Difference between Convolution and Correlation

Question

In our lectures at the university, we got following definition for Correlation with a Kernel K with dimension n:

sum of sum of K(i,j) * I(x+i, y+j), where i,j goes from -n to n.

Convolution is defined as follows:

sum of sum of K(i,j) * I(x-i, y-j), where i,j goes from -n to n.

However, looking at the animation here:

The way they do the convolution is how correlation is defined.

Whats going on here? Is the definition given at the lectures wrong?

Answer 1

I consulted the professor. Turns out the animation in Wikipedia is wrong. Even though thanks to the symmetry the result is the same.

Answer 2

The definition is absolutely correct.

Important point to note here is, both correlation and convolution are identical only when the filter I is symmetric.