# how could correlation-based image patches matching works?

In general, correlation-based image matching can be referred to as $$c(I_1,I_2) = \sum_{x \in patch} f(I_1(x), I_2(x))$$ , I do think normalized cross-correlation like $$ncc(I_1, I_2) = \sum_{x \in patch}\frac{(I_1(x) - \mu_1)(I_2(x) - \mu_2)}{\delta_1\delta_2}$$. is a good indicator to show if 2 patches match or not.

BUT my problem is that, if $$\begin{eqnarray*} f(I_1(x), I_2(x)) &=& \sum_{x \in patch}I_1(x) \cdot I_2(x) \end{eqnarray*}$$ , then I don't think $c(I_1, I_2)$ will be a good, right?

Furthermore, this type of correlation-based matching techniques won't work well if one of the images rotates, right?