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Proceedings, XXth congress

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
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
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)
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)

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
e 50m
Figure 3-7. Plane figure for the “Ideal City”