International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B-YF. Istanbul 2004 
  
  
  
  
Figure 2. Schematic of perspective projection 
Where E shows eye point, VC shows the view center, LH shows 
the horizon line, PP shows the painting plane, and GP shows 
the ground plane. 
The basic points for the one point perspective projection are as 
follows. The depth is expressed toward the center in the picture, 
and the straight line toward the center that extends from right to 
leave intersects at one point. This point becomes the vanishing 
point in the painting, and lines which join to the same height 
point make the straight line always that expresses the depth 
faces the vanishing point. 
The origin point in ground coordinate system are defined at the 
eye point, similarly origin point in photo coordinate system are 
defined at the vanishing point as shown in Figure 2. 
3. ACQUISITION OF 3D INFORMATION 
As previously stated, the one point perspective projection 
expresses geometrical space in 2-dimension plane. In order to 
acquire 3-dimentional information from 2-dimensional plane, 
perspective geometry should be considered, and detail 
procedures are as follows. 
3.1 Estimation of vanishing point 
In order to acquire depth information from the eye point to an 
object space, vanishing point which is able to detect the point 
where the extensions of the lines concentrate should be detect. 
The vanishing point of the “Ideal City” was detected on the 
front door of the shrine painted at the center as shown in Figure 
3-1. 
The vanishing point is defined as origin point in photoho 
coordinate system as mentioned above, and origin point means 
principal point in photogrammetry. 
  
Estimation of vanishing point 
Figure 3-1. 
154 
3.2 Estimation of focal length 
In order to compute the actual depth distance to the object is 
necessary to estimate distance (/ ) from the eye point to the 
painting plane. Painting plane and the distance / are correspond 
to focal plane and focal length in photogrammetry respectively. 
Figure 3-2 shows relationship between focal length / and angle 
0, and these relationships is expressed as Eq. (1) using w in 
figure 3-2. 
W 
ut c (1) 
f tan Ó 
The size of the “Ideal City” is 2000mm in width and 600mm in 
vertical, then w becomes 1000mm. 
angular field of view (20) equal 60* 
computed from Eq. (1) as 1733mm. 
UT UMMA 
Furthermore, let assume 
ander Cone's theory, / is 
   
/ 
/ 
£ 
Figure 3-2. Relationship between focal length and field angle 
3.3 Estimation of Depth Distance 
As the next step, it is necessary to estimate the depth distances 
from the eye point to objects. Then, let assume L is ground 
distance in a real space; and / is photo distance on the painting 
in figure 3-3, the depth distance Z is computed by Eq.(2). 
In order to compute the depth distance, the width of the door at 
the center of picture was assumed as 6ft, and the photo distance 
for the width is measured as 38mm. Therefore, the depth 
distance is computed as 83.4m using Eq.(2), and the plane 
include the door was defined as datum plane in photogrammetry 
in this paper. Then, it can be said that the depth distance 83.4m 
is flying height above datum plane in photogrammetry. 
Zi (2) 
  
  
  
  
  
Figure 3-3. Outline of depth distance