Question

The power-law transformation is given as: s = crᵞ, c and ᵞ are positive constants, and r is the gray-level of image before processing and s after processing. Then, for what value of c and ᵞ does power-law transformation becomes identity transformation?

(a) c = 1 and ᵞ < 1

(b) c = 1 and ᵞ > 1

(c) c = -1 and ᵞ = 0

(d) c = ᵞ = 1

I got this question in an interview.

My query is from Basic Grey Level Transformation topic in chapter Image Enhancement of Digital Image Processing

Answer 1

Right option is (d) c = ᵞ = 1

To elaborate: For c = ᵞ = 1 the power-law transformations s = crᵞ become s = r that is an identity transformations.