SCALE INVARIANCE
A problem for all keypoints detectors is that at different scales some features are detectable as others are not
One of the main concept for dealing with this problem is to compute the keypoints on a set of images down-sampled from the original one and smoothed in order to change the scale of the detected features
If some mathematical properties are satisfied this set of images is called scale space
SCALE SPACE
A Scale-Space is a one-parameter family of images created from the original one so that the structures at smaller scales are successively suppressed by smoothing operations. Moreover, one would not wish to create new structures while smoothing the images. In other words, a scale-space should continuously simplify the image without introducing artifacts.
A scale space can be obtained by Gaussian smoothing as:
So each level of the Gaussian scale space is obtained by tuning the parameter (eg smoothing the image with larger Gaussian functions)
The Gaussian scale space does not give ways to find features nor their characteristic scale