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I'm trying to find an approach for integral image resizing. I found out that I can do it with a bilinear interpolation method, but with this approach I can only resizing by the factor which is a power of two.

I found a paper (Speeding Up Object Detection Fast Resizing in the Integral Image Domain) which describes a formula which allows to resize arbitrarily:

$$II_r(x,y) \approx \frac{1}{4a^2}\space \cdot bilinear(II, (2ax + b, 2ay+b))$$

$$2a \space - resizing\space factor$$ $$b \space - resizing\space filter\space offset$$

I would like to ask about explanation of this formula. I assume that I have to find a correct value of resizing filter offset but I don't know how to do this.

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