# How does SURF handle image boundaries in key point description?

I am stuck on the key point description stage of my SURF implementation, which is based on An Analysis of the SURF Method.

The authors extend the image borders through a mirroring process that extends each image direction by the maximum filter size. They have not explicitly stated what the actual padding is but I believe it should be at least $$L_\text{max}+(L_\text{max}-1)/2$$.

The descriptors supposedly use a $$20\sigma\times20\sigma$$ window centered around each key point to obtain the necessary information, with $$\sigma=0.4L$$, $$L$$ referring to the scale parameter of each key point.

My confusion arises because this requires the descriptor of a key point with $$L=49$$ to look for information in a $$392\times392$$ window. In reality, the actual filter size that is used is based on $$l=\lceil0.8L\rfloor$$, but this does not resolve anything, it does not even account for the fact that each sampled position is the centre of its own $$(2L+1)\times(2L+1)$$ window.

These dimensions seem much too large, given that the images that the algorithm is tested on are comparable to the window calculated above.

Padding the images with additional mirroring does not seem like a reasonable solution, given that it would require entire copies of the original images to be mirrored. Excluding the key points that include the boundaries does not seem reasonable either, otherwise there would be no point identifying them as key points. I could scale down the $$\sigma$$ parameter, but it seems like I should be able to get things working without doing this. Is my understanding of this description process flawed?