The document discusses morphological image processing, focusing on operations such as erosion, dilation, opening, and closing, which are used to analyze and enhance image features. It explains the mathematical foundations, including set theory and structuring elements, to manipulate image boundaries and shapes. Additionally, it outlines practical applications and advantages of these morphological techniques in image analysis.

1. COMPUTER GRAPHICS & IMAGE PROCESSING
COM2304
Morphological Image Processing
K.A.S.H.Kulathilake
B.Sc. (Hons) IT (SLIIT), MCS (UCSC), M.Phil (UOM), SEDA(UK)
Rajarata University of Sri Lanka
Faculty of Applied Sciences
Department of Physical Sciences

2. Learning Outcomes
COM2304 - Computer Graphics & Image
Processing
• At the end of this lecture, you should be
able to;
– describe the importance of morphological
features in an image.
– describe the operation of erosion, dilation,
open and close operations.
– identify the practical advantage of the
morphological operations.
– apply morphological operations for problem
solving.
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3. Introduction
• Mathematical morphology is a tool for
extracting image components that are useful
in the representation and description of the
region shape, such as boundaries and
skeletons.
• Morphological operations are typically applied
to remove imperfections introduced during
segmentation, and so typically operate on bi-
level images.
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4. Introduction (Cont…)
• The language of mathematical morphology is set
theory.
• Sets in mathematical morphology represent objects
in an image.
– Ex: binary image – set represents 2D integer space
denoted as Z2 and consists of x,y coordinates.
– Gray scale image – set represents components in
Z3 which means x,y coordinates and discrete
intensity value.
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5. Introduction (Cont…)
• The concept of set reflection
and translation are extensively
used in mathematical
morphology.
• In reflection the set of points
in B whose ( x, y) coordinates
have been replaced by (-x,-y).
• In translation the set of points
in B whose ( x, y) coordinates
have been replaced by (x+z1,
y+z2).
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Reflection
Translation

6. Introduction (Cont…)
• Structure elements (SE)
– Small sets or sub-images used to probe an image
under study for properties of interest.
– Structuring elements can be any size and make
any shape.
– However, for simplicity we will use rectangular
structuring elements with their origin at the
middle pixel.
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7. Introduction (Cont…)
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8. Introduction (Cont…)
• Unlike convolution kernels, morphological
kernels/ structuring elements do not require
numerical values.
• OpenCV support to create SE of different
shapes like; rectangular, cross shape, elliptical
and user defined shapes.
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9. Introduction (Cont…)
B
A
C
Structuring Element
Structuring Elements, Hits &
Fits:
Fit: All on pixels in the
structuring element cover on
pixels in the image
Hit: Any on pixel in the
structuring element covers an
on pixel in the image
All morphological processing operations are based on
these simple ideas
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10. Introduction (Cont…)
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Accommodate the
entire structuring
elements when its
origin is on the
border of the
original set A
Origin of B visits
every element of A
At each location of
the origin of B, if B is
completely
contained in A, then
the location is a
member of the new
set, otherwise it is
not a member of the
new set.
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11. Introduction (Cont…)
• Fundamentally morphological image
processing is very like spatial filtering.
• The structuring element is moved across every
pixel in the original image to give a pixel in a
new processed image.
• The value of this new pixel depends on the
operation performed.
• There are two basic morphological operations:
erosion and dilation
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12. Erosion and Dilation
• 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:
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



otherwise0
fitsif1
),(
fs
yxg

13. Erosion and Dilation (Cont…)
Structuring Element
Original Image Processed Image With Eroded Pixels
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14. Erosion and Dilation (Cont…)
Structuring Element
Original Image Processed Image
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15. Erosion and Dilation (Cont…)
Watch out: In these examples a 1 refers to a black pixel!
Original image Erosion by 3*3
square structuring
element
Erosion by 5*5 square
structuring element
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16. Erosion and Dilation (Cont…)
Erosion can split apart joined objects
Erosion can strip away extrusions
Watch out: Erosion shrinks objects
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17. Erosion and Dilation (Cont…)
• 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:
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




