I currently read and try to understand this paper and stumbled upon the following sentence:
Given a distribution of vectors $x$ on the $d$-dimensional unit sphere, we consider a set...
and later:
and as noted above, for a vector distribution on the unit sphere (as SIFT descriptors are)...
What do these statements mean? What are "vectors on the unit sphere", or more specifically "on the $d$-dimensional unit sphere"? Does this mean the vectors $x$ are $l_2$-normalized?