Question

The probability density function p_s (s) of the transformed variable s can be obtained by using which of the following formula?

(a) p_s (s)=p_r (r)|dr/ds|

(b) p_s (s)=p_r (r)|ds/dr|

(c) p_r (r)=p_s (s)|dr/ds|

(d) p_s (s)=p_r (r)|dr/dr|

The question was asked by my college professor while I was bunking the class.

This is a very interesting question from Histogram Processing in portion Intensity Transformations and Spatial Filtering of Digital Image Processing

Answer 1

The correct choice is (a) p_s (s)=p_r (r)|dr/ds|

The explanation: The probability density function p_s (s) of the transformed variable s can be obtained using a basic formula: p_s (s)=p_r (r)|dr/ds|

Thus, the probability density function of the transformed variable, s, is determined by the gray-level PDF of the input image and by the chosen transformation function.