SIFT - why s+3 scales per octave? I have a problem with SIFT that I do not understand. Lowe [1] proposed in his work the s=3 levels of scale are enough for one octave. Afterwards, he mentioned that you need to compute s+3 levels.

Why there are 3 and not 2 additional levels required. I understand that you require one additional level above and one additional level below the scales since you search for extrema in neighbored scales.

For what is the third additional level of scale?

Thank you very much in advance!

[1] Distinctive Image Features from Scale-Invariant Keypoints
    D. G. Lowe
    Int. Journal of Computer Vision 60(2) (2004), pp. 91--110
We must produce s + 3 images in the stack of blurred images for each
  octave, so that ﬁnal extrema detection covers a complete octave.


For $s=3$ this means you will have $s + 3 = 6$ blurred images (the Gaussian images shown in the paper in Figure 1 on the left). Having $6$ Gaussian images will result in $5$ DoG images (shown in Figure 1 on the right). This will allow you to do the extrema detection on $s=3$ scales (using the method shown in Figure 2).