Describe Thinning and Thickening.

Thinning
Thinning is a morphological operation that is used to remove selected foreground pixels from binary images, somewhat like erosion or opening. It can be used for several applications, but is particularly useful for skeletonization. In this mode it is commonly used to tidy up the output of edge detectors by reducing all lines to single pixel thickness. Thinning is normally only applied to binary images, and produces another binary image as output.
The thinning operation is related to the hit-and-miss transform, and so it is helpful to have an understanding of that operator before reading on.
How It Works
Like other morphological operators, the behavior of the thinning operation is determined by a structuring element. The binary structuring elements used for thinning are of the extended type described under the hit-and-miss transform (i.e. they can contain both ones and zeros).
The thinning operation is related to the hit-and-miss transform and can be expressed quite simply in terms of it. The thinning of an image I by a structuring element J is:
Eqn:eqnthn1
where the subtraction is a logical subtraction defined by Eqn:eqnlsub.

Thickening
Thickening is a morphological operation that is used to grow selected regions of foreground pixels in binary images, somewhat like dilation or closing. It has several applications, including determining the approximate convex hull of a shape, and determining the skeleton by zone of influence. Thickening is normally only applied to binary images, and it produces another binary image as output.

The thickening operation is related to the hit-and-miss transform, and so it is helpful to have an understanding of that operator before reading on.

How It Works
Like other morphological operators, the behavior of the thickening operation is determined by a structuring element. The binary structuring elements used for thickening are of the extended type described under the hit-and-miss transform (i.e. they can contain both ones and zeros).
The thickening operation is related to the hit-and-miss transform and can be expressed quite simply in terms of it. The thickening of an image I by a structuring element J is:
Eqn:eqnthk1
Thus the thickened image consists of the original image plus any additional foreground pixels switched on by the hit-and-miss transform.