Digital Image Processing Chapter 9: Morphological Image …pkalra/csl783/Morphological.pdf · 2013....
Transcript of Digital Image Processing Chapter 9: Morphological Image …pkalra/csl783/Morphological.pdf · 2013....
![Page 1: Digital Image Processing Chapter 9: Morphological Image …pkalra/csl783/Morphological.pdf · 2013. 11. 21. · 2 Mathematic Morphology! used to extract image components that are](https://reader033.fdocuments.in/reader033/viewer/2022060922/60ae2ddabebb8719f6696739/html5/thumbnails/1.jpg)
Chapter 9: Morphological Image Processing
Digital Image Processing
![Page 2: Digital Image Processing Chapter 9: Morphological Image …pkalra/csl783/Morphological.pdf · 2013. 11. 21. · 2 Mathematic Morphology! used to extract image components that are](https://reader033.fdocuments.in/reader033/viewer/2022060922/60ae2ddabebb8719f6696739/html5/thumbnails/2.jpg)
2
Mathematic Morphology n used to extract image components that are
useful in the representation and description of region shape, such as n boundaries extraction n skeletons n convex hull n morphological filtering n thinning n pruning
![Page 3: Digital Image Processing Chapter 9: Morphological Image …pkalra/csl783/Morphological.pdf · 2013. 11. 21. · 2 Mathematic Morphology! used to extract image components that are](https://reader033.fdocuments.in/reader033/viewer/2022060922/60ae2ddabebb8719f6696739/html5/thumbnails/3.jpg)
3
Basic Set Theory
![Page 4: Digital Image Processing Chapter 9: Morphological Image …pkalra/csl783/Morphological.pdf · 2013. 11. 21. · 2 Mathematic Morphology! used to extract image components that are](https://reader033.fdocuments.in/reader033/viewer/2022060922/60ae2ddabebb8719f6696739/html5/thumbnails/4.jpg)
4
Reflection and Translation
} ,|{ˆ Bfor bbwwB ∈−∈=
} ,|{)( Afor azaccA z ∈+∈=
![Page 5: Digital Image Processing Chapter 9: Morphological Image …pkalra/csl783/Morphological.pdf · 2013. 11. 21. · 2 Mathematic Morphology! used to extract image components that are](https://reader033.fdocuments.in/reader033/viewer/2022060922/60ae2ddabebb8719f6696739/html5/thumbnails/5.jpg)
5
Example
![Page 6: Digital Image Processing Chapter 9: Morphological Image …pkalra/csl783/Morphological.pdf · 2013. 11. 21. · 2 Mathematic Morphology! used to extract image components that are](https://reader033.fdocuments.in/reader033/viewer/2022060922/60ae2ddabebb8719f6696739/html5/thumbnails/6.jpg)
Structuring element (SE)
6
§ small set to probe the image under study § for each SE, define origo § shape and size must be adapted to geometric properties for the objects
![Page 7: Digital Image Processing Chapter 9: Morphological Image …pkalra/csl783/Morphological.pdf · 2013. 11. 21. · 2 Mathematic Morphology! used to extract image components that are](https://reader033.fdocuments.in/reader033/viewer/2022060922/60ae2ddabebb8719f6696739/html5/thumbnails/7.jpg)
Basic morphological operations n Erosion
n Dilation n combine to
n Opening object n Closening background
7
keep general shape but smooth with respect to
![Page 8: Digital Image Processing Chapter 9: Morphological Image …pkalra/csl783/Morphological.pdf · 2013. 11. 21. · 2 Mathematic Morphology! used to extract image components that are](https://reader033.fdocuments.in/reader033/viewer/2022060922/60ae2ddabebb8719f6696739/html5/thumbnails/8.jpg)
Erosion n Does the structuring element fit the set?
