The contrast Stretching Tx function increases the dynamic range of modified image.

It is defined as S= T(r)

Where T is contrast Stretching Tx function such that,

$$S=\begin{bmatrix} αr&0 ≤ r ≤ a \\S_1+β(r-a)&a \lt r ≤ b \\ S_2+γ(r-b)&b \lt r ≤ L-1 \end{bmatrix}$$

Thresholding Transformation function is defined as S=T(r),

Such that,

$$S=\begin{bmatrix}L-1 & if r≥Threshold=T \\ 0 & Otherwise\end{bmatrix}$$

After n repeated applications of the contrast stretching transformation function, on an input image we get an image having only two grey levels :’0’ and ‘255’. This is a Binary Image.

Where as when Thresholding is applied once to an input image it gives Binary output Image.

• Contrast Stretching Tx function increases the dynamic range of modified image.

• It is defined as S=T(r)

  Where T is Contrast Stretching Tx function such that,

$$S=\begin{bmatrix} αr&0 ≤ r ≤ a \\S_1+β(r-a)&a \lt r ≤ b \\ S_2+γ(r-b)&b \lt r ≤ L-1 \end{bmatrix}$$

• When contrast stretching transformation is repeatedly applied, all the input pixel values r ≤ a will get reduced further in the output Image.After n successive applications the pixel value will become “0”.

• Similarly all the input pixels r >b will be amplified in the output image .After n successive applications,the pixel value will become “255”.

• That means that after n repeated applications of the contrast stretching transformation function,we get an image having only two grey levels :”0” and “255”. This is a thresholding.
• Since Thresholding Tx gives a binary output image,

• Thresholding function is defined as,

  $s =\bigg\{^{255 \ \ \ \ if r≥100}_{0 \ \ \ \ otherwise}$