# SURF normalisation and Haar wavelet

I am reading the SURF paper (Speeded-Up Robust Features (SURF)) but can't understand two things. In 3.2 it says:

Furthermore, the filter responses are normalised with respect to their size. This guarantees a constant Frobenius norm for any filter size, an important aspect for the scale space analysis as discussed in the next section.

How is the normalisation done? Dividing each element of the matrix by width * height? This doesn't work because the Frobenius norm isn't constant.

The second thing I dont understand is in 4.1:

In keeping with the rest, also the size of the wavelets are scale dependent and set to a side length of 4s. Therefore, we can again use integral images for fast filtering.

Why we can use integral image and what size is the filter of Haar?

For the first question, I understand that the filters are normalized in energy. Suppose that we first consider uniform or box filters of size $$(2L+1)\times(2L+1)$$ and unit amplitude. Their Frobenius norm are $$2L+1$$. If you divide the amplitude by $$(2L+1)^2$$, then the Frobenius not of all filters will be exactly one.