Think of it as scaling the template image to the size of the input image.
[Xt,Yt] = vector NtEt
[Wt,Ht] = template image size
[Xi,Yi] = vector NiEi
[Wi,Yi] = input image size
[Xn,Yn] = normalized vector
Since the vector is 2 dimensional, the norm of vector [Xt,Yt] with respect to the template image
[Wt,Ht] = [Xt/sqrt(Wt^2 +Ht^2 ), Yt/sqrt(Wt^2 +Ht^2 )] = [Xn,Yn]
To denormalize with respect to the input image [Wi,Wi], means to obtain [Xi,Yi] from [Xn,Yn]
So [Xi,Yi] = [Xn\*sqrt(Wi^2 +Hi^2 ), Yn\*sqrt(Wi^2 +Hi^2 )]
Essentially, you are finding the ratio between template size and image size Rti, where
Rti= sqrt(Wi^2 +Hi^2 )/sqrt(Wt^2 +Ht^2 ),
and scaling the vector by Rti.