## Power Law Transformations (Gamma Correction) in Image Processing

The **Power Low Transformations** can be given by the expression:

**s=cr^i**

where,

**s** is the output pixels value

**r** is the input pixel value

** c** and** i **are the real numbers

- For various values of
**i**different levels of enhancement can be obtained. - This technique is quite commonly called as Gamma Correction, used in monitor displays.
- Varying gives a whole family of curves
- c and
**i**are positive constants - Power-law curves with fractional values of
**i**map a narrow range of dark input values into a wider range of output values, with the opposite being true for higher values of input levels. - c =
**i**= 1 Identity function - We usually set
*c*to 1 - Grey levels must be in the range [0.0, 1.0]

**Also Read:** Low Pass Filter in Image Processing

## Gamma Correction

- Cathode ray tube (CRT) devices have an intensity-to-voltage response that is a power function, with i varying from 1.8 to 2.5
- The picture will become darker.
- Gamma correction is done by pre-processing the image before inputting it to the monitor with s = cr s = cr1/ 1/ i

### Example : MRI

- a magnetic resonance image of an upper thoracic human spine with a fracture-dislocation and spinal cord impingement
- The picture is predominately dark
- An expansion of gray levels are desirable needs i < 1

- result after power-law transformation with Î³ = 0.6, c=1
- transformation with i = 0.4 (best result)
- transformation with i = 0.3 (under acceptable level)

### Effect of Decreasing Gamma

When the **i** is reduced too much, the image begins to reduce contrast to the point where the image started to have very slight **wash-out** look, especially in the background