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

The probability density function p_s (s) of the transformed variable s

1.	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» 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.

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