## 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

1. 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
2. result after power-law transformation with Î³ = 0.6, c=1
3. transformation with i = 0.4 (best result)
4. 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