How do we represent images as functions, since it seems like the intensity of each pixel can be fairly random?

Dalyons

I might've missed it, but is there a mathematical/intuitive reason we only keep the norm as [0,1]? Or, is there a version of norm for other intervals (i.e. divide by length or something)?

Zishen

Same as Dalyons, a little lost when it came to only having [0,1] for L2 norm

Mogician

If the L2 norm of a vector comes from an intuition of length or distance, what is the motivation for us to extrapolate the idea to function? Or in other words, is there any application for this math tool?

jonasjiang

Is there any application of this definition? Or it is only the necessary part of viewing functions as vectors.

vtnguyen

In computer graphics, in what case will we use L2 norm for vectors and in what case we use L2 norm for functions?

madi_davis

In computer graphics what is the significance of other definitions of the norm (i.e. the L0 norm, L1 norm, L-infinity norm etc.) of functions?

large_monkey

What is the significance of the L2 norm in graphics in particular, as compared to other function norms? Intuitively I would suspect that the idea of an L2 norm on a function is fairly abstract (I find it hard to associate this with the concept of distance as in the euclidean case), and the supremum or L-infinity norm would have a more tangible or useful idea.

shough

Why would we care about using different definitions of a vector norm?

How do we represent images as functions, since it seems like the intensity of each pixel can be fairly random?

I might've missed it, but is there a mathematical/intuitive reason we only keep the norm as [0,1]? Or, is there a version of norm for other intervals (i.e. divide by length or something)?

Same as Dalyons, a little lost when it came to only having [0,1] for L2 norm

If the L2 norm of a vector comes from an intuition of length or distance, what is the motivation for us to extrapolate the idea to function? Or in other words, is there any application for this math tool?

Is there any application of this definition? Or it is only the necessary part of viewing functions as vectors.

In computer graphics, in what case will we use L2 norm for vectors and in what case we use L2 norm for functions?

In computer graphics what is the significance of other definitions of the norm (i.e. the L0 norm, L1 norm, L-infinity norm etc.) of functions?

What is the significance of the L2 norm in graphics in particular, as compared to other function norms? Intuitively I would suspect that the idea of an L2 norm on a function is fairly abstract (I find it hard to associate this with the concept of distance as in the euclidean case), and the supremum or L-infinity norm would have a more tangible or useful idea.

Why would we care about using different definitions of a vector norm?

when do we use this in computer graphics?