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The relative height ordering relationship between contour lines 
and inter-contour regions can be intuitively realized from the 
tree structure. Each contour line may have many upper 
neighbors, but may have only one enclosing neighbor. A 
branch in a tree represents a divergence where there exists two 
or more contour lines of the same elevation that are enclosed by 
a common neighbor. 
Topological Rules of Contours 
Contour lines are of a relatively simple form among the 
topographic map features in the sense of feature shape and size, 
and associated attribute data. During the map generalization 
and reproduction process, a map compiler has, to a large 
extent, verified the correctness and the consistency of map 
features to ensure the map quality. This makes it possible to 
derive some general rules of elevation ordering about the 
contours. 
There are four basic rules that guide contour elevation ordering: 
1. Truncate rule (Fig. 3a) 
The elevation of a closed contour, which has a spot height 
enclosed, is the truncated elevation of the spot height. 
2. Equal height rule (Fig. 3b) 
If two neighboring closed contour lines A and B are both 
enclosed by a common closed contour C, then A and B are of 
the same elevation. 
3. Enclosing rule (Fig. 3c) 
If there exists two neighbored closed contours A and B, and if 
A is enclosing B, then elevation of B is one contour-interval 
higher than elevation of A. Note that in case of depression, 
which is symbolized with many regular short line segments 
perpendicular to the contour line, the elevation is one contour- 
interval lower. 
4. A local peak has only one neighbor (Fig. 3d). 
  
if: [ contour_interval = n meter 
is_closed (A) 
p_spot_height = h meter 
A is_inside(p, A) ] 
X 180 then: 
p187 elevation (A) 
= truncate (h,n) meter 
  
Fig.3a: Spot height rule 
  
if: [ is neighbor (C,A) 
is. neighbor (C,B) 
is. closed (A), is closed (B) 
is closed (C) 
is enclosing (C,A) 
is_enclosing (C,B) ] 
then: 
  
  
  
elevation (A) = elevation (B) 
  
Fig.3b: Equal elevation rule 
  
if: [ is neighbor (A,B) 
is closed (A) 
is. closed (B) 
is. enclosing (B,A) ] 
Com then: 
elevation (B) : 
180 = elevation (A) - contour_interval 
  
  
  
Fig.3c: Enclosing rule 
  
Boundary Boundary 
| | 
A a 
Bal LH I 
Gee pere DE 
A local peak (G and E) has only 
one neighbor. 
Fig.3d: Local peak rule 
  
  
  
  
267 
Levels of Problem Solving 
In the A/D conversion process, various problems may be 
solved at different levels, namely the raster level, the contour 
tree level, and the topological level. The raster level is the 
digitization of the relief plate by raster scanner. The contour 
tree level is the phase of building undirected contour tree from a 
raster image. The topographic level is the stage that applies 
topological rules to label the contour tree. 
In the raster level, basically all types of image processing 
techniques can be employed to improve the quality of the 
scanned image, given knowledge about the paper map. Noise 
can be detected and eliminated. Small holes and discontinuities 
of a contour line are filled and connected for a given threshold. 
Smoothing and thinning are also possible (Musavi et. al., 
1988); (Drummond et. al., 1991). A special case exists when 
the contour indexes are superimposed on the contour lines, then 
separation and extraction of the index from the contour is 
required (Yang, 1990). 
In the contour tree level, errors in the relief plate such as the 
merge of lines, and discontinuities of a line, can be detected by 
checking the connectivity of the contour tree. Normally due to 
the resolution of the scanner, cliff terrain is likely to create 
merges. Practically speaking, a series of tests should be 
conducted prior to the scanning process in order to select a 
proper resolution power; the closer the lines, the greater the 
resolution required. A locally symmetric graph pattern is the 
criteria for detecting the correctness of cliff terrain. The 
contour lines of a cliff are so merged that they usually cannot be 
split easily. One suggested method is that of "line peeling'. 
Figure 4 illustrates the method. The method begins by 
matching the most outer in-coming left half contour line and 
finds the corresponding (possibly the most outer) out-going 
right half contour line. The pair of half contour lines are 
temporary removed once it finds the match. This operation is 
repeated until no more merges are found in the merged area. 
  
  
  
  
find the most outdr 
segment pair 
  
  
  
  
  
  
  
NY L^ 
peel the pair 
  
repeat process 
  
  
  
  
  
  
wq 
*: in-coming left segment 
*%*: out-going right segment 
  
  
  
Fig.4: Line peeling method to solve the merge 
of contours 
In the topological level, contour labeling is basically an iterative 
process. In the first iteration; it starts at the most simplest 
contour relation such as the peak rule, enclosing rule, or equal 
elevation rule, to derive a unique solution for the contour. 
Unique solution means that the elevation of this contour can be 
uniquely defined. The second iteration will use the elevation 
derived from the first iteration and so on. A consistency check 
of the elevation is done at this level. A search path of the 
contour tree from a high elevation node to a low elevation node 
(or vice versa) supports the consistency check. Finally, 
unsolvable contours are highlighted at this level. Unsolvable 
contours are mostly caused by the non-closed nature of the 
contour. There is no solution to labeling a non-closed contour 
without utilization of additional information (such as 
hydrology). A compromised suggestion is that the system 
should provide information on where and how many height 
information are required to label the undirected tree.