David Lowe's SIFT and Scale Space to Pixel Space - Arrow Over Edge of Image Border

I have been using many implementation of SIFT. Some of the features when drawn extend over the edge of the image. They tend t开发者_StackOverflow社区o use a conversion of 6 * sigma to convert from scale space to pixel space as a approximation of the radius of the area used to calculate the descriptor.

I don’t understand how the arrows can represent the radius of the region used to compute the descriptor if it is larger than the image. Including blank space from outside the image to compute the descriptor would make it unstable and unreliable for matching so I don’t understand why the arrow would ever be larger than the image if they represent the radius of the region in which the descriptor is computed. It seems to be common across all implementations of SIFT that I have seen.

Here is a picture with an example from page 15 of David Lowe's 2004 paper:

http://maym86.com/post/6751229699/how-can-sift-features-extend-over-the-borders-of