International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B-YF. Istanbul 2004 
  
3.4 Estimation of Shrine Size 
Utilizing photo and ground distance of the height and width for 
the front entrance gate, the depth distance to the center of both 
left and right side entrance gates are computed as figure 3-4, 
and the depth distance to the center of the shrine is estimated as 
the depth distance to the center of both left and right side 
entrance gates. As the results, diameter of the shrine is 
estimated as 35.4m. 
On the other hand, in order to compute the height of shrine, 
photo coordinate for the center of the shrine are requested. 
Therefore, oval general form are used to compute the photo 
coordinate for the center of the shrine since the circle on a real 
space is expressed as an oval on the picture, and a quadrangle 
diagonal intersection that encloses the oval become center of a 
circle. 
However, an oval center is not projected to center of a circle in 
the perspective projection. Then, in order to compute a center of 
circle using oval general form, major axis (a), minor axis (5), 
and center coordinates (0;) are requested. The diagonal 
intersection means a point projected as center of circle (0,) in 
figure 3-5, and 28.2m is computed as the height of the shrine. 
Furthermore, height of the eye point is computed as 3.3m from 
the difference of photo coordinates in y direction, and exposure 
position is also estimated as (0, 0, 0). 
| . 
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
D | le 
= | 
D qd 
83.4m 81.3m 97.2m 99.0m 
Figure 3-4. Depth distance to the center of the shrine 
  
  
Figure 3-5. Relationship between oval and circle center 
155 
3.5 3D Coordinate of the Objects 
Let assume the photo and ground coordinates for two points 
which locate on the vanishing line, a (x,, y;), f (xy, y;). And A 
(X4, Y4, Zu) and B (Xs, Ya, Zp) respectively in Figure 3-6. The 
depth distance to the plane including point 4 is computed by 
Eq.(2) since the horizontal line have the same value with the 
height of eye point, therefore X, and Y, is computed by Eqs (3). 
  
Figure 3-6. Photo coordinates and 3D coordinate 
Z X, 7 
X, Erde (3) 
Vf 
y Am ze = 20)+ Y, 
Where, (X, Y,, Z; ) is 3D coordinate of the eye point (exposure 
station), and x,, y, is photo coordinate for the vanishing point. 
> 
Z, = 27, (4) 
Y» 
On the other hand, take into account that the Y coordinate on 
the same vanishing line have equal value, and Z, equal 0 in this 
paper, following equation is obtained from Eqs.(4), and X,Y 
coordinate for the point B are also computed by Egs.(3). 
Similarly, 3D coordinate for the other objects are computed by 
the same procedures, and the height of right and left buildings 
are about 20m. Figure 3-7 shows the plane figure for the “ Ideal 
City”. 
e 50m 
Figure 3-7. Plane figure for the “Ideal City”