Invariant feature descriptors such as SIFT and GLOH
have been demonstrated to be very robust for image matching
and visual recognition. However, such descriptors are
generally parameterised in very high dimensional spaces
e.g. 128 dimensions in the case of SIFT. This limits the
performance of feature matching techniques in terms of
speed and scalability. Furthermore, these descriptors have
traditionally been carefully hand crafted by manually tuning
many parameters. In this paper, we tackle both of
these problems by formulating descriptor design as a nonparametric
dimensionality reduction problem. In contrast
to previous approaches that use only the global statistics
of the inputs, we adopt a discriminative approach. Starting
from a large training set of labelled match/non-match
pairs, we pursue lower dimensional embeddings that are
optimised for their discriminative power. Extensive comparative
experiments demonstrate that we can exceed the
performance of the current state of the art techniques such
as SIFT with far fewer dimensions, and with virtually no
parameters to be tuned by hand.