1. Lecture Two for teens

2. Introduction to Morphological Operators

3. About this lecture
In this lecture we introduce INFORMALLY the most important operations based on morphology, just to give you the intuitive feeling.
In next lectures we will introduce more formalism and more examples.

4. Binary Morphological Processing
Non-linear image processing technique
Order of sequence of operations is important
Linear: (3+2)*3 = (5)*3=15
3*3+2*3=9+6=15
Non-linear: (3+2)2 + (5)2 =25 [sum, then square]
(3)2 + (2)2 =9+4=13 [square, then sum]
Based on geometric structure
Used for edge detection, noise removal and feature extraction
 Used to ‘understand’ the shape/form of a binary image

5. Introduction Structuring Element Erosion Dilation Opening Closing
Hit-and-miss
Thinning
Thickening

6. 1D Morphological Operations

7. Example for 1D Erosion 1 1 Input image Structuring Element1
Structuring Element
Output Image

8. Example for Erosion
Input image 1 1
Structuring Element
Output Image

9. Example for Erosion
Input image 1 1
Structuring Element
Output Image

10. Example for Erosion
Input image 1 1
Structuring Element
Output Image

11. Example for Erosion 1 1 1 Input image Structuring Element Output Image1
Structuring Element
Output Image 1
Structured element is completely included in set of ones

12. Example for Erosion
Input image 1 1
Structuring Element
Output Image 1

13. Example for Erosion
Input image 1 1
Structuring Element
Output Image 1

14. Example for Erosion
Input image 1 1
Structuring Element
Output Image 1

15. Example for 1D Dilation 1 1 1 Input image Structuring Element1
Structuring Element
Output Image 1
Structuring element overlaps with input image

16. Example for Dilation 1 1 1 Input image Structuring Element1
Structuring Element
Output Image 1

17. Example for Dilation 1 1 1 Input image Structuring Element1
Structuring Element
Output Image 1

18. Example for Dilation 1 1 1 Input image Structuring Element1
Structuring Element
Output Image 1

19. Example for Dilation 1 1 1 Input image Structuring Element1
Structuring Element
Output Image 1

20. Example for Dilation 1 1 1 Input image Structuring Element1
Structuring Element
Output Image 1

21. Example for Dilation 1 1 1 Input image Structuring Element1
Structuring Element
Output Image 1

22. Example for Dilation 1 1 1 Input image Structuring Element1
Structuring Element
Output Image 1

23. 2D Morphological Operations

24. Image – Set of Pixels
Basic idea is to treat an object within an image as a set of pixels (or coordinates of pixels)
In binary images, pixels that are ‘off’, set to 0, are background and appear black.
Foreground pixels (objects) are 1 and appear white

25. Neighborhood
Set of pixels defined by their location relation to the pixel of interest
Defined by structuring element
Specified by connectivity
Connectivity-
‘4-connected’
‘8-connected’

26. Labeling Connected Components
Label objects in an image
4-Neighbors
8-Neighbors p p

27. 4 and 8 Connect
Input Image – Connect Connect

28. Morphological Image Processing
Basic operations on shapes
From: Digital Image Processing, Gonzalez,Woods
And Eddins

29. Morphological Image Processing
From: Digital Image Processing, Gonzalez,Woods
And Eddins

30. Operations on binary images in MATLAB
From: Digital Image Processing, Gonzalez,Woods
And Eddins

31. Translation of Object A by vector b
Define Translation ob object A by vector b:
At = { t  I2 : t = a+b, a  A }
Where I2 is the two dimensional image space that contains the image
Definition of DILATION is the UNION of all the translations:
A B =  { t  I2 : t = a+b, a  A } for all b’s in B

32. Structuring Element (Kernel)
Structuring Elements can have varying sizes
Usually, element values are 0,1 and none(!)
Structural Elements have an origin
For thinning, other values are possible
Empty spots in the Structuring Elements are don’t care’s!
Box
Disc
Examples of stucturing elements
24-Apr-17