erosion of a set A by structuring element B: all z in A such that B is in A when origin of B=z
shrink the object
8
}{ Az|(B)BA z ⊆=−
![Page 9: Digital Image Processing Chapter 9: Morphological Image …pkalra/csl783/Morphological.pdf · 2013. 11. 21. · 2 Mathematic Morphology! used to extract image components that are](https://reader033.fdocuments.in/reader033/viewer/2022060922/60ae2ddabebb8719f6696739/html5/thumbnails/9.jpg)
Erosion
9
![Page 10: Digital Image Processing Chapter 9: Morphological Image …pkalra/csl783/Morphological.pdf · 2013. 11. 21. · 2 Mathematic Morphology! used to extract image components that are](https://reader033.fdocuments.in/reader033/viewer/2022060922/60ae2ddabebb8719f6696739/html5/thumbnails/10.jpg)
Erosion
10
![Page 11: Digital Image Processing Chapter 9: Morphological Image …pkalra/csl783/Morphological.pdf · 2013. 11. 21. · 2 Mathematic Morphology! used to extract image components that are](https://reader033.fdocuments.in/reader033/viewer/2022060922/60ae2ddabebb8719f6696739/html5/thumbnails/11.jpg)
11
Erosion
}{ Az|(B)BA z ⊆=−
![Page 12: Digital Image Processing Chapter 9: Morphological Image …pkalra/csl783/Morphological.pdf · 2013. 11. 21. · 2 Mathematic Morphology! used to extract image components that are](https://reader033.fdocuments.in/reader033/viewer/2022060922/60ae2ddabebb8719f6696739/html5/thumbnails/12.jpg)
Dilation n Does the structuring element hit the set?
n dilation of a set A by structuring element B: all z in A such that B hits A when origin of B=z
n grow the object 12
}ˆ{ ΦA)Bz|(BA z ≠∩=⊕
![Page 13: Digital Image Processing Chapter 9: Morphological Image …pkalra/csl783/Morphological.pdf · 2013. 11. 21. · 2 Mathematic Morphology! used to extract image components that are](https://reader033.fdocuments.in/reader033/viewer/2022060922/60ae2ddabebb8719f6696739/html5/thumbnails/13.jpg)
Dilation
13
![Page 14: Digital Image Processing Chapter 9: Morphological Image …pkalra/csl783/Morphological.pdf · 2013. 11. 21. · 2 Mathematic Morphology! used to extract image components that are](https://reader033.fdocuments.in/reader033/viewer/2022060922/60ae2ddabebb8719f6696739/html5/thumbnails/14.jpg)
Dilation
14
![Page 15: Digital Image Processing Chapter 9: Morphological Image …pkalra/csl783/Morphological.pdf · 2013. 11. 21. · 2 Mathematic Morphology! used to extract image components that are](https://reader033.fdocuments.in/reader033/viewer/2022060922/60ae2ddabebb8719f6696739/html5/thumbnails/15.jpg)
15
Dilation
}ˆ{ ΦA)Bz|(BA z ≠∩=⊕
B = structuring element
![Page 16: Digital Image Processing Chapter 9: Morphological Image …pkalra/csl783/Morphological.pdf · 2013. 11. 21. · 2 Mathematic Morphology! used to extract image components that are](https://reader033.fdocuments.in/reader033/viewer/2022060922/60ae2ddabebb8719f6696739/html5/thumbnails/16.jpg)
16
Dilation : Bridging gaps
![Page 17: Digital Image Processing Chapter 9: Morphological Image …pkalra/csl783/Morphological.pdf · 2013. 11. 21. · 2 Mathematic Morphology! used to extract image components that are](https://reader033.fdocuments.in/reader033/viewer/2022060922/60ae2ddabebb8719f6696739/html5/thumbnails/17.jpg)
useful n erosion
n removal of structures of certain shape and size, given by SE
n Dilation n filling of holes of certain shape and size,
given by SE
17
![Page 18: Digital Image Processing Chapter 9: Morphological Image …pkalra/csl783/Morphological.pdf · 2013. 11. 21. · 2 Mathematic Morphology! used to extract image components that are](https://reader033.fdocuments.in/reader033/viewer/2022060922/60ae2ddabebb8719f6696739/html5/thumbnails/18.jpg)
Combining erosion and dilation
n WANTED: n remove structures / fill holes n without affecting remaining parts
n SOLUTION: n combine erosion and dilation n (using same SE)
18
