Let us compare the present model with low level vision MRF models prototyped by that of Geman and Geman [Geman and Geman 1984]. The present model is similar to the MRF models for piecewise constant image restoration, edge detection and texture segmentation in that labels are discrete. Of course, their prior distributions must be different to cope with different tasks.
In surface reconstruction involving discontinuities
[Marroquin 1985,Blake and Zisserman 1987,Chou and Brown 1990,Szeliski 1989,Geiger and Girosi 1991],
there are commonly two coupled MRFs, a surface field and a line process
field. The former field is defined on 
, the domain of an image
grid. It assumes configurations in the space 
where
is a real interval. The latter is defined on 
, the dual
of 
. It assumes configurations in the space 
where
is the set of labels such as {edge, non-edge}. These fields
are coupled to each other by the relation of interaction between the
line process variable and the neighboring pixels.
The concept of discontinuity in the high level is the breakage of
relational bond in the scene RS. For example, when none of 
and
assumes the NULL
value, i and 
are relationally
constrained; otherwise when 
or 
, the relational bond
between i and 
is broken. This corresponds to the line process.
The main difference between this high level model and those low level models is in the encoding of higher order relational constraints. Low level models use unary observation only, such as pixel intensity; although intensity difference between neighboring pixels is also used, it is derived directly from the intensity. The present model uses relational measurements of any orders. This is important for high level problems in which contextual constraints play a more important role. Moreover, in the present model, the neighborhood system is non-homogeneous and anisotropic, which also differs from the image case.
The matching method we have presented is based on a pre-requisition that invariants are available for object representation under the concerned group of transformations. If geometric variants are also used as sources of constraints, object poses have to be resolved during the computation of matching. See the next section.