Please refer to Figure 5.10. There are
eight model jigsaw objects in this experiment. The scene contains
rotated, translated and scaled parts of the model objects some of which
are considerably occluded. Boundaries are computed from the image using
the canny detector followed by hysteresis and edge linking. After that,
corners of the boundaries are located as 
.
The sites correspond to the corners on the scene curve and the labels
correspond to the feature points on the considered model curve. The
neighbors of a site is defined as the 5 forward points and the 5
backward points. Invariant relations are derived from the boundaries as
well as the corners based on a similarity-invariant representation of
curves [Li 1993]. No unary properties are used (
). Only
binary relations are used, which are the following five types (
):
: ratio of curve arc-length 
and chord-length 
,
: ratio of curvature at 
and 
,
: invariant coordinates vector,
: invariant radius vector, and
: invariant angle vector
The involved parameters are supplied by an automated optimal estimation
procedure (see Chapter 7) with the following values
, 
, 
,
, 
and
. The minimal labeling 
is found by
using a deterministic relaxation labeling algorithm
[Hummel and Zucker 1983]. The final result of recognition is shown in
Figure 5.11 in which model objects are aligned with
the corresponding (sub-) parts in the scene. Note that most of the
model objects share common structures of round extrusion and intrusion.
This means ambiguities exist extensively and have to be resolved by
using context.
Figure 5.10:
(Top) The eight model jigsaw objects; From (Li 1995c) with permission; © 1995 Kluwer.
(Bottom) An overlapping scene.
Figure 5.10:
(Top) Boundaries detected from the scene.
(Bottom) Matched objects are aligned with the scene;
From (Li 1994b) with permission; © 1994 IEEE.