![Page 19: Digital Image Processing Chapter 9: Morphological Image …pkalra/csl783/Morphological.pdf · 2013. 11. 21. · 2 Mathematic Morphology! used to extract image components that are](https://reader033.fdocuments.in/reader033/viewer/2022060922/60ae2ddabebb8719f6696739/html5/thumbnails/19.jpg)
19
Erosion : eliminating irrelevant detail
structuring element B = 13x13 pixels of gray level 1
![Page 20: Digital Image Processing Chapter 9: Morphological Image …pkalra/csl783/Morphological.pdf · 2013. 11. 21. · 2 Mathematic Morphology! used to extract image components that are](https://reader033.fdocuments.in/reader033/viewer/2022060922/60ae2ddabebb8719f6696739/html5/thumbnails/20.jpg)
Opening erosion followed by dilation, denoted ∘
n eliminates protrusions n breaks necks n smoothes contour
20
BBABA ⊕−= )(
![Page 21: Digital Image Processing Chapter 9: Morphological Image …pkalra/csl783/Morphological.pdf · 2013. 11. 21. · 2 Mathematic Morphology! used to extract image components that are](https://reader033.fdocuments.in/reader033/viewer/2022060922/60ae2ddabebb8719f6696739/html5/thumbnails/21.jpg)
Opening
21
![Page 22: Digital Image Processing Chapter 9: Morphological Image …pkalra/csl783/Morphological.pdf · 2013. 11. 21. · 2 Mathematic Morphology! used to extract image components that are](https://reader033.fdocuments.in/reader033/viewer/2022060922/60ae2ddabebb8719f6696739/html5/thumbnails/22.jpg)
Opening
22
![Page 23: Digital Image Processing Chapter 9: Morphological Image …pkalra/csl783/Morphological.pdf · 2013. 11. 21. · 2 Mathematic Morphology! used to extract image components that are](https://reader033.fdocuments.in/reader033/viewer/2022060922/60ae2ddabebb8719f6696739/html5/thumbnails/23.jpg)
23
Opening
BBABA ⊕−= )(})(|){( ABBBA zz ⊆∪=
![Page 24: Digital Image Processing Chapter 9: Morphological Image …pkalra/csl783/Morphological.pdf · 2013. 11. 21. · 2 Mathematic Morphology! used to extract image components that are](https://reader033.fdocuments.in/reader033/viewer/2022060922/60ae2ddabebb8719f6696739/html5/thumbnails/24.jpg)
Closing dilation followed by erosion, denoted • n smooth contour n fuse narrow breaks and long thin gulfs n eliminate small holes n fill gaps in the contour
24
BBABA −⊕=• )(
![Page 25: Digital Image Processing Chapter 9: Morphological Image …pkalra/csl783/Morphological.pdf · 2013. 11. 21. · 2 Mathematic Morphology! used to extract image components that are](https://reader033.fdocuments.in/reader033/viewer/2022060922/60ae2ddabebb8719f6696739/html5/thumbnails/25.jpg)
Closing
25
![Page 26: Digital Image Processing Chapter 9: Morphological Image …pkalra/csl783/Morphological.pdf · 2013. 11. 21. · 2 Mathematic Morphology! used to extract image components that are](https://reader033.fdocuments.in/reader033/viewer/2022060922/60ae2ddabebb8719f6696739/html5/thumbnails/26.jpg)
Closing
26
![Page 27: Digital Image Processing Chapter 9: Morphological Image …pkalra/csl783/Morphological.pdf · 2013. 11. 21. · 2 Mathematic Morphology! used to extract image components that are](https://reader033.fdocuments.in/reader033/viewer/2022060922/60ae2ddabebb8719f6696739/html5/thumbnails/27.jpg)
27
Closing
BBABA −⊕=• )(
![Page 28: Digital Image Processing Chapter 9: Morphological Image …pkalra/csl783/Morphological.pdf · 2013. 11. 21. · 2 Mathematic Morphology! used to extract image components that are](https://reader033.fdocuments.in/reader033/viewer/2022060922/60ae2ddabebb8719f6696739/html5/thumbnails/28.jpg)
28
Properties
Opening (i) A°B is a subset (subimage) of A (ii) If C is a subset of D, then C °B is a subset of D °B (iii) (A °B) °B = A °B
Closing (i) A is a subset (subimage) of A•B (ii) If C is a subset of D, then C •B is a subset of D •B (iii) (A •B) •B = A •B
Note: repeated openings/closings has no effect!