33. Reflection of the structuring element
From: Digital Image Processing, Gonzalez,Woods
And Eddins

34. Idea of DILATION versus TRANSLATION
Object B is one point located at (a,0) A1: Object A is translated by object B
Since dilation is the union of all the translations, A B =  At where the set union  is for all the b’s in B, the dilation of rectangle A in the positive x direction by a results in rectangle A1 (same size as A, just translated to the right)

35. DILATION – B has 2 Elements
A A1
(part of A1 is under A2)
-a a a a
Object B is 2 points, (a,0), (-a,0)
There are two translations of A as result of two elements in B
Dilation is defined as the UNION of the objectsA1 and A2.
NOT THE INTERSECTION

36. 2D DILATION

37. DILATION Rounded corners
Round Structuring Element (SE) can be interpreted
as rolling the SE around the contour of the object.
New object has rounded corners and is larger in every direction by
½ width of the SE

38. DILATION Rounded corners
Square Structuring Element (SE) can be interpreted
as moving the SE around the contour of the object.
New object has square corners and is larger in every direction by
½ width of the SE

39. DILATION
The shape of B determines the final shape of the dilated object.
B acts as a geometric filter that changes the geometric structure of A

40. 2D EROSION

41. Another important operator
Introduction to Morphological Operators
Used generally on binary images, e.g., background subtraction results!
Used on gray value images, if viewed as a stack to binary images.
Good for, e.g.,
Noise removal in background
Removal of holes in foreground / background
Check:

42. A first Example: Erosion
Erosion is an important morphological operation
Applied Structuring Element:

43. Dilation versus Erosion
Basic operations
Are dual to each other:
Erosion shrinks foreground, enlarges Background
Dilation enlarges foreground, shrinks background

44. Erosion
Erosion is the set of all points in the image, where the structuring element “fits into”.
Consider each foreground pixel in the input image
If the structuring element fits in, write a “1” at the origin of the structuring element!
Simple application of pattern matching
Input:
Binary Image (Gray value)
Structuring Element, containing only 1s!

45. Another example of erosion
White = 0, black = 1, dual property, image as a result of erosion gets darker

46. Introduction to Erosion on Gray Value Images
View gray value images as a stack of binary images!
Intensity is lower so the image is darker

47. Erosion on Gray Value Images
Images get darker!

48. Example: Counting Coins
Counting coins is difficult because they touch each other!
Solution: Binarization and Erosion separates them!

49. DILATION
more details

50. Example: Dilation Dilation is an important morphological operation
Applied Structuring Element:

51. Dilation
Dilation is the set of all points in the image, where the structuring element “touches” the foreground.
Consider each pixel in the input image
If the structuring element touches the foreground image, write a “1” at the origin of the structuring element!
Input:
Binary Image
Structuring Element, containing only 1s!!

52. Another Dilation Example
Image get lighter, more uniform intensity

53. Dilation on Gray Value Images
View gray value images as a stack of binary images!

54. Dilation on Gray Value Images
More uniform intensity

55. Edge Detection Edge Detection Dilate input image
Subtract input image from dilated image
Edges remain!

56. Illustration of dilation
From: Digital Image Processing, Gonzalez,Woods
And Eddins
Illustration of dilation

57. Example of Dilation in Matlab
>> I = zeros([13 19]);
>> I(6,6:8)=1;
>> I2 = imdilate(I,se);

58. Imdilate function in MATLAB
IM2 = IMDILATE(IM,NHOOD) dilates the image IM, where NHOOD is a
matrix of 0s and 1s that specifies the structuring element
neighborhood. This is equivalent to the syntax IIMDILATE(IM,
STREL(NHOOD)). IMDILATE determines the center element of the
neighborhood by FLOOR((SIZE(NHOOD) + 1)/2).
>> se = imrotate(eye(3),90)
se =
>> ctr=floor(size(se)+1)/2
ctr =

