# Power Law Transformations (Gamma Correction) in Image Processing

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

The Power Low Transformations can be given by the expression:

s=cr^γ

where,

s is the output pixels value

r is the input pixel value

c and γ are the real numbers

• For various values of γ 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 γ are positive constants
• Power-law curves with fractional values of γ 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 = γ = 1 Identity function • We usually set c to 1
• Grey levels must be in the range [0.0, 1.0]

##  • Cathode ray tube (CRT) devices have an intensity-to-voltage response that is a power function, with γ 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/ γγ

###  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 γ < 1
2. result after power-law transformation with γ = 0.6, c=1
3. transformation with γ = 0.4 (best result)
4. transformation with γ = 0.3 (under acceptable level)

### Effect of Decreasing Gamma

When the γ 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