661e432fd7a2bWeek6,7.pdf digital image processing

It the slides of digital image processing

1. Digital Image Processing
Spring 2024
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2. Material taken from:
Digital Image Processing by Gonzalez and Woods –4
th
Edition
Week 6, 7
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3. Morphological Image Processing
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4. •In image processing, we use morphology with two types of sets of pixels: objects
and structuring elements (SE’s).
•Typically, objects are defined as sets of foreground pixels.
•Structuring elements can be specified in terms of both foreground and background pixels.
•In forming rectangular arrays for digital image processing we assign a background
value to all pixels that are not members of object sets
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5. Structuring elements
•A structuring element is a small image –used as a moving window
Structuring elements and their reflections about the origin
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6. •MorphologicalImageprocessingislikespatialfiltering,inthatthe
structuringelementismovedlikeawindowacrossthewholeimage,
tofindvaluesofpixelsinanewimage.
•Thevalueofthisnewpixeldependsontheoperationperformed
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7. Basic Morphological Operations
•Erosion
•ErosionofAbyBisthesetofallpointszsuchthatB,translatedbyz,is
containedinA
•Inabinaryimage,ifanyofthepixel(intheneighbourhooddefinedby
structuringelement)is0,thenoutputis0
•Dilation
•DilationofAbyBisthesetofalldisplacements,z,suchthattheforeground
elementsofB̂overlapatleastoneelementofA
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8. 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:
��,�=
1??????���??????���
0??????�ℎ���??????��
•For each foreground pixel, superimpose the structuring element on top of
the input image so that the origin of the structuring element coincides with
the input pixel position.
•If for every pixel in the structuring element, the corresponding pixel in the
image underneath is a foreground pixel, then the input pixel is left as it is.
•If any of the corresponding pixels in the image are background, however,
the input pixel is also set to background value.
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9. Erosion
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Input Image Output Image
Structuring Element
https://penny-xu.github.io/blog/mathematical-
morphology

11. Erosion
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12. •Erosion can split apart joined objects
•Erosion can remove extrusions
•Erosion shrinks objects
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13. Erosion
•A binary image of a wire-
bond mask in which
foreground pixels are shown
in white.
•Image eroded using square
structuring elements of sizes
11x11 15x15 and 45x45
elements, respectively, all
valued 1.
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14. •Count the number of objects using MATLAB
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15. Dilation
•Dilationofimagefbystructuringelementsisgivenbyf⊕s
•Thestructuringelementsispositionedwithitsoriginat(x,y)andthenewpixel
valueisdeterminedusingtherule:
•��,�=
1??????��ℎ??????���
0??????�ℎ���??????��
•Foreachbackgroundpixelsuperimposethestructuringelementontopofthe
inputimagesothattheoriginofthestructuringelementcoincideswiththeinput
pixelposition
•Ifatleastonepixelinthestructuringelementcoincideswithaforegroundpixelin
theimageunderneath,thentheinputpixelissettotheforegroundvalue
•Ifallthecorrespondingpixelsintheimagearebackground,however,theinput
pixelisleftatthebackgroundvalue
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16. Dilation
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Input Image Output Image
Structuring Element
https://penny-xu.github.io/blog/mathematical-
morphology

18. Dilation
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19. •Dilation can
•Repair breaks
•Repair intrusions
•Enlarge objects
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21. Compound Operators
•Combinations of erosion and dilation
•Opening
•Closing
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22. Opening
•Erosion followed by dilation
•Denoted by f⃝s
•f⃝s = (f⊖ s)⊕s
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23. Opening
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24. Closing
•Dilation followed by erosion
•Denoted by f●s
•f●s = (f⊕ s)⊖ s
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25. Closing
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27. Hit or Miss Transform
•I ◉B= {z|(B )
Z ⊆I }
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30. Morphological Algorithms
•Boundary Extraction
•Region Filling
•Connected Components Extraction
•Skeleton Extraction
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31. Boundary Extraction
•TheboundaryofsetAdenotedbyβ(A)isobtainedbyfirsterodingA
byasuitablestructuringelementBandthentakingthedifference
betweenAanditserosion.
•ꞵ(A) = A–(A⊖ B)
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32. •Boundary extraction using a 3 x 3 square structuring element
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33. Region Filling
•Ahole may be defined as a background region surrounded by a
connected border of foreground pixels.
•Steps:
•Start from a known point p and take X
0= p,
•Then take the next values of X
kas: X
k= (X
k-1⊕ B ) ⋂ A
C
•Terminate iterations if X
k= X
k-1
•The intersection of dilation and the complement of A limits the result to
inside the region of interest
•The set union of X
kand A contains the filled set and its boundaries
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36. Extraction of connected components
•Steps:
•Start from a known point p and take X
0= p,
•Then take the next values of X
kas: X
k= (X
k-1⊕ B ) ⋂ A
•Terminate iterations if X
k= X
k-1
•The component Y is given as Y = X
k
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38. Skeleton
•If z is a point of S(A), and (D)
Zis the largest disk centeredat z and
contained in A, one cannot find a larger disk (not necessarily centered
at z) containing (D)
Z and simultaneously included in A. A disk (D)
Z
satisfying these conditions is called a maximum disk.
•If (D)
Z is a maximum disk, it touches the boundary of A at two or more
different places.
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39. Skeleton
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42. End
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