Power Law Transformations (Gamma Correction) in Image Processing
The Power Low Transformations can be given by the expression:
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
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 γ < 1
- result after power-law transformation with γ = 0.6, c=1
- transformation with γ = 0.4 (best result)
- 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