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Thinning with Example.
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In thinning the boundary of the object is subtracted from the object.

For a image A and a Composite structuring element $B = (B_1,B_2),$Thinning can be defined as,

AØB = A∩(A B)

Eg: A

0 0 0 0 0 0 0 0
0 1 1 1 1 1 1 0
0 1 1 1 1 1 1 0
0 1 1 1 1 1 1 0
0 1 1 1 1 1 1 0
0 1 1 1 1 1 1 0
0 0 0 0 0 0 0 0

A B

0 0 0 0 0 0 0 0
0 1 1 1 1 1 1 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0

AØB = A∩(A B)

0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 1 1 1 1 1 1 0
0 1 1 1 1 1 1 0
0 1 1 1 1 1 1 0
0 1 1 1 1 1 1 0
0 0 0 0 0 0 0 0