59. MATLAB Dilation Example
>> I = zeros([13 19]);
>> I(6, 6:12)=1;
>> SE = imrotate(eye(5),90);
>> I2=imdilate(I,SE);
>> figure, imagesc(I)
>> figure, imagesc(SE)
>> figure, imagesc(I2)

60. INPUT IMAGE
DILATED IMAGE SE

61. I I2
>> I(6:9,6:13)=1;
>> figure, imagesc(I)
>> I2=imdilate(I,SE);
>> figure, imagesc(I2) SE

62. I I2
SE =

63. Dilation and Erosion

64. Dilation and Erosion
DILATION: Adds pixels to the boundary of an object
EROSIN: Removes pixels from the boundary of an object
Number of pixels added or removed depends on size and shape of structuring element

65. Illustration of Erosion
From: Digital Image Processing, Gonzalez,Woods
And Eddins

66. MATLAB Erosion Example
2 pixel
wide
SE = 3x3
I3=imerode(I2,SE);

67. Illustration of erosion
From: Digital Image Processing, Gonzalez,Woods
And Eddins

68. Combinations
In most morphological applications dilation and erosion are used in combination
May use same or different structuring elements

69. Opening & Closing Important operations
Derived from the fundamental operations
Dilatation
Erosion
Usually applied to binary images, but gray value images are also possible
Opening and closing are dual operations

70. OPENING

71. Opening Similar to Erosion Erosion next dilation
Spot and noise removal
Less destructive
Erosion next dilation
the same structuring element for both operations.
Input:
Binary Image
Structuring Element, containing only 1s!

72. Opening
Take the structuring element (SE) and slide it around inside each foreground region.
All pixels which can be covered by the SE with the SE being entirely within the foreground region will be preserved.
All foreground pixels which can not be reached by the structuring element without lapping over the edge of the foreground object will be eroded away!
Opening is idempotent: Repeated application has no further effects!

73. Opening
Structuring element: 3x3 square

74. Opening Example
Opening with a 11 pixel diameter disc

75. Opening Example
3x9 and 9x3 Structuring Element
3*9
9*3

76. Opening on Gray Value Images
5x5 square structuring element

77. Use Opening for Separating Blobs
Use large structuring element that fits into the big blobs
Structuring Element: 11 pixel disc

78. CLOSING

79. Closing Similar to Dilation
Removal of holes
Tends to enlarge regions, shrink background
Closing is defined as a Dilatation, followed by an Erosion using the same structuring element for both operations.
Dilation next erosion!
Input:
Binary Image
Structuring Element, containing only 1s!

80. Closing
Take the structuring element (SE) and slide it around outside each foreground region.
All background pixels which can be covered by the SE with the SE being entirely within the background region will be preserved.
All background pixels which can not be reached by the structuring element without lapping over the edge of the foreground object will be turned into a foreground.
Opening is idempotent: Repeated application has no further effects!

81. Closing
Structuring element: 3x3 square

82. Closing Example Closing operation with a 22 pixel disc
Closes small holes in the foreground

83. Closing Example 1 Thresholded closed Threshold
Closing with disc of size 20
Thresholded closed

84. skeleton of Thresholded
Closing Example 2
Good for further processing: E.g. Skeleton operation looks better for closed image!
skeleton of Thresholded
skeleton of Thresholded and next closed

85. Closing Gray Value Images
5x5 square structuring element

86. Opening & Closing Opening is the dual of closing
i.e. opening the foreground pixels with a particular structuring element
is equivalent to closing the background pixels with the same element.

