Please refer to Fig.5.6. There are three model objects as shown in (a) -- (c) of the figure. Each of the objects consists of three types of point features shown in different sizes. The scene in (d) is generated from the model objects as follows: (1) Take a subset of features from each of the three objects, (2) do a transformation (rotation and translation) on each of the subsets, (3) mix the subsets together after that, (4) randomly deviate the locations of the points using either Gaussian or uniform noise, and (5) add spurious point features.
In this case of point matching, there is only one unary property, i.e.
the point size, denoted 
. Each 
takes a value
. There is only binary relation, i.e.
the Euclidean distance
between two points 
. The points, their sizes and
the distances constitute an RS. The unary property is symbolic and this
restricts the set of admissible labels for each 
as 
. The parameters is chosen as
.
Figure 5.6: Matching objects of points. (a-c) The model objects.
(d) The scene.
Fig.5.7 shows the matching results in which the matched object points are aligned with the scene in (d). The black points in (a) correspond to points 5, 6, 7, 11, 12, 14, 15, 17 and 19 of the object in Fig.5.6(a). Those in (b) correspond to points 3, 5, 8, 9, 10, 11, 12, 13, 16, 17 and 18 of the object in Fig.5.6(b). Those in (c) are points 4, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 and 21 of the object in Fig.5.6(c). In (d) is shown the union of all the individual results. The spurious points 2, 8, 10, 27, 35 and 40 in Fig.5.6(d) have found no counterparts in the three objects. They are correctly classified as the NULL . There is one mis-match: point 19 in Fig.5.6(d) is matched to the NULL while its correct home should be point 10 of Fig.5.6(a).
Figure 5.6: Results of matching objects of points.
(a-c) Matched points (in black) from the respective models aligned with
the scene.
(d) All matched points aligned with the scene.