[ptx] SIFT algorithm question

[Sebastian Nowozin]

Hi guys (especially the math freaks ;)


I started implementing the SIFT algorithm, and while I understand the main
concept, I have some detail question in the "Key localization" section of the
Lowe99 paper (http://citeseer.nj.nec.com/lowe99object.html).

There is a description how to build the image pyramid which I do not quite
understand and I think the text is a bit ambiguous:

  "The input image is first convolved with the Gaussian function using
sigma = sqrt(2) to give an image A. This is then repeated a second time with a
further incremental smoothing of sigma = sqrt(2) to give a new image, B, which
now has an effective smoothin of sigma = 2. The difference of Gaussian function
is obtained by subtracting image B from A, resultin in a ratio of 2/sqrt(2) =
sqrt(2) between the two Gaussians.
  To generate the next pyramid level, we resample the already smoothed image B
using bilinear interpolation with a pixel spacing of 1.5 in each direction.
..."


>From this and the previous paragraph I think the pyramid contains always the
same image, just scaled at a factor of 1.5. Within each pyramid level the image
is processed to a difference map between a sigma=sqrt(2) and a sigma=2
gaussian-smoothed image. To save the time to comput the sqrt(2) smoothed image
at each level, he recommends the resampling of the smoothed image. Is this
observation correct?

If I implement it like this, all I get (after normalization) are rather
thick-lined images. (I put up a screenshot of the pyramid created from an image
at http://cs.tu-berlin.de/~nowozin/try1.png).

Anyone interprets this part of Lowe's paper in a more correct way than me and
can tell me what I do wrong?


Also, it is unclear to me how he threshholds or limits his minima/maxima to a
certain number, as if consequently thought to the end, he would have only one
remaining feature (when arriving at the top image of the pyramid, having only
one pixel).


bye,
Sebastian

-- 
nowozin at cs.tu-berlin.de --- http://user.cs.tu-berlin.de/~nowozin/