DILATION

1. Dilation is defined as A(+)B={ Z|(B)∩A ≠ ɸ }.
2. Dilation of A with B is a set of all displacements, Z, such that (B ̂) and A overlap by at least one element.
3. Dilation adds pixels to the boundaries of objects in an image.
4. Dilation increases the brightness of an image.
5. Dilation supports the commutative property A(+)B = B(+)A.
6. Dilation supports the associative property [A(+)B] (+)C=A(+) [B (+)C].

7. If B contains the origin, that is, if 0∊B, then A(+)B⊇A.

   

EROSION

1. Erosion is defined as A ϴ B={Z|(B ̂)Z ϵ A}.
2. 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.
3. Erosion removes pixels on object boundaries.
4. Erosion decreases brightness.
5. Erosion does not support the commutative property AϴB ≠ BϴA.
6. Erosion does not support the associative property [AϴB]ϴC≠Aϴ [BϴC].

7. If B contains the origin, that is, if 0∊B, then A ϴ B⊆A.