I'm reading the Digital Image Processing Using Matlab 2nd Edition of page 81. There is a question that confuses me. As you see in the following passage

But I don't understand why the probability density will be 0 and 1. For example this image:

Mathematica graphics

I can plot its PDFs histogram : Mathematica graphics

Then I can plot its CDF : Mathematica graphics

It is clearly not 0 and 1

  • $\begingroup$ This property holds for the transformed values, not the original ones. $\endgroup$
    – user65203
    Jul 20, 2017 at 11:45
  • $\begingroup$ @YvesDaoust Please note that is $P_s(s)$ $\endgroup$
    – mayi
    Jul 20, 2017 at 12:03
  • $\begingroup$ After having transformed the PDF should become uniform. $\endgroup$ Jul 20, 2017 at 12:07
  • $\begingroup$ @mathreadler But the transormed formula just is an integral transform $\endgroup$
    – mayi
    Jul 20, 2017 at 12:09
  • $\begingroup$ Yes, but over which domain are we integrating? $\endgroup$ Jul 20, 2017 at 12:11


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