52 
distance 
Fig. 2. Two level image of contour line 
the preprocessing is to produce a black-and-white 
contour line image that meets the following 
requirements : 
(i) Noises, e.g.•intermediate grayness, superfluous 
spikes and dots should be removed. 
(ii) Each contour line should be an unbroken curve, 
either start and end at the edge of the image, or be 
a closed curve by itself. 
(iii) Each contour line should represent one 
elevation value only. In other words, contour lines 
are not allowed to intersect with each other. 
(iv) Each contour line should be one pixel in 
thickness. However, for our purpose this is not 
essential. 
The preprocessing consists of the following steps: 
Step 1. Take the image of a blank white paper with 
the vidicon camera, then substract it from the image 
to be processed. This step eliminates the background 
noises originated from the environment. 
Step 2. Using the technique of threshold to produce 
a two-level image (Fig.2). (Duda & Hart, 1973, 
Rosenfeld & Kek, 1982) 
Step 3. Isolated dots can be eliminated by medium 
filtering(Pratt, 1978). 
Step 4. Thinning of the contour line can be carried 
out by the methods suggested by (Japouetti(1984). 
Step 5. Spurious spikes should be removed. 
Entangled curves should be separated. Some contour 
lines may become broken in the foregoing 4 steps, and 
thus, they have to be mended. 
Step 6. Each contour line should be labeled with 
the elevation value. 
The steps 1-4 can be carried out automatically, but 
the last two steps have to be done, at the best, 
semi-automatically. An interactive processing 
system, such as IDIMS (Interactive Digital Image 
Manipulation System by TRW/ESL), affords great 
facilities for these steps. 
then Z 1 
However, 
Z 2 , and 
at P is 
where i 
weighting 
decreseii 
1/D(P,Z) 
Some c 
closed cc 
a terra: 
and the 
above f 
different 
simplici 
same ele 
or valle 
the re 
prepoces 
resel. 
applied i 
5. A fast 
Fig. 3. The effective distance between two points P 
and Q within a resel is the minimum length of all j n a j 
possible paths that connect P and Q within the resel. by a p a j 
Heavy solid lines are the contour line, and dotted With th« 
lines are the possible paths within the resel. The last sect 
dash-dotted line has the minimum length of all 
possible paths. Note that all the line segments are E(i, 
either horizontal, vertical or slant with 45°. 
Subscript 
Dg) assc 
For f c 
' 0 if i-m=0 and j-n=0 method is 
^(P,Q)= 1 I if either one of the (i-m) and and E's. 
(j-n) is zero essentia] 
, J if both (i-m) and (j-n) are not (1) Ir 
zero line, lc 
contour 
The ratio I/J is /2 for Euclidean distance. For easy line, le 
computation, we find it adequate to let J=3 and 1=2. E^=Eg=0 
A "path" C consists of a series adjacent points P 
(ii.ji). PzUz.jz) PkUk.Jk-). The length of 
this path is defined as L(C)= JE ^(P a »Pi+i)- The 
effective distance between two points P,Q within a 
resel is, then defined as 
D(P,Q)=Min L(C K ) 
k 
Where C K represents all possible paths within the 
resel that connects P and Q (see Fig.3). 
Now, let Z denote a contour line which delineates 
the resel, and P denotes any point on Z. The 
effective distance between a point Q within the resel 
to Z is then defined as 
D(Q,Z)=Min D(Q,P) 
p«z 
d 4 m- 
D.CI- 
V'- 
C* < < - 
E, < 1- 
E t < 1 - 
3. Effective distance within a resel 
A resel is a connected blank area within a contour 
line image. It is always bounded by one or more 
contour lines and, sometimes, by the edge of the 
image. 
Let's define the effective distance between two 
adjacent pixels, P(i,j) and Q(m,n) with |i-m|<l, 
|j-n|<1, as follows: 
4. Interpolation Scheme 
For a given resel, in addition to the bordering 
contour lines, there may exist some closed contour 
lines or isolated peaks within it. Let denote 
these as Z i, Z2 and their elevation values 
as Ei, E2 For each interior point P of this 
resel, we choose two lines with different E's which 
are the nearest ones to P in terms of the effective 
Fig. 4. ' 
pixel. T] 
for the 
(5), (6) 
scanning i