87. Morphological Opening and Closing
Opening of A by B  A B
Erosion of A by B, followed by
the dilation of the result by B
Closing of A by B  A B
Dilation of A by B, followed by
the erosion of the result by B
MATLAB: imopen(A, B)
imclose(A,B)

88. MATLAB Function strel
strel constructs structuring elements with various shapes and sizes
Syntax: se = strel(shape, parameters)
Example:
se = strel(‘octagon’, R);
R is the dimension – see help function

89. Opening of A by B  A B
Erosion of A by B, followed by the dilation of the result by B
Erosion- if any element of structuring element overlaps with background output is zero
FIRST - EROSION
>> se = strel('square', 20);fe = imerode(f,se);figure, imagesc(fe),title('fe')

90. Dilation of Previous Result
Outputs 1 at center of SE when at least one element of SE overlaps object
SECOND - DILATION
>> se = strel('square', 20);fd = imdilate(fe,se);figure, imagesc(fd),title('fd')

91. FO=imopen(f,se); figure, imagesc(FO),title('FO')

92. What if we increased size of SE for DILATION operation??
se = se = 30
se = strel('square', 25);fd = imdilate(fe,se);figure, imagesc(fd),title('fd')
se = strel('square', 30);fd = imdilate(fe,se);figure, imagesc(fd),title('fd')

93. Closing of A by B  A B
Dilation of A by B
Outputs 1 at center of SE when at least one element of SE overlaps object
se = strel('square', 20);fd = imdilate(f,se);figure, imagesc(fd),title('fd')

94. Erosion of the result by B
Erosion- if any element of structuring element overlaps with background output is zero

95. ORIGINAL
OPENING CLOSING

96. Fingerprint problem From: Digital Image Processing, Gonzalez,Woods
And Eddins

97. HIT and MISS

98. Hit or Miss Transformation
“Hit or Miss” Called also “Hit and Miss” is useful to identify specified configuration of pixels.
For instance, such combinations as:
isolated foreground pixels
or pixels at end of lines (end points)
A B = (A  B1)  (Ac  B2)
A eroded by B1, intersection A complement eroded by B2 (two different structuring elements)

99. Hit or Miss Example: Find cross shape pixel configuration1
MATLAB Function: C = bwhitmiss(A, B1, B2)

100. Complement of Original Image and B2
Original Image A and B1
A eroded by B1
Complement of Original
Image and B2
Erosion of A complement
And B2
Intersection of eroded images
From: Digital Image Processing, Gonzalez,Woods
And Eddins

101. Hit or Miss
Have all the pixels in B1, but none of the pixels in B2

102. Hit or Miss Example #2
Locate upper left hand corner pixels of objects in an image
Pixels that have east and south neighbors (Hits) and no NE, N, NW, W, SW Pixels (Misses)
B1 = B2 = 1 1
Don’t
Care about SE

103. Hit or Miss in Matlab G = bwhitmiss(f, B1, B2); Figure, imshow(g)
From: Digital Image Processing, Gonzalez,Woods
And Eddins

104. bwmorph(f, operation, n)
Implements various morphological operations based on combinations of dilations, erosions and look up table operations.
Example: Thinning
>> f = imread(‘fingerprint_cleaned.tif’);
>> g = bwmorph(f, ‘thin’, 1);
>> g2 = bwmorph(f, ‘thin’, 2);
>> g3 = bwmorph(f, ‘thin’, Inf);

105. Morphological Image Processing
Chapter 9
Morphological Image Processing
Input
From: Digital Image Processing, Gonzalez,Woods
And Eddins
>> f = imread(‘fingerprint_cleaned.tif’);
>> g = bwmorph(f, ‘thin’, 1);
>> g2 = bwmorph(f, ‘thin’, 2);
>> g3 = bwmorph(f, ‘thin’, Inf);

106. From: Digital Image Processing, Gonzalez,Woods
And Eddins

107. Hit-and-miss Transform is used for “Pattern Matching”
Hit and Miss is used to look for particular patterns of foreground and background pixels
It allows a recognition of very simple objects
All other morphological operations can be derived from it!!
Input:
Binary Image
Structuring Element, containing 0s and 1s!!

