0 00 5 5 5 5 5 5 5 5 5 5 5 0 0
00 5 5 5 5 5 5 5 5 5 5 5 0 0 00 5 5 5 5 5 5 5 5 5 5 5 0 0
0 5 5 5 5 5 5 5 5 5 5 5 0 03 5 5 5 5 5 5 5 5 5 5 5 3 0
0 5 5 5 5 5 . 5 5 5 5 5 0 03 5 5 5 5 5 5 5 5 5 5 5 3 0
0 5 . 5 5 . . . 5 5 . 5 0 03 5 5 5 5 5 5 5 5 5 5 5 3 0
0 5 5 5 5 5 . 5 5 5 5 5 0 03 5 5 5 5 5 5 5 5 5 5 5 3 0
0 5 5 5 5 5 5 5 5 5 5 5 0 03 5 5 5 5 5 5 5 5 5 5 5 3 0
00 5 5 5 5 5 5 5 5 5 5 5 0 0 00 5 5 5 5 5 5 5 5 5 5 5 0 0
00 5 5 5 5 5 . 5 5 5 5 5 0 0 00 5 5 5 5 5 5 5 5 5 5 5 0 0
00 0 5 5 5 5 5 5 5 5 5 0 0 0 00 0 5 5 5 5 5 5 5 5 5 0 0 0
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00 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0
(d) (e) (f)
Figure 3.15: Multiple closings for outline smoothing. (a) Glyph from Figure 3.12a after
a depth 2 closing. (b) After a depth 3 closing. (c) A chess piece. (d) Thresholded chess
piece showing irregularities in the outline and some holes. (e) Chess piece after closing.
(f) Chess piece after a depth 2 closing.

Figure 3.16 is a sample reservoir rock pore image having a size of 300x300
pixels. The results of opening using the distance encoded image are identical
with the results from the traditional erode-dilate method, although all openings
were found in only three passes through the image. Two sample openings
are shown, with the deleted pixels shown in grey. The roughness spectrum
can be calculated by repeatedly thresholding the image and counting the
pixels remaining after each step, but there is an easier way. The roughness
spectrum can now be found by simply computing the grey-level histogram of
the globally opened image.

3.3.6 MAX—A High-Level Programming Language
for Morphology

Many of the tools needed for experimenting with morphology are provided
in this chapter and on the accompanying website in the form of C func-
tions and procedures. However, their use requires a certain fluency in the
C language, and any given experiment may involve a sequence of compi-
lation/test/debug steps that can be time consuming. To avoid this, and to