# Gaussian Pyramid - Expand Operator

I'm trying to understand the EXPAND operator in Burt and Adelson's paper (https://s3.amazonaws.com/content.udacity-data.com/courses/ud810/readings/Burt-Adelson1983Laplacian-Pyramid.pdf) and I'm a bit confused. The equation is shown as this in the paper: Now, however I'm confused about how to go about finding the intensities when g l,n-1 has negative indices.

For instance, if I am calculating below:

$$g_{l,j}(i,j) = 4* \sum_{m=-2}^2 \sum_{n=-2}^2 = w(m,n) * g_{l,n-1}(\frac{i-m}{2},\frac{j-n}{2})$$

$$g_{l,j}(0,0) = 4 * ( [ w(-2,2)*g_{l,n-1}(\frac 22, \frac 22) + w(-2,-1)*\color{red}{g_{l,n-1}(\frac 22, \frac 12)} + ... + w(-2,2)*\color{green}{g_{l,n-1}(\frac 22, \frac {-2}{2})}] + [ ... ] + [ ... ] + ... )$$

The paper mentions that indices that aren't integers are just ignored, so the term outlined in red is just taken as 0, but what about the term outlined in green?

What I'm unsure about is if the (0,0) point on the g l,n-1 is located in the center of the image. Then perhaps it would make sense but it doesn't clearly state that in the paper.