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CHAPTER
3

Digital Morphology

3.1 Morphology Defined

‘‘Morphology’’ means the form and structure of an object, or the arrangements
and interrelationships between the parts of an object. Morphology is related
to shape, and digital morphology is a way to describe or analyze the shape of
a digital, most often raster, object.
The oldest uses of the word relate to language and to biology. In linguistics
morphology is the study of the structure of words, and this has been an area of
study for a great many years. In biology, morphology relates more directly to
the shape of an organism — the shape of a leaf can be used to identify a plant,
and the shape of a colony of bacteria can be used to identify its variety. In
each case there is an intricate scheme for classification, based on overall shape
(elliptical, circular, etc.), type and degree of irregularities (convex, rough or
smooth outline, etc.), internal structures (holes, linear or curved features) that
has been accumulated over many years of observation. In all cases, shape is a
key concept.
The science of digital or mathematical morphology is relatively new, since
it is only recently that digital computers have made it practical. On the other
hand, the mathematics behind it is simply set theory, which is a well-studied
area. The idea underlying digital morphology is that images consist of a set
of picture elements (pixels) that collect into groups having a two-dimensional
structure (shape). Certain mathematical operations on the set of pixels can
be used to enhance specific aspects of the shapes so that they might be, for
example, counted or recognized. Basic operations are erosion,inwhich pixels

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