An image can be thought of in two ways:

1. a 2d array/matrix of values (“pixel values”)
2. a function of two discreet variables
• x,y or i, j (row, column)

A color image can be thought of as a 3d array/matrix or a 3d function. Or it can be thought of as 3 seperate 2d functions, one for each channel (red, green, and blue). We won’t talk about color images because they complicate the discussion and everything we say about black and white images applies to color images. Plus we can easily convert a color image to black and white (we can take one particular channel, or we can “combine” 2 or more channels).

The range of the pixel values has some minimum possible value and some maximum possible value. The minimum possible value, when visualized represents the blackest black, the maximum possible value represents the whitest white. All values in between the minimum possible and maximum possible are in between black and white, scaled linearly.

So you can represent an image by saying that the minimum possible value is 0, maximum possible value is 255. Or you can say that the minimum is -1 and the maximum is 1.

So in a way, you are really concerned about the relative change between locations (x,y or i,j) in an image. The actual scale used doesn’t really matter!