Solution:

1. Dynamic range compression (log transformation):-

At times the dynamic range of the image exceeds the capability of the display device - What happens is that some pixel values are so large that the other low-value pixel gets obscured.

Image processing is a classic example of such large differences in grey. the level is the Fourier spectrum only some of the values are very large while most of the values are too small.

The dynamic range of pixels is of the order of $10^{16}$

Hence when we plot the Fourier spectrum we see only small dots which represent the large values.

Something needs to be done to see the small values as well.

This technique of compressing the dynamic range is known as dynamic range Hence the dynamic range compression is achieved by wing a log operator $\longrightarrow C$ is the normalization constant.

$ s=c \log (1+|\gamma|) $

2. Gray level slicing:

a specific range of grey values like for example enhancing the flaws in an x-ray or a CT image $\longrightarrow$ In such circumstances, we use a transformation known as. Gray-level slicing. $\rightarrow$ The transformation is shown in fig.

This can be implemented using the formulation,

$ \begin{aligned} &s=\alpha-1 \quad \text { if } a \leq r \leq b \\ &=0 \text { othenoise } \\ & \end{aligned} $

This method is known as Greylerel slicing without background.

This is because in this process we have completely lost the background.

In some applications we not only need to enhance a band of grey levels but abo needs to retain the background.

This technique of retaining background is called a Grey level slicing with the background.