1SPRS, Vol.34, Part 2W2, “Dynamic and Multi-Dimensional GIS”, Bangkok, May 23-25, 2001 
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Figure 1: Skeleton and circumcentres 
Two techniques have been developed, each with its own 
physical interpretation. The first, following Thibault and Gold 
(2000), uses Blum’s (1967) concept of height as a function of 
distance from the curve or polygon boundary, with the highest 
elevations forming the crest at the skeleton line. 
Figure 2: Elevation model of Fig. 7 
Figure 3: Skeleton of a summit 
This is illustrated in Figs. 7 and 8, where points on a simple 
closed curve are used to generate the crust and skeleton. In Fig. 
7, the circumcentres of the skeleton points are given an 
elevation equal to the circumradius. The resulting interpolated 
model is shown in Fig. 8. This model Is based on the idea that all 
slopes are identical, and thus the radius is proportional to the 
height of the skeleton point. Of course, in the case of a real 
summit as in Fig. 9, the slope would initially be unknown, and 
would be estimated from the circumradius of the next contour 
level down. 
Figure 4: Estimating skeleton heights from circumradii 
In the case of a ridge or valley, the circumradius may also be 
used, as in Fig. 10, to estimate skeleton heights based on the 
hypothesis of equal slopes. The larger circle, at the junction of 
the skeleton branches, has a known elevation - half way 
between the contours - and may be used to generate the local 
slope. The elevation of the center of the smaller circle is thus 
based on the ratio of the two radii. For more details see Thibault 
and Gold (2000). 
Figure 5: Estimating skeleton heights from ridge or valley 
lengths 
While this method is always available, it is not always the 
preferred solution where constant slope down the drainage 
valley, rather than constant valley-side slope, is more 
appropriate. In a second approach, illustrated in Fig. 11, the line 
of the valley is determined by searching along the skeleton, and 
heights are assigned based on their relative distance along this 
line. This may be complicated where there are several valley 
branches - in which case the longest branch is used as the 
reference line. This involves careful programming of the search 
routines, although the concept is simple. In practice, an 
automated procedure has been developed, which uses the 
valley length approach where possible, and the side-slope 
method when no valley head can be detected, such as at 
summits and passes.