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This is an image for the explanation of Logarithmic Transformation of an Image. I want to ask considering a input pixel value rk, Value of nth root of rk should be greater than corresponding value of log(rk). But this image is not accordance with that?

Log Transformations

Can someone explain ?

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Mathematicaly, inverse logarithm (or exponential) should indeed grow faster than powers, and logarithm is slower than roots... at infinity. Here, their range is limited to finite interval, so with proper scaling, you may observe such behaviors. I will come back later with numerical examples.

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  • $\begingroup$ Here the range is limited to [0,255] and I have tried values from the range, still nth root should be greater than log $\endgroup$
    – amangupta
    Oct 13 '20 at 14:35
  • $\begingroup$ I got a hint, It might be related to double value of r ranging from [0,1], may be...here the log function is s = clog(1+r) $\endgroup$
    – amangupta
    Oct 13 '20 at 14:50
  • $\begingroup$ Indeed. Plus, scaled powers $\frac{y^\lambda-1}{\lambda}$ tend to $\log$ as $\lambda\to 0$, hence the hierarchy $x, x^{1/n},\log$ $\endgroup$ Oct 13 '20 at 16:31

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