54 
Fig. 5. The contour line map after preprocessing and 
color labeling. 
6. Discussions and Conclusions 
The major purpose of our algorithm is to produce a 
consistent interpolation of a contour-line image, 
derived from a line-drawn contour map. By 
"consistent", we mean that, within each resel, the 
interpolated elevation value is a continuous function 
of position and lies between the high and low level 
specified by the contour lines delineating the resel. 
In this connection, the requirement iv in Section II, 
i.e., each contour line is one pixel in thickness, is 
actually not essential. This requirement is simply 
for cosmetic purpose, and makes the contour line map 
look nicer. One must realize that our algorithms are 
good for first-order interpolation only. In other 
words, the derivatives of the contours, i.e., its 
slopes are not expected to be continuous. Fig. 7(a) 
depicts the slope map covering the same area as that 
in Fig. 6. The light (or dark) tone represents high 
(or low) slope. The contour lines in red color are 
superimposed for comparisons. Generally speaking, 
the ridges and traughs of the terrains are clearly 
delineated. The slope map, nevertheless, is not 
immune from defects. A portion of Fig 7(a) near the 
upper-left corner is blown up for illustration (see 
Fig. 7(b)). Notice that a sharp straight edge 
appears near the middle and top side of Fig. 7(b). 
This is, of course, entirely fictitious and is, 
probably, due to the irregularity of the contour 
lines in the vicinity. 
Fig. 6. The final result after the interpolation in 
color scale with the original contour line overlay on 
it. Red hue indicates the highest elevation level 
and purple hue indicates the lowest elevation level. 
Fig. 7(a). The slop map overlaped with the original 
contour line. Darker areas have lower slop, while 
lighter areas indicate higher slop. 
Fig. 7(b). A portion of Fig. 7(a). A ridge line is 
indicated by the "dashes" in the right half of the 
picture. 
To further demonstrate the capability of our 
algorithms, we construct a "synthetic image", as 
shown in Fig. 8, based on the computed digital 
elevation model in Fig. 6. The grey level at each 
pixel is proportional to the cosine of the angle 
between the directions of the sun-light and local 
surface normal when the angle is the range of 0° and 
90°. The grey level is set to be zero when the angle 
exceeds these limits. For comparisons, a protion of 
Landsat 5 scene taking on August 22, 1984 over the 
same area is displayed in Fig. 9. The band 4 of TM 
data is used for this image. The similarities 
between the synthetic image and the TM image are 
rather impressive. Major ridges, valleys and 
isolated peaks are neatly reproduced in Fig. 8. Most 
of fine drainage patterns are fairly visible in the 
figure. Needlessly to say, the matching can not be 
perfect. For example, one notices that the ridge at 
the upper-left corner bends somewhat less in Fig. 8 
than in Fig. 9. 
In general, it is not easy to locate the ground 
control points between a topmap and a satellite 
imagery. The difficulty arises from the fact that 
the topmap can not provide a sense of stereography, 
compared to that in satellite imagery. With the help 
of the synthetic image, locating the control points 
becomes rather straight-forward. Indeed, Fig. 8 is 
registered into Fig. 9. 30 ground control points are 
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REFERENCE 
Capouetti 
Venezia 
Contour 
Analysi 
Colwell, 
Chap. 1 
Duda, R. 
And See 
362. 
Faintich, 
Needs F 
ISPRS,