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Now, we use two methods to do the morphological dilation to image A with B:
A: B:+
+: the origin
Method 1, which is provided in our ‘Solutions’.
A: B:+
A: B:+
A: B:+
A: B:+
A: B:+
A: B:+
Method 2, which is you mentioned.
A: B:+
First, we get the reflection of B:
A:+
B̂
The result should be the set of all displacements,so that and A overlap by at least one element.
A: B̂
B̂
+
For example, in this case, A and has one pixel overlapped, so the + will be one element of the set.
A:+
B̂
+
B̂
+
A:+
B̂
In this case, A and has one pixel overlapped, so the + will be one element of the set.
+
A:+
B̂
B̂
+
+ +
A:+
B̂
+
A:+
B̂+
In this case, A and has two pixels overlapped, so the + will also be one element of the set.
B̂
+
+
A:+
B̂
+
+
A:+
B̂
+
+
+
+
Similarly, A and has two pixels overlapped, so the + will also be one element of the set.
B̂
+
+ A:
+B̂
+
+
+
+ A:
+B̂
+
+ +
+
+ + A:
+B̂
+
+
+
+ + A:
+B̂
+
+ +
+
+ + + A:
+B̂
+
+
+
+ + + A:
+B̂
+
+
+
+
+ + +
+
A:+
B̂
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+
+
+ + +
+
A:+
B̂
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+ + +
+ +
A:+
B̂
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+ +
A:+
B̂
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+ + +
A:+
B̂
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A:+
B̂
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A:+
B̂
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A:+
B̂
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A:+
B̂
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A:+
B̂
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A:+
B̂
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A:+
B̂
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A:+
B̂
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+ + + +
+ +
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A:+
B̂
+
+
In this way, we get the final set, which is same result as using method 1.
You can test ‘Exercise 5’ 1(a) with the comparison of method 1and 2. They would lead to the same result as well.
As said in our textbook, the definition of dilation is not unique but equivalent.Here, we recommend to use the method 1 which is more intuitive. Note to use the tips we mentioned in ‘Solutions’ when deal with the situation with 0 as the origin.
To evaluate results of morphological operations, an easier way is to turn to the Matlab. We have provided source code of ‘Exercise 5’ 1 and 2. Refer to thefunctions called corresponding to different operations.
