Normalized Cross Correlation Operation
From what the paper described, I think $\hat G$ is achieved by standardized normalization on $u$ and $v$ before you implement the formula (1) on $G$:

x = -filtSizeL : filtSizeR; 
y = x;
u = x * cos(theta) + y * sin(theta);
v = -x * sin(theta) + y * cos(theta);
u = (u - mean(u))/std(u);
v = (v - mean(v))/std(v);


The filter is still separable after this normalization step, but I don't think you need to implement that, because it is just equivalent to select a different $\sigma$ value in the filter.