1. Morphological Image Processing
EE 7730
Morphological Image Processing

2. Example Two semiconductor wafer images are given. You are supposed to
determine the defects based on these images.
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3. Example
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4. Example
Absolute value of the difference
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5. Example >> b = zeros(size(a)); >> b(a>100) = 1;
>> figure; imshow(b,[ ]);
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6. Example >> c = imerode(b,ones(3,3));
>> figure; imshow(c,[]);
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7. Example >> d = imdilate(c,ones(3,3));
>> figure; imshow(d,[]);
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8. Mathematical Morphology
We defined an image as a two-dimensional function, f(x,y), of discrete (or real) coordinate variables, (x,y).
An alternative definition of an image can be based on the notion that an image consists of a set of discrete (or continuous) coordinates.
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9. Morphology A binary image containing two object sets A and B
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10. Morphology
Sets in morphology represent the shapes of objects in an image.
For example, the set A = {(a1,a2)} represents a point in a binary image.
The set of all black pixels in a binary image is a complete description of the image.
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11. Morphology Morphology can be extended to gray-scale images.
In gray-scale images, sets consist of elements whose components are in a 3D space.
For example, the set A = {(a1,a2,a3)} is a point at coordinates (a1,a2) with gray-scale intensity (a3).
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12. Mathematical Morphology
Morphology is a tool for extracting and processing image components based on shapes.
Morphological techniques include filtering, erosion, dilation, thinning, pruning.
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13. Basic Set Operations
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14. Some Basic Definitions
Let A and B be sets with components a=(a1,a2) and b=(b1,b2), respectively.
The translation of A by x=(x1,x2) is
A + x = {c | c = a + x, for a  A}
The reflection of A is
Ar = {x | x = -a for a  A}
The complement of A is
Ac = {x | x  A}
The union of A and B is
A  B = {x | x  A or x  B }
The intersection of A and B is
A  B = {x | x  A and x  B }
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15. Some Basic Definitions
The difference of A and B is.
A – B = A  Bc = {x | x  A and x  B}
A and B are said to be disjoint or mutually exclusive if they have no common elements.
If every element of a set A is also an element of another set B, then A is said to be a subset of B.
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16. Some Basic Definitions
Dilation
A  B = {x | (B + x)  A  }
Dilation expands a region.
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17. Some Basic Definitions
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18. Some Basic Definitions
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19. Some Basic Definitions
Erosion
A  B = {x | (B + x)  A}
Erosion shrinks a region.
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20. Some Basic Definitions
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21. Some Basic Definitions
Opening is erosion followed by dilation:
A  B = (A  B)  B
Opening smoothes regions, removes spurs, breaks narrow lines.
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22. Some Basic Definitions
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23. Some Basic Definitions
Closing is dilation followed by erosion:
A  B = (A  B)  B
Closing fills narrow gaps and holes in a region.
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24. Some Basic Definitions
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25. Some Basic Definitions
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26. Some Morphological Algorithms
Opening followed by closing can eliminate noise:
(A  B)  B
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27. Some Morphological Algorithms
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28. Some Morphological Algorithms
Boundary of a set, A, can be found by
A - (A  B) B
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29. Some Morphological Algorithms
A region can be filled iteratively by
Xk+1 = (Xk  B)  Ac ,
where k = 0,1,…
and X0 is a point inside the region.
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30. Some Morphological Algorithms
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31. Some Morphological Algorithms
Connected components can be extracted iteratively by
Xk+1 = (Xk  B)  A ,
where k = 0,1,…
and X0 is the initial point.
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32. Some Morphological Algorithms
Application example: Using connected components to detect foreign objects in packaged food.
There are four objects with significant size!
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33. Some Basic Definitions
Hit-or-miss operation detects shapes
A  B = (A  X)  [Ac  (W-X) ]
where A consists of shape X and other shapes,
B consists of shape X only,
and W is a window that is larger than X.
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34. Some Morphological Algorithms
Thinning: Thin regions iteratively; retain connections and endpoints.
Skeletons: Reduces regions to lines of one pixel thick; preserves shape.
Convex hull: Follows outline of a region except for concavities.
Pruning: Removes small branches.
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35. Skeleton
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36. Pruning
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37. Summary
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38. Summary
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39. Summary
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40. Summary
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41. Summary
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42. Extensions to Gray-Scale Images
Dilation
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43. Extensions to Gray-Scale Images
Erosion
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44. Extensions to Gray-Scale Images
Dilation:
Makes image brighter
Reduces or eliminates dark details
Erosion:
Makes image lighter
Reduces or eliminates bright details
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45. Extensions to Gray-Scale Images
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46. Extensions to Gray-Scale Images
Opening: Narrow bright areas are reduced.
Closing: Narrow dark areas are reduced.
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47. Extensions to Gray-Scale Images
Opening followed by closing Morphological smoothing operation. Removes or attenuates both bright and dark artifacts/noise.
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48. Extensions to Gray-Scale Images
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49. Application Example
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50. Application Example-Segmentation
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51. Application Example-Granulometry
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