title: Image convolution with even-sized kernel
body: <p>I want to perform a simple 2D image convolution but my kernel is even-sized. Which indices I should pick for my kernel center? I tried googling for an answer and looking existing codes. People usually center their kernel so there would be one sample more before the new 0. So, if we have a 4x4 kernel the centered indices should be <code>-2 -1 0 +1</code>. Is that correct? And if it is, why is that so? Can someone explain why <code>-2 -1 0 +1</code> is correct while <code>-1 0 +1 +2</code> is not? Keep in mind that I want to perform the convolution without using FFT.</p>