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# Relative Boundary Orientation

The angular relationships between sections of a segmented boundary are also a distinctive characteristic of the surface. The angle between the tangents before and after the segmentation point is a potential measurement, but this would not discriminate between a short and a long arc smoothly joined to a straight segment (recalling that the boundary is segmented by orientation and curvature discontinuities). Further, estimation of the tangent angle is less reliable. Hence, the measurement chosen was the angle between the vectors through the segment endpoints, as illustrated in Figure 6.4. Partial occlusion of the boundary will affect this measurement for curved segments. However, if enough of the boundary is visible, the estimate will be close (assuming small curvatures).

Some of the join angles for complete object surfaces are reported in Table 6.4. The average angular estimation error is about 0.1 radian, so this estimation process is acceptable.

Table 6.3: Parallel Boundary Group Counts
REGION BOUNDARIES PARALLEL IN DATA BOUNDARIES PARALLEL IN MODEL
8 2 2
9 2 2
16 2 2
26 1 1
29 0 0

Table 6.4: Boundary Join Angles
REGION SEGMENTS DATA ANGLE MODEL ANGLE ERROR
26 1 - 2 3.14 3.14 0.0
26 2 - 1 3.14 3.14 0.0
8 3,4,5 - 6 1.40 1.57 0.17
8 6 - 7,8,9,10 1.79 1.57 0.22
9 11,12 - 13 1.73 1.70 0.03
9 13 - 14,15,16 1.64 1.70 0.06
9 14,15,16 - 17,18,19,20 1.45 1.44 0.01
9 17,18,19,20 - 11,12 1.45 1.44 0.01

Next: Surface Curvature Up: Description of Three Dimensional Previous: Parallel Boundaries
Bob Fisher 2004-02-26