**1 Answer**

written 8.1 years ago by |

**Thinning:**

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,

$A Ø B = A ∩ (A \otimes B)^C$

**Thickening:**

In Thickening a part of boundary of the background is added to the object.

For a image A and a Composite structuring element B = (B1,B2),Thickening can be defined as,

$A ʘ B = A U (A \otimes B)$

Thinning and Thickening are dual operations.i.e.,

$(A ʘ B)^C = A^C Ø B;$

Thinning and Thickening transformations are very often used sequentially,

Let $B = {B_1,B_2,……B_n}$ denote a sequence of composite structuring elements.Here Bn is the rotated version of Bn-1.Sequential Thinning can then be expressed as,

$A Ø {B} = (((A Ø B_1) Ø B_2) Ø B_3)Ø………B_n).$

And sequential thickening as,

$A ʘ {B} = (((A ʘ B_1) ʘ B_2) ʘ B_3) ʘ………B_n).$

The process to thin image A by $B_1$ then thin the result with $B_2$ ans so on until A is thinned with $B_n$ similarly,D is thickened by apply $B_1,B_2……B_n$.

Note: Thinning and Thickening can be explained by solving an example if asked for 10 Mks.