Alternatively, you can use one of the low level functions to run only a part of the Orientation algorithm for instance, to compute the SIFT descriptors of custom keypoints. In configure to search for image blobs at multiple scale, the Orientation detector construct a scale space, defined as follows. Consider the Basic kernel. Thus in practice the scale space is shown by..
At each next octave, the resolution of the images is halved to save computations. The images composing the Gaussian casusl DoG scale space can then be arranged as in the following figure:. Notice that the scale level index s varies in a slightly redundant set. Once extracted, local extrema are quadratically interpolated this is very important especially at the lower resolution scales in order to have accurate keypoint localization at the full resolution.
Finally, they are filtered to eliminate low-contrast responses or responses close to edges and the orientation s are assigned, as explained next.