otherwise0
hitsif1
),(
fs
yxg

18. Erosion and Dilation (Cont…)
Structuring Element
Original Image Processed Image
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19. Erosion and Dilation (Cont…)
Structuring Element
Original Image Processed Image With Dilated Pixels
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20. Erosion and Dilation (Cont…)
Structuring element
Original image After dilation
ImagestakenfromGonzalez&Woods,DigitalImageProcessing(2002)
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21. Erosion and Dilation (Cont…)
Dilation can repair breaks
Dilation can repair intrusions
Watch out: Dilation enlarges objects
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22. Morphological Gradient
Gradient(src) = dilate(src) – erode(src)
• The effect of this operation on a Boolean image
would be simply to isolate perimeters of existing
blobs.
• With a grayscale image we see that the value of
operator is telling us something about how fast
the image brightness is changing.
• Morphological gradient is often used when we
want to isolate the perimeters of bright regions
so we can treat them as whole objects.
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23. Morphological Gradient (Cont…)
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24. Opening and Closing
• More interesting morphological operations
can be performed by performing
combinations of erosions and dilations.
• The most widely used of these compound
operations are:
– Opening
– Closing
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25. Opening and Closing (Cont…)
• Opening
– The opening of image f by structuring element s,
denoted f ○ s is simply an erosion followed by a
dilation
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26. Opening and Closing (Cont…)
Original
Image
Image
After
Opening
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27. Opening and Closing (Cont…)
Structuring Element
Original Image Processed Image
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28. Opening and Closing (Cont…)
Structuring Element
Original Image Processed Image
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29. Opening and Closing (Cont…)
• Closing
– The closing of image f by structuring element s,
denoted f • s is simply a dilation followed by an
erosion.
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30. Opening and Closing (Cont…)
Original
Image
Image
After
Closing
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31. Opening and Closing (Cont…)
Structuring Element
Original Image Processed Image
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32. Opening and Closing (Cont…)
Structuring Element
Original Image Processed Image
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33. Opening and Closing (Cont…)
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34. Opening and Closing (Cont…)
• Opening generally smoothes the contour of an
object, breaks narrow isthmuses, and
eliminates thin protrusions.
• Closing smoothes sections of contours, but
opposed to opening.
• It generally fuses narrow breaks and long thin
gulfs, eliminates small holes, and fills gaps in
the contour.
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35. Top Hat and Black Hat
• These operators are used to isolate patches
that are, respectively brighter or dimmer than
their immediate neighbors.
• You would use these when trying to isolate
parts of an object that exhibits brightness
changes relative only to the object to which
they have attached.
• This often occurs with microscope images of
organisms or cells.
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36. Top Hat and Black Hat (Cont…)
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TopHat (src) =
src – open(src)
Subtracting the
open from src
should reveal
areas that are
lighter than the
surrounding
region of src.

37. Top Hat and Black Hat (Cont…)
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Black Hat (src) =
close (src)- src
Back hat
operation reveals
areas that are
darker than the
surrounding
region of src.

38. Boundary Extraction
A simple image and the result of performing boundary
extraction using a square 3*3 structuring element
Original Image Extracted Boundary
B(A) = A – (A  B)
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39. Region Filling
Given a pixel inside a boundary, region filling
attempts to fill that boundary with object pixels
(1s)
Given a point inside
here, can we fill the
whole circle?
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40. Region Filling (Cont…)
• The key equation for region filling is;
Where X0 is simply the starting point inside the
boundary, B is a simple structuring element and
Ac is the complement of A.
• This equation is applied repeatedly until Xk is
equal to Xk-1
• Finally the result is unioned with the original
boundary
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.....3,2,1)( 1   kABXX c
kk

41. Region Filling (Cont…)
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https://www.youtube.com/watch?v=5DcCI2HCi8k

42. Reference
• Chapter 09 of Gonzalez, R.C., Woods, R.E.,
Digital Image Processing, 3rd ed. Addison-
Wesley Pub.
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43. Learning Outcomes Revisit
• Now, you should be able to;
– describe the importance of morphological
features in an image.
– describe the operation of erosion, dilation,
open and close operations.
– identify the practical advantage of the
morphological operations.
– apply morphological operations for problem
solving.
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Processing
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44. QUESTIONS ?
Next Lecture – Segmentation Techniques
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