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Dr. Chittaranjan Verma delivered this lecture for Digital Image Processing course at B R Ambedkar National Institute of Technology. It includes: Announcement, Erosion, Dilation, Closing, Opening, Hit, Transforms, Compared
Typology: Slides
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Quiz # 3 will be held on Friday May 7, 2010^
Starting time: 8:15am ^
Syllabus: Chapters 6 (Color image processing) & 9(Morphological image processing) ^
Pattern of this quiz will be same as that of Quiz # 1 & 2
The best 2 quizzes of each student are included inthe final grading
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Recap ^
DilationExpands the size of 1-valued objects, Smooth object boundaries,Closes holes and gaps ^
ErosionShrinks the size of 1-valued objects, Smooth object boundaries,Removes small objects ^
ClosingErosion followed by Dilation
breaks narrow joints and eliminates
thin protrusions ^
OpeningDilation followed by Erosion
Fill gaps, eliminate small holes,
fuses narrow breaks ^
Hit or Miss transformA tool for shape detection or for the detection of a disjoint region inan image
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is obtained by
first eroding A by a suitable structuring element B andthen taking the difference between A and its erosion,i.e.
(^
)^
(^
)
A
A
A
B
Note: Using a 5x5 structuring element of 1s would results in a boundarybetween 2 and 3 pixels thick
3x3 structuringelement of 1s
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Example:
(^
)
1, 2,3,
c
k^
k
X
X
B
A
k
NOTE:The intersection ofdilation and thecomplement of Alimits the result toinside the region ofinterest
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Example:
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Convex setA set
A
is said to be convex if any straight line segment
joining two points of
A
lies within
A
^
Example: R
1
is convex as line segment pq lies within set
R
1
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To find the Convex Hull
C(A)
of a set
A
the following
simple morphological algorithm can be used: ^
Let
B
i , where
i^
= 1, 2, 3, 4, represent four structuring elements
^
Implement: ^
Starting with: ^
Repeat 2
nd
step until convergence, i.e.
^
Convex Hull
C(A)
1^ is given by:
i^
i
k^
k
i
1
i^
i^
i^
i
conv
k^
k
4 1
(^
)^
i
i
C A
D
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The method consists of iteratively applying the hit-or-miss transform to
with
1 ; when no further
changes occur, we perform the union with A and callthe result
1
The method is repeated with
3
and
4
resulting
in
3
and
(^4)
The union of four
Ds
constitutes the convex hull of
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ShortcomingConvex hull can grow beyond the minimumdimensions required to guarantee convexity
Possible solutionLimit growth so that it does not extend past thevertical and horizontal dimensions of the original setof points
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Thinning of a set
by the structuring element
can
be defined in terms of hit-or-miss transform as:
Symmetric thinning: Sequence of structure elements
The process is to thin
A
by one pass with
B
1 , the thin the result with
one pass of
B
2 , and so on, until
A
is thinned with one pass of
B
n.
The entire process is repeated until no further changes occur
1
2
3
1
where
,^ is a rotated version of
,^
,^
,
i
n
i
B
B
B B
B
B
B
1
2
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As in thinning, thickening of a set
by the
structuring element
can be defined in terms of hit-
or-miss transform as: where
is a structuring element
Thickening can also be defined as a sequentialoperation
(^
)
A
B
A
A
B
1
2
(^
((
)^
)^
) n
A
B
A
B
B
B
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Thickening is dual of thinning
Note: A separate algorithm for thickening is usuallynot implemented, rather the thinning algorithm isused
by
providing
the
complement
of
and
by
interchanging
the
1s
and
0s
in
the
structuring
element. The result is complemented in order to getthe thickened version
