Zuxun Zhang 
  
(X; = Xi) DY + (Xp Ag 2X) AN HA A AM + (2) 
Yo) Ak tO +1 y= 20 AY, +07 - 9) Ea Lip =O 
2) Collinear constraint condition of three points 
As illustrated in the Figure 3, the projections of thc three points, i-l, is 
i+1, of the gable roof on the XY plane should be in the same line. That is 
they are collinear: 
      
   
     
NR 
x NO 
pM 
  
      
dy=1,=0 i-1 
-(X,4 - X,)sin 0 + (Y,,, - Y,)cos0 - 0 
Figure 3. Collinearity 
The collinear condition of three points is: 
Q; -Y,)AX, (4 - AX, Q4 7 Y)AX,u + 
(E a RAT. FUR DAT HOS EAR, 
(3) Equal height constraint condition 
No matter the houses with (lat roof or gable roof, there should be some roof point, which have the same height, then 
they should be under the condition of equal height: 
Zu 7% =kh=0 | 
M. 4M,-L-0 (4) 
Listed above are some basic geometric constraint-conditions for houses. According to the different types of houses, 
some other relative geometric conditions can be added. Combining the adjustment model (1) with the geometric 
constraint condition (2), (3) and (4), the least squares matching model, which is based on geometric constraint condition 
in object space, could be used in the extraction of houses. 
3. The results of implementation 
The initial values could be detected by DSM, or to be determined by the rectangle, which is parallel to the (x, y) 
coordinate axes of image, as illustrated in the Figure 4a. In order to examine the validity of the model mentioned above, 
the initial values are determined by the polygon parallel to the boundary of the house, just like the rectangle with black 
line in Figure 4a. Figure 4b is the result of thc adjustment model mentioned above. 
* P 25 
T 5 
Sane 
Snes 
25 
PON on 
  
Figure 4. Result of the precise position of the flat floor house. 
Tne initial values of gable roof are determined by pointed out the approximate position of the roof boundary, as 
illustrated in the Picture 5a. The result of the adjustment model mentioned above is shown in Fig 5b. The superposition 
of the original scanned image enlarged to 4 times and the result of precise position is illustrated in Figure 6. It shows 
that the result of precise matching could bc perfect and satisfying, because of using optimal matching with all 
information of house boundary and combining the geometric conditions. 
  
1024 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.