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9.1 Introduction
Morphology, or morphology for short, is a branch of image processing which is particularly useful for
analyzing shapes in images.9.2 Basic ideas
The theory of mathematical morphology can be developed in many different ways.Reflection
If
is set of pixels, then its reflection, denoted
, is obtained by reflecting
in the origin:
For examples, in figure 9.2, the open and closed circles form sets which are reflections oWe shall develop basic morphological tools for investigation of binary
images, and then show how to extend these tools to greyscale images.Translation
Suppose that
is a set of pixels in a binary image, and
is a particular coordinate point.
9.1 Introduction
Morphology, or morphology for short, is a branch of image processing which is particularly useful for
analyzing shapes in images. We shall develop basic morphological tools for investigation of binary
images, and then show how to extend these tools to greyscale images. Matlab has many tools
for binary morphology in the image processing toolbox; most of which can be used for greyscale
morphology as well.
9.2 Basic ideas
The theory of mathematical morphology can be developed in many different ways. We shall adopt
one standard method which uses operations on sets of points. A very solid and detailed account
can be found in Haralick and Shapiro [5].
Translation
Suppose that
is a set of pixels in a binary image, and
is a particular coordinate point.
Then is the set
“translated” in direction
. That is
For example, in figure 9.1,
is the cross shaped set, and
. The set
has been shifted in
the
and
directions by the values given in
. Note that here we are using matrix coordinates,
rather than Cartesian coordinates, so that the origin is at the top left,
goes down and
goes
across.
Reflection
If
is set of pixels, then its reflection, denoted
, is obtained by reflecting
in the origin:
For examples, in figure 9.2, the open and closed circles form sets which are reflections o
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