Examples of Surface Cluster Formation

To show that the implemented computation produced suitable results, an example is given here, using the surface hypotheses of the test image (see Figure 4.8). Some of the surface clusters for this scene are shown in Figures 5.5, 5.6 and 5.7.

Figure 5.5: Several Primitive Clusters

Figure 5.6: An Equivalent Depth Cluster

Figure 5.7: Several Depth Merged Clusters

As can be seen in these examples, the surface clusters form object level "chunks" of the image, and correspond to the primitive ASSEMBLYs of the models given in Chapter 7. In Table 5.1, there is a listing of the surface cluster to model ASSEMBLY correspondences for the test image. Clearly, the surface cluster formation process isolates the key features into what corresponds to structurally based intuitive "objects".

Table 5.1: Surface Cluster To Model Correspondences

SURFACE CLUSTER	CLUSTER TYPE	IMAGE REGIONS	MODEL
1	PRIMITIVE	20,21,30
2	PRIMITIVE	27
3	PRIMITIVE	16,26	robshldbd
4	PRIMITIVE	8	robbody
5	PRIMITIVE	29	robshldsobj
6	PRIMITIVE	33,34,35,36,37
7	PRIMITIVE	12,18,31	lowerarm
8	PRIMITIVE	9,28,38	trashcan
9	PRIMITIVE	17,19,22,25,32	upperarm
10	EQUIVALENT	20,21,27,30
11	EQUIVALENT	8,16,26,29	robshould + robbody
12	EQUIVALENT	9,12,18,28,31,38	lowerarm + trashcan
13	DEPTH	9,12,17,18,19,22,25,28,31,32,38	armasm + trashcan
14	DEPTH	8,16,17,19,22,25,26,29,32
15	DEPTH	8,9,12,16,17,18,19,22,25,26,28,29,31,32,38	link + robot + trashcan
16	DEPTH	8,16,20,21,26,27,29,30
17	DEPTH	8,16,17,19,20,21,22,25,26,27,29,30,32
18	DEPTH	8,9,12,16,17,18,19,20,21,22,25,26,27,28,29,30,31,32,38

Figure 5.8: Surface Cluster Hierarchy

Figure 5.8 shows the surface clusters of Table 5.1 organized to make explicit their hierarchical relationships. Clusters designated by squares closely correspond to models.

For the example above, the primitive and equivalent depth surface clusters are appropriate. What seems to be a problem is the number of depth merged surface clusters, which depend on combinatorial groupings of equivalent depth surface clusters. For the test scene, there are 9 primitive, 3 equivalent depth and 6 depth merged surface clusters. Here, the number of depth merged surface clusters is not such a problem as the object also has a strong depth order, so 2 of the 6 correspond to ASSEMBLYs. In other test images, shallower depth ordering causes more serious combinatorial grouping. Hence, an alternative process should be considered.

Though several surface clusters contained multiple ASSEMBLYs, this caused no recognition failures.