Do the image downsampling after normalization

Image downsampling changes the image range. For example, if you have an image of size $4\times 4$.

$$I_0=\left(\begin{array}{rlrlrlr}16& & 15& & 14& & 13\\ 12& & 11& & 10& & 9\\ 8& & 7& & 6& & 5\\ 4& & 3& & 2& & 1\end{array}\right)$$

If we downsampling the image into a size of $2\times 2$ by taking $I_0[0:2:end,0:2:end]$, then the result becomes

$$I_1=\left(\begin{array}{rlr}16& & 14\\ 8& & 6\end{array}\right)$$

Now the range of $I_1$ is $[6,16]$, while the range of $I_0$ is $[1,16]$. Correspondingly, if you normalize $I_1$ based on one equation

$$I_{1,norm}=\frac{I_1-\min (I_1)}{\max (I_1)-\min (I_1)}$$

The scale of $I_1$ would differ from direct normalization upon $I_0$. And once you denormalize the real value out of the wrong result, severe mistakes would occur.