  We study the structure of representations, defined as approximations of
minimal sufficient statistics that are maximal invariants to nuisance factors,
for visual data subject to scaling and occlusion of line-of-sight. We derive
analytical expressions for such representations and show that, under certain
restrictive assumptions, they are related to features commonly in use in the
computer vision community. This link highlights the condition tacitly assumed
by these descriptors, and also suggests ways to improve and generalize them.
This new interpretation draws connections to the classical theories of
sampling, hypothesis testing and group invariance.
