along several different directions. In our experiment, four 
main directions of east-west, south-north, northeast- 
southwest and southeast-northwest are chosen to 
compute the profiles. Meanwhile, the scale limits is 
ranged from 5m to 60m, and the window size of adaptive 
analysis is about 110m. The results of adaptive analysis 
are shown in table 1 and table 2. 
  
  
  
  
  
  
  
  
  
Be s oe local fractal feature H— ^ 
„0.992 ; 0.995 | 0.579 | 0.629 | 0.986 
0.948 : 0.991 : 0.806 0.660 i 0.999 
0.897 0.973 : 0.986 0.919 { 0.387 
0.888 | 0.783 | 0.947 | 0.999 | 0.859 
0,897 | 0.987 | 0.928 | 0.955 | 0.935 
  
  
Table 1: the results(H) of adaptive fractal analysis of 
studied DEM 
  
  
  
  
  
  
  
  
local fractal feature: o 
„0.159 ] 0.072 | 0.146 [0.116 | 0.039 _ 
„0.387 0.212 1 0.137 0.098 : 0.025. 
0.673 | 0.456 | 0.567 | 0.123 i 0.180 
0.739 j 0.941 | 0.569 | 0.389 : 0.181 
10.674 | 0.593 | 0.745 | 0.428 ; 0.749 | 
Table 2: the results(c) of adaptive fractal analysis of 
studied DEM 
Figure 3 illustrates the shading display of original DEM, 
it is easy to see that the surface is very smooth, because 
there is no details. 
   
Figure 3. the shading display of original DEM 
Based on the adaptive fractal features extracted from 
DEM, after 1 recursive subdivising by means of the 
model expressed in Eqs.(17), a new DEM which has 
139x139 points with 5m interval is obtained, and its 
shading display is illustrated in figure 4. It is obvious 
that such display is more vivid and intuitive, because the 
micro relief of the real terrain has been reconstructed 
  
realistically. 
  
Figure 4: the shading display of the results of adaptive 
local stationary fractal interpolation of studied DEM 
5. CONCLUSION 
Generally, the applications of fractal theory to real terrain 
surfaces (usually the DEMs) are rarely discussed with 
respect to surface analysis and realistic reconstruction, 
even though there are some examples in a simple way. 
In this paper, the author wants to stress that the fractal 
model fBf is useful for digital terrain analysis and 
interpolation. For practical applications, both the two 
features H and o are important in describing the terrain 
relief, and an adaptive analysis is also necessary for 
most cases. For realistic 3D visualization applications, 
in order to provide a more accurate visual model, the 
local stationary property and adaptive interpolation is 
needed in any approximation to fBf model. The adaptive 
local stationary midpoint displacement tehnique 
introduced in this paper is a good choice for such 
purpose. 
6. REFERENCES 
Fourier,A.,et al.,1982. Computer Rendering of stochastic 
Models,communications of ACM,25(6),pp.371-384. 
Musgravem,F.K.,eet al., 1989. The Synthesis and 
„Rendering of Eroded Fractal Terrains, Computer 
Graphics, 23(3),pp.41-48. 
Pentland,A.P.,1984. Fractal Based Description of 
1010 
Natural Scenes, IEEE Trans. PAMI-6(6),pp.661-674. 
Polidori,L.,1991. Description of Terrain as a Fractal 
Surface, and Application to Digital Elevation Model 
Quality Assessment, PE&RS ,57(10),pp.1329-1332. 
Qing Zhu,Qinghang Zhang,1995. The Digital terrain 
Reconstruction Based on Adaptive Fractal Interpolation, 
Journal of Northern Jiaotong University, 19(1), pp.159- 
164. 
Voss,R.F.,1985. ,Fundamental Algorithms for Computer 
Graphics. Springer-Verlag, pp.805-835. 
Yokaya,N.,et al, 1989. Fractal Based Analysis and 
Interpolation of 3D Natural Surface Shapes and Their 
Application to Terrain Modelling, CVGIP-46,pp.284-302. 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B4. Vienna 1996