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Currently I am reading Principal Component Analysis-Based Low-Light Image Enhancement Using Reflection Model. That article proposes a way for obtaining the illumination coefficient of the original image (enter image description here). This is a quotation from it, after extracting illumination coefficient:

enter image description here

Suppose:

  • enter image description here is the enhanced image.
  • enter image description here is the extracted illumination.
  • K is a constant which K >= 0.

Now I want to know:

  • What is the meaning of enter image description here, while 255 is the maximum possible value for intensity and K >= 0? I think in image processing it is always 255. So why isn't its constant value written?
  • How is Eq.(6) related to Fechner law? I see that law says: enter image description here is the minimum gray level difference which may be discriminated by the human eye when the brightness level is I. For this question a link to any relative resource which demonstrates how this equation is obtained, is very helpful.
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  • $\begingroup$ @PeterK. Exactly, it should mean the same. Why didn't it come to my mind? And ... do you have any idea in about second question? $\endgroup$ May 23, 2023 at 15:14
  • $\begingroup$ @PeterK. Thank you for your time. Can you add your comments as an answer? then I can accept it and it may be useful for others. $\endgroup$ May 27, 2023 at 3:27
  • $\begingroup$ Done!!!!!!!!!!!! $\endgroup$
    – Peter K.
    May 28, 2023 at 18:28

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I know it doesn't help, but I have no idea what they are trying to say with $I_v(255 + K)$... unless it's really $I_v \times [ 255 + K ]$ ?

I think the reason it doesn't come to mind is because, in the paper, immediately before that section, they use $I_v(x,y)$ and then change notation for (6).

If the original image has any pixel $I_v/\max(I_v) \lt 0.01$ then (6) makes the difference $0.01 \times \frac{255 + K}{K}$ bigger, which seems to go with their "enhancement" idea, provided $K \ll \max(I_v)$.

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