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 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
- 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