In matching schemes based on invariants, the features chosen to represent the object modeled and the scene are invariant to the expected transformations from the object to the observation for the process of cognition to be accomplished. The more complicated the transformations are, the higher the order of features is needed for the invariant object representation [Li 1992b]; the order needed may be higher than two.
In previous subsections, only constraints of up to the second order are
considered. Incorporation of higher order constraints can be achieved by
adding higher order energy terms. A clique of order n>2 is an
n-tuple 
in which 
and 
(
)
are neighbors to each other. The incorporation is done as follows.
Firstly, the following 
order a priori clique potentials
are add to the prior energy 
where 
is a prior penalty constantly. Secondly, the
likelihood energy for the 
order observation has the following
likelihood potentials
The corresponding posterior can be obtained using the Bayes rule,
resulting in the following 
order energy
Adding together all the energy terms yields
where H is the highest order.
