derived from the given contours since they represent 
structures on the terrain surface, that are reflected by 
shapes of contours as well (Finsterwalder, 1986; 
Ebner/Tang, 1989; Aumann et al., 1990; Tang, 1991, 
1992b). 
Medial axis is a descriptor of shape (Blum, 1967) and 
finds a lot of applications in computer vision, graphics 
and image processing as well as computational geo- 
metry. Intuitively, the medial axis of a 2-dimensional 
object is the set of points within the object figure that 
are medial between the boundaries. The corres- 
ponding operation is called medial axis transformation 
(MAT), which has different synonyms such as symme- 
tric axis transform, skeletonization or thinning accord- 
ing to purposes and customs. The MAT can take 
place either in a vector (e.g. Lee, 1982) or in a raster 
world (e.g. Arcelli, 1981). In the latter case the crite- 
rion of local maxima of distances to boundaries can be 
applied to locating the medial axis or skeleton pixels 
(Arcelli, 1981). 
Treating contours as boundaries of shapes, the medial 
axes between them can be obtained then by a MAT al- 
gorithm. Figure 7 shows an example. There are two 
types of medial axes to be distinguished: the medial 
axes that lie between neighbouring contours and the 
ones that are found between two parts of the same 
contour or between different contours of the same 
elevation. The former and the latter are called the 
normal and the special medial axes, respectively. 
Comparing Figure 7 with Figures 5 and 6, one can find 
out that the special medial axes just occur in the criti- 
cal regions and approximate geomorphological ele- 
ments to a certain extent. This leads to the idea that 
special medial axes should be used for tracing geo- 
morphological elements. To realize this idea two pro- 
cedures are necessary: locating geomorphological 
elements and assigning elevations to them. 
32, Lorati bolosicelel 
The MAT algorithm based on the local maxima crite- 
rion can locate medial axes between the given con- 
tours, but is not able to distinguish them. As 
mentioned above, only the special medial axes are of 
interest. So an algorithm based on QVD was pro- 
posed for locating special medial axes since Voronoi 
edges are medial axes as well (Tang, 1991). 
As described in section 2, given contours are at first 
mapped onto the two arrays as feature pixels. By way 
of contrast, contour edges are represented here by 8- 
paths and nodes of each continuous contour line are 
labelled by successive numbers. In addition, all L-pix- 
els get the same initial value zero in the distance array 
as P-Pixels. In this way, contour pixels will propagate 
themselves in every direction during the DT in both 
arrays, and as a result a desired QVD is obtained. 
570 
Voronoi edges in this QVD can be classified into 
three groups: a Voronoi edge between (a) two nodes 
of a contour edge, (b) two different contours and (c) 
two parts of the same contour. The differentiation of 
them is realized by checking the codes which are in- 
volved in the edge detection (cf. Figure 2). For 
example, if the code difference is equal 1, the Voronoi 
edge belongs to the group (a), else it is a member of 
the group (b) or (c). Obviously, the Voronoi edges in 
group (a) are neither the normal nor the special me- 
dial axes and should be left out of consideration. In 
order to distinguish the special from the normal me- 
dial axes among the rest two groups, elevation should 
be taken into account, i.e. if the involved codes indi- 
cate the contour points which have the same elevation, 
the Voronoi edge is the special medial axis, else the 
normal one. 
There are three types of special medial axes: they 
occur (1) in peak or pit regions, (2) in saddle regions 
and (3) in ridge or valley regions. To differentiate 
them Voronoi nodes are used. Two kinds of Voronoi 
nodes are of interest, i.e. the ones that are shared by 
the special and the normal medial axes and the ones 
to that only the special medial axes are incident. In the 
following, the former is referred to as SN-node and 
the latter as SO-node. While a SN-node indicates the 
connection to the neighbouring contour, a SO-node 
relates only with the contour from which the special 
medial axis comes into being. According to the nodc 
status of each special medial axis, it can be classified 
into a certain geomorphological element: it is of type 
(1) if both nodes are SO-nodes; it is of type (2) if both 
nodes are SN-nodes; it is of type (3) if one node is a 
SN-node and the other a SO-node. Connecting each 
special medial axis with the corresponding contour 
points the geomorphological elements are then lo- 
cated (cf. Figure 8). 
33. Elevati 
For further uses, e.g. for terrain modelling, appropri- 
ate elevations should be assigned to points of located 
geomorphological elements. Depending on types, dif- 
ferent strategies are used for the elevation assignment. 
In the following, the elevtion of the contour from 
which the special medial axis comes into being is 
denoted as H1 and the elevtion of the neighbouring 
contour as H2. 
For type (1): At first, H2 should be found out by 
searching the neighbouring contour since it is not in- 
cluded in the SO-nodes. Then, if H1 « H2 holds the 
geomorphological element contains a pit else a peak. 
For selection of the pit or peak point on the medial 
axis the criterion of symmetry is applied, ie. the 
middle point. Since no additional information is avail- 
able in the concerned region it is quite reasonable to 
assign to the middle point an elevation of (H1 - the