I'm learning the Chapter 9.1 of the Deep Learning book.
Per post Does $(x*w)$ denote the resulting composite function, given $*$ denotes the convolution operation?, I guess I could consider $I*K$ a composite function, which means that $I$ is a function.
The book uses $I$ to denote a two-dimensional image, which leads to the image is being considered a function, does it make sense?
Why would it not make sense?
It is standard (and useful) in signal processing to consider a quantity that varies over time, whether it is voltage, air pressure or light intensity, as a function $t \mapsto f(t)$ where $t$ is time. Not only is this a natural way of modelling a physical phenomenon, it also gives you all the mathematical tools that functions offer (convolution being just one example).
Here you are just considering an image as a function $(x,y) \mapsto I(x,y)$ that tells you how pixel intensity (or something) varies when you move in $x$ and $y$ directions. The reasons for treating it as a function are similar to the one-dimensional case.
The $*$ is not function composition but convolution, just like the text says.
