Power law transformation

Basic form

	(1)

where C and r are +ve constants

As in log transformation, power- law curves with

For —> maps a narrow range of dark i/p values into a wider range of o/p values and with the opposite being true for higher values of i/p. By varying we obtain a family of possible transformation:

For curves generated with values —>effect is opposite to . Finally the transformation (1) reduces to identity transformation for

A variety of devices for image capture, printing, and display respond according to a power law. The exponent in power law equation is referred to as gamma Þ process used to correct this power law response phenomena is called gamma correction. eg. CRT devices have intensity.. vs voltage response as a power function with varying from 1.8 to 2.5. With =2.5, the CRT would produce images darker than intended.

eg. i/p is a simple gray scale linear wedge .To reproduce colors accurately also requires knowledge of gamma correction as changing the value of gamma changes not only the brightness but also the color ratios of R:G:B.

Gamma correction is extremely important as use of digital images for commercial purposes over the internet has increased.

Figure(5.17)