How correctly define the pixel intensity of an image? Let's do easy:
I have an image IM and p(i,j) is the discrete intensity value of a pixel in the image IM (not necessarily 2-dimensional)..... How can I mathematically correctly define this?
Thank you so much!
 A: It depends on what you exactly mean by "intensity". I suggest you familiarize yourself with different color models and the difference between additive and subtractive colors. 
After this (probably too generic) answer, I'll give it a shot, whilst making some assumptions:


*

*You're talking additive colorspace

*You mean how "bright" a pixel shines, regardless of its color.

*You want to calculate this "intensity" based on the RGB values of the image. 


In that case, you'll find the HSL and/or HSV (Hue, Saturation and Lightness/Value, which are slightly different!) colorspaces useful. Check the link - it contains a lot of good information. I'll cite the lightness, value and intensity definitions from that page:

Brightness: The "attribute of a visual sensation according to which an
  area appears to emit more or less light". 
Lightness or Value: The
  "brightness relative to the brightness of a similarly illuminated
  white".

Now, to the concretely answer of your question, in mathematical terms: 


*

*Value = max( R, G, B )

*Lightness = 1/2 * max( R, G, B ) + 1/2 * min( R, G, B )


Where R, G and B are the values of a pixel in Red, Green and Blue colorspace. 
Please refer to the previously mentioned link about HSV and HSB for a more elaborate explanation and some second thoughts. 