108. Example for a Hit-and-miss Structuring Element
Contains 0s, 1s and don’t care’s.
Usually a “1” at the origin!

109. Hit-and-miss Transform as pattern matching
It is one variant of a general to Pattern Matching approach:
If foreground and background pixels in the structuring element exactly match foreground and background pixels in the image,
then the pixel underneath the origin of the structuring element is set to the foreground color.

110. EXAMPLE: Corner Detection with Hit-and-miss Transform
Structuring Elements representing four corners

111. Corner Detection with Hit-and-miss Transform
Apply Hit-&-Miss with each Structuring Element
Use OR operation to combine the four results
Allows to describe approximate shape of an object

112. Basic THINNING

113. Thinning Used to remove selected foreground pixels from binary images
After edge detection, lines are often thicker than one pixel.
Thinning can be used to thin those line to one pixel width.
Thinning

114. Definition of Thinning
Let K be a kernel and I be an image
with 0-1=0!!
If foreground and background fit the structuring element exactly, then the pixel at the origin of the SE is set to 0
Note that the value of the SE at the origin is 1 or don’t care!

115. Example Thinning with two H&M transforms
We use two Hit-and-miss Transforms

116. Basic THICKENING

117. Thickening Used to grow selected regions of foreground pixels
E.g. applications like approximation of convex hull

118. Definition Thickening
Let K be a kernel and I be an image
with 1+1=1
If foreground and background match exactly the SE, then set the pixel at its origin to 1!
Note that the value of the SE at the origin is 0 or don’t care!

119. Example Thickening
If foreground and background match exactly the SE, then set the pixel at its origin to 1! 1 1

120. Skeletonization Bone Image Skeleton obtained using function bwmorph
From: Digital Image Processing, Gonzalez,Woods
And Eddins
Bone Image
Skeleton obtained using function bwmorph
Resulting Skeleton obtained after pruning with function endpoints

121. Objects in Images
In many cases we want to find some known objects in images
Image containing ten objects
A subset of pixels from the Image
From: Digital Image Processing, Gonzalez,Woods
And Eddins

122. Finding objects in pictures
Pixel p and its diagonal neighbors
Pixel p and its 8- neighbors
Pixel p and its 4-neighbors
Pixels that are 8 adjacent but not 4 adjacent
4 and 8 adjacent pixels
These pixels are 4 and 8 connected
These pixels are 8 connected but not 4 connected
From: Digital Image Processing, Gonzalez,Woods
And Eddins

123. How many objects are really in a picture?
From: Digital Image Processing, Gonzalez,Woods
And Eddins

124. Connected Components
Center of mass is another useful concept in object recognition
From: Digital Image Processing, Gonzalez,Woods
And Eddins

125. Morphological Reconstruction
Original image (the mask)
Intermediate image after 100 iterations
Marker image

126. Morphological Reconstruction
Chapter 9
Morphological Image Processing
From: Digital Image Processing, Gonzalez,Woods And Eddins

127. Translation and Reflection
From: Digital Image Processing, Gonzalez,Woods
And Eddins

128. Reflection Dilation definition:
“Dilation of A by B is the set consisting of all structuring element origin locations where the reflected and translated B overlaps at least some portion of A”
If structuring element is symmetric with respect to origin, reflection of B has no effect

129. PROBLEMS TO THINK

130. Images of lanes and corridors

131. Problems
Consider the images on slide 17! Why are the images getting darker under erosion? Explain!
Consider the images on slide 31! Why are the intensities becoming more uniform? Explain!
Compare Dilatation and Erosion! How are they related? Verify your answers with Matlab!
Apply Erosion and Dilatation for noise removal!
Consider slide 38: Remove the artefacts remaining with the horizontal lines.

132. Problems
Derive dilatation and erosion from the Hit-and-miss transformation
How to use these all operations to find some good features in our FAB building corridors and halls so that the robot can recognize the object such as door or windows?

133. Volker Krüger Rune Andersen . Roger S. Gaborski
Sources Used
Volker Krüger
Rune Andersen
. Roger S. Gaborski