What are we referring to as the 1D continuous signal in this context? I'm struggling to see how images can be represented as 1D continuous signals, so I was thinking this might refer to RGB channels instead.
motoole2
You're correct. When it comes to images, we would (typically) use 2D functions, e.g., $$f(x,y)$$. So if we wanted to perform a convolution operation, we would have to do a 2D version of the integral:
(The reason for this slide is to introduce convolutions slowly, starting with 1D convolutions first. The next slide goes into discrete 2D convolutions.)
What are we referring to as the 1D continuous signal in this context? I'm struggling to see how images can be represented as 1D continuous signals, so I was thinking this might refer to RGB channels instead.
You're correct. When it comes to images, we would (typically) use 2D functions, e.g., $$f(x,y)$$. So if we wanted to perform a convolution operation, we would have to do a 2D version of the integral:
$$(f * g)(x,y) = \iint_{-\infty}^{\infty} f(u,v) g(x-u,y-v)~du~dv$$
(The reason for this slide is to introduce convolutions slowly, starting with 1D convolutions first. The next slide goes into discrete 2D convolutions.)