# An image brightness improvement scheme based on the Fechner principle

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 (). This is a quotation from it, after extracting illumination coefficient:

Suppose:

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

Now I want to know:

• What is the meaning of , 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: 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.
• @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? May 23, 2023 at 15:14
• @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. May 27, 2023 at 3:27
• Done!!!!!!!!!!!!
– Peter K.
May 28, 2023 at 18:28

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 $$K \ll \max(I_v)$$.