I couldn't figure out below paragraph on SURF paper and hope that someone can help me to understand it.
The large scale changes, especially between the first filter within these octaves (from 9 to 15 is a change of 1:7), renders the sampling of scales quite crude. Therefore, we have also implemented a scale space with a finer sampling of the scales. This first doubles the size of the image, using linear interpolation, and then starts the first octave by filtering with a filter of size 15. Additional filter sizes are 21, 27, 33, and 39. Then a second octave starts, again using filter which now increase their sizes by 12 pixels, after which a third and fourth octave follow. Now the scale change be- tween the first two filter is only 1.4 (21/15). The lowest scale for the accurate version that can be detected through quadratic interpolation is s = (1.2(18/9)/2)=1.2.
is that mean they used two different scale space at same time or they used each one individually and choose the one with better result?