I couldn't figure out below paragraph on SURF paper and hope that someone can help me to understand it. Why image rotations around odd multiples of $\frac{\pi}{4}$ lead to a loss of repeatability?
Bay H., Ess A., Tuytelaars T. Van Gool L. - Speed-Up Robust Features (SURF), page 3, column 2
Gaussians are optimal for scale-space analysis, but in practice they have to be discretized and cropped (figure 2 left half). This leads to a loss in repeatability under image rotations around odd multiples of $\frac{\pi}{4}$. This weakness holds for Hessian-based detectors in general. Figure 3 shows the repeatability rate of two detectors based on the Hessian matrix for pure image rotation. The repeatability attains a maximum around multiples of $\frac{\pi}{2}$. This is due to the square shape of the filter.
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