Show that the normalized correlation coefficient r is invariant to linear brightness changes in the scene s (or template m). This means you need to prove r(m,s) = r(m,as+b) for images m and s, and some constants a and b.

We defined the normalized correlation coefficient in class as r= 1/n _i [(s_i - mean(s)) (m_i- mean(m)) / (_s _m)], where s_i and m_i are the respective brightness values of the ith pixel, mean(m) and _m are mean and standard deviation of all pixels in the template and mean(s) and _s are mean and standard deviation of all pixels in the sub-image of the scene.