Shoichi Horiguchi 
n 
1 ^ m 
(m) 42 
— 17 Ji +—1 
> 72 ( fi ) 5 ogg Nn (6) 
Equation (6) exhibits a minimum, which represents the optimal degree of the model. 
In the case of figure 4, the degree of the approximate line is 2 (m=2), that is to say, the approximate line is straight, and 
we reconstruct the road surface model by treating intersections C and D as one polygon model whose length is L, width 
is Wave; vertices are 1, 2, 3 and 4. 
If the actual road is actually straight, the road 
   
  
  
  
  
surface model should be a polygon model such of Rod P 
degree one like model (a) in Figure 5. But, if the — B 
actual road changes in height often, its model Relative 
should consist of several polygons like model (b). A height 
In this case we face the problem of determining y A 
how many polygons the optimum surface model (a) (b) 
should consist of; we optimize each surface model 
by applying the MDL principle. 
The degree of the polynomial calculated by the Figure 5. Different road surface model 
MDL principle correlates to the number of 
polygon connecting points. If degree m is 2 then the number of connecting points is 0. If degree m is 3 then the number 
of connecting points is 1. Consequently the number of connecting point is expressed m-2. 
We reconstruct road surface models based on the number of connecting points. This allows us to reconstruct the optimal surface model based on the 
optimal degree acquired by the MDL principle. 
2.5 Reconstructing Block surface model 
Finally this section describes the reconstruction of block surface models by using the road network contained in the 
— digital 2D map. This technique extracts block surfaces as areas enclosed by road surface models and intersection 
— surface models. In Figure 4 and Figure 5 the rectangle enclosed by intersections A, B, C and D corresponds to a block 
— surface model. 
3 RECONSTRUCING OF 3D DIGITAL CITY 
We combine the surface models with building models. The building models were reconstructed using our previous 
technique (Horiguchi et al, 1999). Building model position was decided on building position as indicated in a digital 2D 
map. Building model height was calculated from the points of contact between building and surface models. Each 
model acquired by our approach, that is to say, Road, Intersection, Block and Building models, agrees with the object 
figure information shown on the digital 2D map. 
A previous paper described how to project textures onto surface models and building models (Horigutchi et al., 1999). 
The visible points on the image that correspond to the vertexes of surface model are computed by the technique of 
perspective projection. 
4 EXPERIMENTS 
4.1 Results of reconstructing Surface model 
Figures 6 and 7 show a block surface model and road and intersection surface model, respectively. 
is as 
Figure 6. Results of Block surface model 
  
International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000. 417