![Page 29: Digital Image Processing Chapter 9: Morphological Image …pkalra/csl783/Morphological.pdf · 2013. 11. 21. · 2 Mathematic Morphology! used to extract image components that are](https://reader033.fdocuments.in/reader033/viewer/2022060922/60ae2ddabebb8719f6696739/html5/thumbnails/29.jpg)
Duality n Opening and closing are dual with respect
to complementation and reflection
29
)ˆ()( BABA cc =•
![Page 30: Digital Image Processing Chapter 9: Morphological Image …pkalra/csl783/Morphological.pdf · 2013. 11. 21. · 2 Mathematic Morphology! used to extract image components that are](https://reader033.fdocuments.in/reader033/viewer/2022060922/60ae2ddabebb8719f6696739/html5/thumbnails/30.jpg)
30
![Page 31: Digital Image Processing Chapter 9: Morphological Image …pkalra/csl783/Morphological.pdf · 2013. 11. 21. · 2 Mathematic Morphology! used to extract image components that are](https://reader033.fdocuments.in/reader033/viewer/2022060922/60ae2ddabebb8719f6696739/html5/thumbnails/31.jpg)
31
![Page 32: Digital Image Processing Chapter 9: Morphological Image …pkalra/csl783/Morphological.pdf · 2013. 11. 21. · 2 Mathematic Morphology! used to extract image components that are](https://reader033.fdocuments.in/reader033/viewer/2022060922/60ae2ddabebb8719f6696739/html5/thumbnails/32.jpg)
Useful: open & close
32
![Page 33: Digital Image Processing Chapter 9: Morphological Image …pkalra/csl783/Morphological.pdf · 2013. 11. 21. · 2 Mathematic Morphology! used to extract image components that are](https://reader033.fdocuments.in/reader033/viewer/2022060922/60ae2ddabebb8719f6696739/html5/thumbnails/33.jpg)
Application: filtering
33
![Page 34: Digital Image Processing Chapter 9: Morphological Image …pkalra/csl783/Morphological.pdf · 2013. 11. 21. · 2 Mathematic Morphology! used to extract image components that are](https://reader033.fdocuments.in/reader033/viewer/2022060922/60ae2ddabebb8719f6696739/html5/thumbnails/34.jpg)
Hit-or-Miss Transformation ⊛ (HMT)
n find location of one shape among a set of shapes ”template matching
n composite SE: object part (B1) and background part (B2)
n does B1 fits the object while, simultaneously, B2 misses the object, i.e., fits the background?
34
![Page 35: Digital Image Processing Chapter 9: Morphological Image …pkalra/csl783/Morphological.pdf · 2013. 11. 21. · 2 Mathematic Morphology! used to extract image components that are](https://reader033.fdocuments.in/reader033/viewer/2022060922/60ae2ddabebb8719f6696739/html5/thumbnails/35.jpg)
35
Hit-or-Miss Transformation
)]([)( XWAXABA c −−∩−=∗
![Page 36: Digital Image Processing Chapter 9: Morphological Image …pkalra/csl783/Morphological.pdf · 2013. 11. 21. · 2 Mathematic Morphology! used to extract image components that are](https://reader033.fdocuments.in/reader033/viewer/2022060922/60ae2ddabebb8719f6696739/html5/thumbnails/36.jpg)
36
Boundary Extraction
)()( BAAA −−=β
![Page 37: Digital Image Processing Chapter 9: Morphological Image …pkalra/csl783/Morphological.pdf · 2013. 11. 21. · 2 Mathematic Morphology! used to extract image components that are](https://reader033.fdocuments.in/reader033/viewer/2022060922/60ae2ddabebb8719f6696739/html5/thumbnails/37.jpg)
37
Example
![Page 38: Digital Image Processing Chapter 9: Morphological Image …pkalra/csl783/Morphological.pdf · 2013. 11. 21. · 2 Mathematic Morphology! used to extract image components that are](https://reader033.fdocuments.in/reader033/viewer/2022060922/60ae2ddabebb8719f6696739/html5/thumbnails/38.jpg)
38
Region Filling ,...3,2,1 )( 1 =∩⊕= − kABXX c
kk
![Page 39: Digital Image Processing Chapter 9: Morphological Image …pkalra/csl783/Morphological.pdf · 2013. 11. 21. · 2 Mathematic Morphology! used to extract image components that are](https://reader033.fdocuments.in/reader033/viewer/2022060922/60ae2ddabebb8719f6696739/html5/thumbnails/39.jpg)
39
Example