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EE 4780
Morphological Image Processing
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Bahadir K. Gunturk 2
Example
Two semiconductor wafer images are given. You are supposed to determine the defects based on these images.
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Bahadir K. Gunturk 3
Example
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Bahadir K. Gunturk 4
Example
Absolute value of the difference
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Bahadir K. Gunturk 5
Example
>> b = zeros(size(a));>> b(a>100) = 1;>> figure; imshow(b,[ ]);
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Bahadir K. Gunturk 6
Example
>> c = imerode(b,ones(3,3));>> figure; imshow(c,[]);
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Bahadir K. Gunturk 7
Example
>> d = imdilate(c,ones(3,3));>> figure; imshow(d,[]);
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Bahadir K. Gunturk 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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Bahadir K. Gunturk 9
Morphology
B = {(0,0), (0,1), (1,0)} A = {(5,0), (3,1), (4,1), (5,1), (3,2), (4,2), (5,2)}
A binary image containing two object sets A and B
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Bahadir K. Gunturk 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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Bahadir K. Gunturk 11
Mathematical Morphology Morphology is a tool for extracting and processing image
components based on shapes. Morphological techniques include filtering, thinning,
pruning.
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Bahadir K. Gunturk 12
Basic Set Operations
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Bahadir K. Gunturk 13
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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Bahadir K. Gunturk 14
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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Bahadir K. Gunturk 15
Some Basic Definitions Dilation
A B = {x | (B + x) A } Dilation expands a region.
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Bahadir K. Gunturk 16
Some Basic Definitions
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Bahadir K. Gunturk 17
Some Basic Definitions
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Bahadir K. Gunturk 18
Some Basic Definitions Erosion
A B = {x | (B + x) A} Erosion shrinks a region.
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Bahadir K. Gunturk 19
Some Basic Definitions
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Bahadir K. Gunturk 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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Bahadir K. Gunturk 22
Some Basic Definitions
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Bahadir K. Gunturk 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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Bahadir K. Gunturk 24
Some Basic Definitions
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Bahadir K. Gunturk 25
Some Basic Definitions
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Bahadir K. Gunturk 26
Some Morphological Algorithms
Opening followed by closing can eliminate noise:(A B) B
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Bahadir K. Gunturk 27
Some Morphological Algorithms
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Bahadir K. Gunturk 28
Some Morphological Algorithms
Boundary of a set, A, can be found byA - (A B)
B
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Bahadir K. Gunturk 29
Some Morphological Algorithms
A region can be filled iteratively byXk+1 = (Xk B) Ac ,
where k = 0,1,… and X0 is a point inside the region.
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Bahadir K. Gunturk 30
Some Morphological Algorithms
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Bahadir K. Gunturk 31
Morphological Operations
BWMORPH Perform morphological operations on binary image. BW2 = BWMORPH(BW1,OPERATION) applies a specific morphological operation to the binary image BW1. BW2 = BWMORPH(BW1,OPERATION,N) applies the operation N times. N can be Inf, in which case the operation is repeated until the image no longer changes.
OPERATION is a string that can have one of these values: 'skel' With N = Inf, remove pixels on the boundaries of objects without allowing objects to break apart 'spur' Remove end points of lines without removing small objects completely. 'fill' Fill isolated interior pixels (0's surrounded by 1's) ...
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Bahadir K. Gunturk 32
Morphological OperationsBW1 = imread('circbw.tif'); BW2 = bwmorph(BW1,'skel',Inf); imshow(BW1);figure, imshow(BW2);
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Bahadir K. Gunturk 33
Morphological OperationsBW1 = imread('circbw.tif'); BW2 = bwperim(BW1); imshow(BW1); figure, imshow(BW2)
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Bahadir K. Gunturk 34
Morphological OperationsPixel Connectivity Connectivity defines which pixels are connected to other pixels. A set of pixels in a binary image that form a connected group is called an object or a connected component.
4-connected 8-connected
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Bahadir K. Gunturk 35
Morphological Operations
X = bwlabel(BW,4); RGB = label2rgb(X, @jet, 'k'); imshow(RGB,'notruesize')
BW = [0 0 0 0 0 0 0 0; 0 1 1 0 0 1 1 1; 0 1 1 0 0 0 1 1; 0 1 1 0 0 0 0 0; 0 0 0 1 1 0 0 0; 0 0 0 1 1 0 0 0; 0 0 0 1 1 0 0 0; 0 0 0 0 0 0 0 0]; X = bwlabel(BW,4) X = 0 0 0 0 0 0 0 0 0 1 1 0 0 3 3 3 0 1 1 0 0 0 3 3 0 1 1 0 0 0 0 0 0 0 0 2 2 0 0 0 0 0 0 2 2 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0
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Bahadir K. Gunturk 36
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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Bahadir K. Gunturk 37
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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Bahadir K. Gunturk 38
Summary
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Bahadir K. Gunturk 39
Summary
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Bahadir K. Gunturk 40
Summary
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Bahadir K. Gunturk 41
Summary
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Bahadir K. Gunturk 42
Extensions to Gray-Scale ImagesDilation
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Bahadir K. Gunturk 43
Extensions to Gray-Scale ImagesDilation
Take the maximum within the window.
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Bahadir K. Gunturk 44
Extensions to Gray-Scale ImagesErosion
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Bahadir K. Gunturk 45
Extensions to Gray-Scale Images
Dilation: Makes image brighter Reduces or eliminates dark details
Erosion: Makes image darker Reduces or eliminates bright details
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Bahadir K. Gunturk 46
Extensions to Gray-Scale Images
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Bahadir K. Gunturk 47
Extensions to Gray-Scale Images
Opening: Narrow bright areas are reduced.Closing: Narrow dark areas are reduced.
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Bahadir K. Gunturk 49
Extensions to Gray-Scale Images
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Bahadir K. Gunturk 50
Application Example
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Bahadir K. Gunturk 51
Application Example-Segmentation
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Bahadir K. Gunturk 52
Application Example-Granulometry