Introduction Set Theory Concepts Structuring Elements , Hits or fits Dilation And Erosion Opening And Closing Hit-or-Miss Transformation Basic Morphological Algorithms Implementation Conclusion
ABSTRCT
Introduction
Morphological – Shape , form , Structure
►Extracting and Describing image component
regions
►Usually applied to binary images
►Based on set Theory
Set Theory
BASICS:
If A and B are two sets then
UNION = AUB
INTERSECTION = A∩B
COMPLIMENT = (A)c
DIFFERENCE = A-B
Structuring elements can be any size
Structuring make any shape
Structuring Elements
1 1 1
1 1 1
1 1 1
0 0 1 0 0
0 1 1 1 0
1 1 1 1 1
0 1 1 1 0
0 0 1 0 0
0 1 0
1 1 1
0 1 0
Rectangular structuring elements with their origin at the middle
pixel
Hits And Fits
Hit: Any on pixel in the structuring element covers an on pixel in the image
B
AC
Structuring Element
Fit: All on pixels in the
structuring element cover
on pixels in the image
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 1 1 0 0 0 0 0 0 0
0 0 1 1 1 1 1 0 0 0 0 0
0 1 1 1 1 1 1 1 0 0 0 0
0 1 1 1 1 1 1 1 0 0 0 0
0 0 1 1 1 1 1 1 0 0 0 0
0 0 1 1 1 1 1 1 1 0 0 0
0 0 1 1 1 1 1 1 1 1 1 0
0 0 0 0 0 1 1 1 1 1 1 0
0 0 0 0 0 0 0 0 0 0 0 0
B C
A
1 1 1
1 1 1
1 1 1
Structuring
Element 1
0 1 0
1 1 1
0 1 0
Structuring
Element 2
Hits And Fits
Dilation
Dilation of image f by structuring element s is given
by f s
The structuring element s is positioned with its origin
at (x, y) and the new pixel value is determined using
the rule:
otherwise 0
hits if 1),(
fsyxg
Erosion
Erosion of image f by structuring element s is given
by f s
The structuring element s is positioned with its
origin at (x, y) and the new pixel value is determined
using the rule:
otherwise 0
fits if 1),(
fsyxg
Erosion v/s Dilation
Erosion
removal of structures of
certain shape and size,
given by SE
Erosion can split apart
joined objects and strip
away extrusions
Dilation
filling of holes of
certain shape and
size, given by SE
can repair breaks
and intrusions
Opening And Closing
Combine to
Opening object
Closing background
keep general shape but
smooth with respect to
can be performed by performing combinations of
erosions and dilations
Opening V/S Closing
Opening
AB is a subset
(subimage) of A
If C is a subset of D,
then C B is a subset
of D B
(A B) B = A B
Closing
A is a subset
(subimage) of AB
If C is a subset of D,
then C B is a subset
of D B
(A B) B = A B
Note: repeated openings/closings has no effect!
Hit or Miss Transformation
Useful to identify specified configuration of pixels,
such as, isolated foreground pixels or pixels at end
of lines (end points)
)2()1(* BABABA
Morphological Algorithms
Using the simple technique we have
looked at so far we can begin to consider
some more interesting morphological
algorithms
We will look at:
Boundary extraction
Extracting the boundary (or outline) of an object
is often extremely useful
The boundary can be given simply as
β(A) = A – (AB)
Boundary Extraction
A simple image and the result of
performing boundary extraction using a
square structuring element
Original Image Extracted Boundary
Example
Conclusion
Morphology is powerful set of tools for extracting
features in an image
We implement algorithms like Thinning thickening
Skeletons etc. various purpose of image
processing activities like semantation.