I would like to improve a simple Harris corner detector by adding more scales.
I don't need scale-invariant interest points, just to detect more points by processing more scales.
The Wikipedia says there are two sigmas involved: a derivative scale $\sigma_{D}$ and an integration scale $\sigma_{I}$.
So after computing derivative images on a given level, I smooth them with Gaussian filter of size $\sigma_{D}$, then for each location $(x,y)$ in the image I have the matrix:
$H(x,y)=\begin{pmatrix}I_{x}^{2} & I_{x}I_{y} \\ I_{x}I_{y} & I_{y}^{2} \end{pmatrix}$
where $I_{x}$ and $I_{y}$ are the smoothed images (with $\sigma_{D})$ on the respective location.
How do I apply the integration scale $\sigma_{I}$ now?
Do I have to store separate images $I_{x}^{2}$, $I_{y}^{2}$ and $I_{x}I_{y}$ and smooth these with $\sigma_{I}$ before computing the matrix and Harris corner response from it?