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130 Chapter 3 ■ Digital Morphology

This method can be applied to a variety of textures, although some experi-
mentation with structuring elements may be needed to achieve good results.

3.4.5 Size Distribution of Objects

The use of morphology for segmenting regions by texture suggests another
application: the classification of objects by their size or shape. Because the use
of shape would require quite a bit of experimenting with different structuring
elements, size classification will be explored here. Quite a variety of objects
are regularly classified according to their size, from biological objects under a
microscope to eggs and apples. A ‘‘grade A large’’ egg, for example, should be
noticeably bigger than a ‘‘medium’’ egg, and it should be possible to create a
program for classifying eggs using grey-level morphology. However, because
eggs are often graded using their weight, we will examine another case close
to all of us — that of money.
As it happens, and not by accident, coins vary in size according to their
value. A dime is the smallest, and a one-dollar coin is, if you can find one, the
biggest. Figure 3.32a shows an image of a small collection of coins on a dark
background. It is a mixture of U.S. and Canadian coins, since it was easy to
obtain a Canadian one-dollar coin (called a loon), but a U.S dollar coin would
have worked as well.

(a) (b) (c)

(d) (e) (f)
Figure 3.32: Classifying coins by their size. (a) The image containing coins to be classified.
(b) After opening by a structuring element of radius 6. (c) After opening by radius 6.5. (d)
Thresholded version of (c), showing that the dimes can be removed. (e) After opening by
radius 8, showing that the pennies have been removed. (f) After opening by radius 10; the
only coin remaining is the one-dollar coin.