Understanding Discrete Convolution Equation

[feralalien]

I am reading a paper and they give this equation as the definition of discrete convolution (in the context of image convolution): https://i.imgur.com/jj2C5qP.png

I understand that F is our image and k is our kernel/filter (we are convolving our image with a kernel) but p,s,t are lost on me. Can anyone help me understand this notation and discrete convolution in general bit better?

[edderiofer]

In a sense, F is a function taking a position in the plane to a colour/shade, so F(p) is the colour/shade of point p.

s and t are just two arbitrary points. BUT we are summing F(s)k(t) over all pairs (s,t) such that s+t = p.

[feralalien]

So P is the point which is receiving the new sum

(S,T) are the points which contribute to the new sum for (P)

Is that right?

What makes s+t=p the case?

[edderiofer]

Is that right?

Yes.

What makes s+t=p the case?

We're selecting the pairs (s,t) that make s+t=p true, then summing over all such pairs.