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.
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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