ISPRS, Vol.34, Part 2W2, “Dynamic and Multi-Dimensional GIS”, Bangkok, May 23-25, 2001 
to the crust and the other to the skeleton. Fig. 2 shows the 
results for a simple contour. Thus skeleton points may be 
inserted into the original diagram, or not, as needed. 
Figure 2: Contour data points 
Figure 3: Crust and skeleton of Fig. 3 data 
In our particular case, the data is in the form of contour lines, 
that we assume are sufficiently well sampled - perhaps derived 
from scanned maps. Despite modern satellite imaging, much of 
the world’s data is still in this form. An additional property is not 
sufficiently appreciated - they are subjective, the result of 
human judgement at the time they were drawn. Thus they are 
clearly intended to convey information about the form of the 
surface - and it would be desirable to preserve this, as derived 
ridges and valleys. 
Fig. 3 shows our raw data set, and Fig. 4 shows the resulting 
crust and skeleton. Fig. 5 shows only those skeleton points that 
provide unique information - ridge and valley lines that separate 
points on the same contour, rather than merely those points that 
separate adjacent contours. Aumann et al., (1991) produced 
somewhat similar results by raster processing. 
Figure 4: Skeleton branches from Fig. 4 
Figure 6 shows a close-up of the test data set, Illustrating a key 
point of Amenta, Bern and Eppstein’s work: if crust edges 
(forming the contour boundary) may not cross the skeleton, then 
inserting the skeleton points will break up non-crust triangle 
edges. In particular, If the skeletons between different contours 
are ignored, then the remaining branch skeleton points will 
eliminate all “flat” triangles formed by triangles connecting points 
at the same elevation. Thus ridge and valley lines are readily 
generated automatically. The challenge is to assign them 
meaningful elevation values. The same is true in the case of 
closed summits.