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Comparison between Dilation and Erosion

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Comparison between Dilation and Erosion

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**DILATION**

- Dilation is defined as A(+)B={ Z|(B)∩A ≠ ɸ }.
- Dilation of A with B is a set of all displacements, Z, such that (B ̂) and A overlap by at least one element.
- Dilation adds pixels to the boundaries of objects in an image.
- Dilation increases the brightness of an image.
- Dilation supports the commutative property A(+)B = B(+)A.
- Dilation supports the associative property [A(+)B] (+)C=A(+) [B (+)C].
If B contains the origin, that is, if 0∊B, then A(+)B⊇A.

**EROSION**

- Erosion is defined as A ϴ B={Z|(B ̂)Z ϵ A}.
- Erosion of A by B is the set of all points Z such that B, translated (Shifted by Z), is a subset of A i.e., B is entirely contained within A.
- Erosion removes pixels on object boundaries.
- Erosion decreases brightness.
- Erosion does not support the commutative property AϴB ≠ BϴA.
- Erosion does not support the associative property [AϴB]ϴC≠Aϴ [BϴC].
If B contains the origin, that is, if 0∊B, then A ϴ B⊆A.

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