1. Introduction to Computer Vision
Lecture 16
Dr. Roger S. Gaborski

2. 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
Roger S. Gaborski

3. 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
Roger S. Gaborski

4. 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’
Roger S. Gaborski

5. Morphological Image Processing
Chapter 9
Morphological Image Processing
From: Digital Image Processing, Gonzalez,Woods
And Eddins
Roger S. Gaborski

6. 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
Roger S. Gaborski

7. DILATION A A1
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)
Roger S. Gaborski

8. 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
Roger S. Gaborski

9. 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 by
½ width of the SE
Roger S. Gaborski

10. 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 by
½ width of the SE
Roger S. Gaborski

11. 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
Roger S. Gaborski

12. Morphological Image Processing
Chapter 9
Morphological Image Processing
From: Digital Image Processing, Gonzalez,Woods
And Eddins
Roger S. Gaborski

13. Morphological Image Processing
Chapter 9
Morphological Image Processing
From: Digital Image Processing, Gonzalez,Woods
And Eddins
Roger S. Gaborski

14. Roger S. Gaborski From: Digital Image Processing, Gonzalez,Woods
And Eddins
Roger S. Gaborski

15. imdilate
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 =
Roger S. Gaborski

16. >> I = zeros([13 19]); >> I(6,6:8)=1;
>> I2 = imdilate(I,se);
Roger S. Gaborski

17. 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)
Roger S. Gaborski

18. INPUT IMAGE
DILATED IMAGE SE
Roger S. Gaborski

19. >> figure, imagesc(I) >> I2=imdilate(I,SE);
Roger S. Gaborski

20. I I2
SE =
Roger S. Gaborski

21. Morphological Image Processing
Chapter 9
Morphological Image Processing
From: Digital Image Processing, Gonzalez,Woods
And Eddins
Roger S. Gaborski

22. 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
Roger S. Gaborski

23. Roger S. Gaborski From: Digital Image Processing, Gonzalez,Woods
And Eddins
Roger S. Gaborski

24. MATLAB Erosion Example
2 pixel
wide
SE = 3x3
I3=imerode(I2,SE);
Roger S. Gaborski

25. Morphological Image Processing
Chapter 9
Morphological Image Processing
From: Digital Image Processing, Gonzalez,Woods
And Eddins
Roger S. Gaborski

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

27. 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)
Roger S. Gaborski

28. 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
Roger S. Gaborski

29. 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')
Roger S. Gaborski

30. 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')
Roger S. Gaborski

31. FO=imopen(f,se); figure, imagesc(FO),title('FO')
Roger S. Gaborski

32. 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')
Roger S. Gaborski

33. 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')
Roger S. Gaborski

34. Erosion of the result by B
Erosion- if any element of structuring element overlaps with background output is zero
Roger S. Gaborski

35. ORIGINAL
OPENING CLOSING
Roger S. Gaborski

36. Morphological Image Processing
Chapter 9
Morphological Image Processing
From: Digital Image Processing, Gonzalez,Woods
And Eddins
Roger S. Gaborski

37. Hit or Miss Transformation
Useful to identify specified configuration of pixels, such 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)
Roger S. Gaborski

38. Hit or Miss Example Find cross shape pixel configuration: 11
MATLAB Function: C = bwhitmiss(A, B1, B2)
Roger S. Gaborski

39. 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
Roger S. Gaborski
From: Digital Image Processing, Gonzalez,Woods
And Eddins

40. Hit or Miss Have all the pixels in B1, but none of the pixels in B2
Roger S. Gaborski

41. 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
Roger S. Gaborski

42. Morphological Image Processing
Chapter 9
Morphological Image Processing
G = bwhitmiss(f, B1, B2);
Figure, imshow(g)
From: Digital Image Processing, Gonzalez,Woods
And Eddins
Roger S. Gaborski

43. 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);
Roger S. Gaborski

44. Morphological Image Processing
Chapter 9
Morphological Image Processing
Input
Roger S. Gaborski
From: Digital Image Processing, Gonzalez,Woods
And Eddins

45. Roger S. Gaborski From: Digital Image Processing, Gonzalez,Woods
And Eddins
Roger S. Gaborski

46. Morphological Image Processing
Chapter 9
Morphological Image Processing
From: Digital Image Processing, Gonzalez,Woods
And Eddins
Roger S. Gaborski

47. Labeling Connected Components
Label objects in an image
4-Neighbors
8-Neighbors p p
Roger S. Gaborski

48. 4 and 8 Connect
Input Image – Connect Connect
Roger S. Gaborski

49. Morphological Image Processing
Chapter 9
Morphological Image Processing
From: Digital Image Processing, Gonzalez,Woods
And Eddins
Roger S. Gaborski

50. Morphological Image Processing
Chapter 9
Morphological Image Processing
From: Digital Image Processing, Gonzalez,Woods
And Eddins
Roger S. Gaborski

51. Morphological Image Processing
Chapter 9
Morphological Image Processing
From: Digital Image Processing, Gonzalez,Woods
And Eddins
Roger S. Gaborski

52. Morphological Image Processing
Chapter 9
Morphological Image Processing
From: Digital Image Processing, Gonzalez,Woods
And Eddins
Roger S. Gaborski

53. Morphological Image Processing
Chapter 9
Morphological Image Processing
From: Digital Image Processing, Gonzalez,Woods
And Eddins
Roger S. Gaborski

54. Morphological Image Processing
Chapter 9
Morphological Image Processing
From: Digital Image Processing, Gonzalez,Woods
And Eddins
Roger S. Gaborski

55. 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
Roger S. Gaborski

56. Morphological Image Processing
Chapter 9
Morphological Image Processing
From: Digital Image Processing, Gonzalez,Woods
And Eddins
Roger S. Gaborski