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[High School Math] How to normalize/de-normalize a vector with the dimensions of an image ?

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Think of it as scaling the template image to the size of the input image.
Let:

[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.
by

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