Lakhasly

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