7.4.1
This experiment performs the recognition of simulated objects of line patterns under 2D rotation and translation. There are six possible model objects (see Fig.7.4). The dotted and dashed lines in Fig.7.5(a) constitute a scene which are generated as follows: (1) Take a subset of lines from each of the three objects in Fig.7.4(a)-(c); (2) rotate and translate each of the subsets, respectively; (3) mix the subsets together after (2); (4) randomly deviate the position of the endpoints of the lines, giving the dotted lines in Fig.7.5(a); and (5) add spurious lines (shown in the dashed lines). Now a scene consists of several subsets of model patterns and spurious lines.
Figure 7.4: The six objects of line patterns in the model base.
From (Li 1995c) with permission; © 1995 Kluwer.
Fig.7.5 shows an exemplary instance 
in which 
is computed from the scene in (b) and 
from
the model shown in (c). The exemplary configuration 
is shown in
(a); the alignment of the dotted lines of the scene and the solid lines
of the model indicate the correspondences in 
; un-aligned parts
of the scene are actually labeled the NULL
.
Figure 7.5: An exemplary configuration (a) for mapping from a scene (b)
to a model (c).
From (Li 1995c) with permission; © 1995 Kluwer.
The following four types of constraining bilateral relations are used
(
):
: the angle between lines i and 
,
: the distance between the mid-points of the
lines,
: the minimum distance between the end-points
of the lines, and
: the maximum distance between the end-points
of the lines.
(
) of the same types. No unary properties are used
(
). Therefore, there are five components (
) in
each x and 
.
Figure 7.6: The optimal parameter estimate learned from the exemplar is
used to recognize other scenes and models (see text).
From (Li 1995c) with permission; © 1995 Kluwer.
The 
-optimal parameters are computed as
{0.58692, 0.30538,
0.17532, 0.37189, 0.62708} which satisfies 
. The
computation takes a few seconds on an HP series 9000/755 workstation. To
be used for recognition, 
is multiplied by a factor of
, yielding the final weights
{0.70000, 0.36422, 0.20910, 0.44354, 0.74789} (our
recognition system requires 
).
The 
is used to define the energy for recognizing other
objects and scenes. Fig.7.6(b)-(f) show the
results. There are two scenes, one in the left column and the other in
the right column, composed the dotted and dashed lines. The one on the
left was the one used in the exemplar and the scene on the right is
generated in a similar way using sub-parts of the model objects in
Fig.7.4(d)-(f). The scenes are matched
against the six model objects. The optimally matched object lines are
shown in solid lines aligned with the scenes. The matched lines in
Fig.7.6(b)-(f) are from models in
Fig.7.4(b)-(f), respectively.