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Digital Image Processing

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Digital Image Processing Chapter 9: Morphological Image Processing 5 September 2007 Skeletons (Images from Rafael C. Gonzalez and Richard E. Wood, Digital Image ... – PowerPoint PPT presentation

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Title: Digital Image Processing


1
Digital Image Processing Chapter 9 Morphological
Image Processing 5 September 2007
2
What are Morphological Operations?
Morphological operations come from the word
morphing in Biology which means changing a
shape.
Morphing
Image morphological operations are used to
manipulate object shapes such as thinning,
thickening, and filling.
Binary morphological operations are derived
from set operations.
3
Basic Set Operations
Concept of a set in binary image morphology
Each set may represent one object. Each pixel
(x,y) has its status belong to a set or not
belong to a set.
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
4
Translation and Reflection Operations
Translation
Reflection
B
A
z (z1,z2)
(A)z
5
Logical Operations
For binary images only
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
6
Dilation Operations
Empty set
Dilate means extend
A Object to be dilated B Structuring element
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
7
Dilation Operations (cont.)
Reflection
Structuring Element (B)
Intersect pixel
Center pixel
Original image (A)
8
Dilation Operations (cont.)
Result of Dilation
Boundary of the center pixels where
intersects A
9
Example Application of Dilation
Repair broken characters
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
10
Erosion Operation
Erosion means trim
A Object to be eroded B Structuring element
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
11
Erosion Operations (cont.)
Structuring Element (B)
Original image (A)
Intersect pixel
Center pixel
12
Erosion Operations (cont.)
Result of Erosion
Boundary of the center pixels where B is inside
A
13
Example Application of Dilation and Erosion
Remove small objects such as noise
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
14
Duality Between Dilation and Erosion
where c complement
Proof
15
Opening Operation
or
Combination of all parts of A that can
completely contain B
Opening eliminates narrow and small details and
corners.
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
16
Example of Opening
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
17
Closing Operation
Closing fills narrow gaps and notches
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
18
Example of Closing
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
19
Duality Between Opening and Closing
Properties Opening
Properties Closing
Idem potent property cant change any more
20
Example Application of Morphological Operations
Finger print enhancement
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
21
Hit-or-Miss Transformation
where X shape to be detected W
window that can contain X
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
22
Hit-or-Miss Transformation (cont.)
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
23
Boundary Extraction
Original image
Boundary
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
24
Region Filling
where X0 seed pixel p
Results of region filling
Original image
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
25
Extraction of Connected Components
where X0 seed pixel p
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
26
Example Extraction of Connected Components
X-ray image of bones
Thresholded image
Connected components
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
27
Convex Hull
Convex hull has no concave part.
Convex hull
Algorithm
where
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
28
Example Convex Hull
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
29
Thinning
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
30
Example Thinning
Make an object thinner.
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
31
Thickening
Make an object thicker
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
32
Skeletons
Dot lines are skeletons of this structure
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
33
Skeletons (cont.)
with
where
k times
and
34
Skeletons
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
35
Pruning
thinning
finding end points
dilation at end points
Pruned result
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
36
Example Pruning
Original image
After Thinning 3 times
End points
Dilation of end points
Pruned result
37
Summary of Binary Morphological Operations
(Tables from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
38
Summary of Binary Morphological Operations
(cont.)
(Tables from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
39
Summary of Binary Morphological Operations
(cont.)
(Tables from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
40
Summary of Binary Morphological Operations
(cont.)
(Tables from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
41
Basic Types of Structuring Elements
x dont care
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
42
Gray-Scale Dilation
1-D Case
2-D Case
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
43
Gray-Scale Dilation (cont.)
Original image
Reflection of B
Subimage

Max
Moving window
Structuring element B
Note B can be any shape and subimage
must have the same shape as
reflection of B.
Output image
44
Gray-Scale Erosion
1-D Case
2-D Case
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
45
Gray-Scale Erosion (cont.)
Original image
Subimage
B
-
Min
Moving window
Structuring element B
Note B can be any shape and subimage
must have the same shape as B.
Output image
46
Example Gray-Scale Dilation and Erosion
Original image
After dilation
Darker
Brighter
After erosion
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
47
Gray-Scale Opening
Opening cuts peaks
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
48
Gray-Scale Closing
Closing fills valleys
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
49
Example Gray-Scale Opening and Closing
Original image
After closing
After opening
Reduce dark objects
Reduce white objects
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
50
Gray-scale Morphological Smoothing
Smoothing Perform opening followed by closing
Original image
After smoothing
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
51
Morphological Gradient
Morphological Gradient
Original image
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
52
Top-Hat Transformation
Results of top-hat transform
Original image
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
53
Example Texture Segmentation Application
Small blob
Original image
Segmented result
Large blob
Algorithm 1. Perform closing on the image by
using successively larger structuring elements
until small blobs are vanished. 2. Perform
opening to join large blobs together 3. Perform
intensity thresholding
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
54
Example Granulometry
Objective to count the number of particles of
each size Method 1. Perform opening using
structuring elements of increasing size 2.
Compute the difference between the original image
and the result after each opening
operation 3. The differenced image obtained in
Step 2 are normalized and used to construct
the size-distribution graph.
Size distribution graph
Original image
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
55
Morphological Watershads
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
56
Morphological Watershads
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
57
Morphological Watershads
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
58
Gradient Image
Surface of
Original image
at edges look like mountain ridges.
59
Morphological Watershads
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
60
Morphological Watershads
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
61
Morphological Watershads
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
62
Convex Hull
(Images from Rafael C. Gonzalez and Richard E.
Wood, Digital Image Processing, 2nd Edition.
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