JonMuchnick

What's the difference between convolution and crosscorrelation? I read the answer below, but I don't know enough math to understand it. Could someone clarify it for me, please? "The meaning is quite different. To see why in a simple setting, consider $X$ and $Y$ independent integer valued random variables with respective distributions $p=(p_n)_n$ and $q=(q_n)_n$. The convolution $p\ast q$ is the distribution $s=(s_n)_n$ defined by $s_n=\sum\limits_kp_kq_{n-k}=P[X+Y=n]$ for every $n$. Thus, $p\ast q$ is the distribution of $X+Y$. The cross-correlation $p\circ q$ is the distribution $c=(c_n)_n$ defined by $c_n=\sum\limits_kp_kq_{n+k}=P[Y-X=n]$ for every $n$. Thus, $p\circ q$ is the distribution of $Y-X$. To sum up, $\ast$ acts as an addition while $\circ$ acts as a difference." http://math.stackexchange.com/questions/353272/whats-the-difference-between-convolution-and-crosscorrelation/353309#353309

Why do we need to flip the kernel in 2D convolution in the first place? What's the benefit of this? So, why can't we leave it unflipped? What kind of terrible thing can happen if you don't flip it? SEE: "First, flip the kernel, which is the shaded box, in both horizontal and vertical direction" http://www.songho.ca/dsp/convolution/convolution2d_example.html