Transcript Lecture slides

EE 4780
Morphological Image Processing
Example
Two semiconductor wafer images are given. You are supposed to
determine the defects based on these images.
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Example
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Example
Absolute value of the difference
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Example
>> b = zeros(size(a));
>> b(a>100) = 1;
>> figure; imshow(b,[ ]);
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Example
>> c = imerode(b,ones(3,3));
>> figure; imshow(c,[]);
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Example
>> d = imdilate(c,ones(3,3));
>> figure; imshow(d,[]);
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Mathematical Morphology
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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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Morphology
A binary image containing two object sets A and B
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B = {(0,0), (0,1), (1,0)}
A = {(5,0), (3,1), (4,1), (5,1), (3,2), (4,2), (5,2)}
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Morphology
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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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Mathematical Morphology
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Morphology is a tool for extracting and processing image
components based on shapes.
Morphological techniques include filtering, thinning,
pruning.
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Basic Set Operations
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Some Basic Definitions
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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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Some Basic Definitions
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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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Some Basic Definitions
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Dilation
A  B = {x | (B + x)  A  }
Dilation expands a region.
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Some Basic Definitions
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Some Basic Definitions
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Some Basic Definitions
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Erosion
A  B = {x | (B + x)  A}
Erosion shrinks a region.
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Some Basic Definitions
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Some Basic Definitions
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Opening is erosion followed by dilation:
A  B = (A  B)  B
Opening smoothes regions, removes spurs, breaks narrow
lines.
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Some Basic Definitions
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Some Basic Definitions
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Closing is dilation followed by erosion:
A  B = (A  B)  B
Closing fills narrow gaps and holes in a region.
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Some Basic Definitions
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Some Basic Definitions
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Some Morphological Algorithms
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Opening followed by closing can eliminate noise:
(A  B)  B
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Some Morphological Algorithms
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Some Morphological Algorithms
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Boundary of a set, A, can be found by
A - (A  B)
B
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Some Morphological Algorithms
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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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Some Morphological Algorithms
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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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Morphological Operations
BW1 = imread('circbw.tif');
BW2 = bwmorph(BW1,'skel',Inf);
imshow(BW1);
figure, imshow(BW2);
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Morphological Operations
BW1 = imread('circbw.tif');
BW2 = bwperim(BW1);
imshow(BW1);
figure, imshow(BW2)
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Morphological Operations
Pixel 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
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Morphological Operations
BW = [0 0 0 0 0 0
0 1 1 0 0 1
0 1 1 0 0 0
0 1 1 0 0 0
0 0 0 1 1 0
0 0 0 1 1 0
0 0 0 1 1 0
0 0 0 0 0 0
X = bwlabel(BW,4)
X =
0 0 0 0 0 0
0 1 1 0 0 3
0 1 1 0 0 0
0 1 1 0 0 0
0 0 0 2 2 0
0 0 0 2 2 0
0 0 0 2 2 0
0 0 0 0 0 0
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1
1
0
0
0
0
0
0;
1;
1;
0;
0;
0;
0;
0];
0
3
3
0
0
0
0
0
0
3
3
0
0
0
0
0
X = bwlabel(BW,4);
RGB = label2rgb(X, @jet, 'k');
imshow(RGB,'notruesize')
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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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Some Morphological Algorithms
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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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Summary
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Summary
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Summary
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Summary
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Extensions to Gray-Scale Images
Dilation
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Extensions to Gray-Scale Images
Dilation
Take the maximum within the window.
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Extensions to Gray-Scale Images
Erosion
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Extensions to Gray-Scale Images
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Dilation:
 Makes image brighter
 Reduces or eliminates dark details
Erosion:
 Makes image darker
 Reduces or eliminates bright details
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Extensions to Gray-Scale Images
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Extensions to Gray-Scale Images
Opening: Narrow bright areas are reduced.
Closing: Narrow dark areas are reduced.
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Extensions to Gray-Scale Images
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Application Example
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Application Example-Segmentation
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Application Example-Granulometry
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