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I am a novice in Digital Image Processing, and while reading the book of DIP by Gonzalez and Woods, I find that they have represented digital image as $f(x,y)$ but nowhere it is mentioned what is $x$ and $y$ actually that we are passing to the function $f?$ Does $f(x,y)$ represent the intensity of the points located at point $(x,y)$, so does $f$ actually returns the intensity of the pixel at that point or is it something else that I am missing?

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Yes, it represent the intensity at that point.

f( x, y ) gives the intensity of a channel at position (x, y) 

Source : https://courses.cs.washington.edu/courses/cse557/00wi/lectures/imageprocessing.pdf

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