The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008 
projection error, relative flying height, height of culture feature, 
focus of aerial camera, tilt angle of photography and bearing of 
radicalization distance of photo nadir point. 
From above formulas, radicalization distance V n , projection 
error 5h a , relative flying height H ,focus of aerial camera f, 
tilted angle of photography CC and bearing of radicalization 
distance of photo nadir point (p should be needed in order to 
get the height information of culture feature Ah . The solving 
process of these parameters involves the interior orientation, 
space resection and other methods. 
3. THE METHOD AND PROCESS OF THE HEIGHT 
INFORMATION EXTRACTION METHOD BASE 
ON THE SINGLE AERIAL PHOTO 
3.1 The interior orientation and space resection for the 
digital image 
In the height solution formula, the radicalization distance Y 
projection error 5h a are the distances under the photo 
coordinate system, the processed images are digital ones, so it is 
necessary to carry through the interior orientation to get the 
relationship between the scanning coordinate system and the 
photo coordinate system, we can use the formulas as follows: 
f x = a 0 + a x • / + a 2 • J 
{ (5) 
\y = K + V 1 + b 2 • J 
®We can use the collinearity condition equation to 
deduce the nadir point calculation formula: 
X„ 
= -/ 
C_j_ 
Cl 
Then with the interior orientation parameters, we can get 
the nadir point coordinates under the scanning coordinate 
system. 
©When the image is tilted, because the projection 
error is on the radial line of the nadir point, so if we get 
some vertical lines of the buildings, the nadir point 
coordinates can be calculated with these lines. To ensure 
the precision, to the best of our abilities, we should capture 
the vertical lines of the tall buildings, because these 
vertical lines are clear, the captured precision is high. 
For these two methods, the first method is suitable for the 
condition that the exterior orientation parameters are known or 
can be calculated. The second method is suitable for any 
condition, but it needs to capture the vertical lines manually, so 
the precision is not high, when we cann’t get the precise exterior 
orientation parameters, we can use this method. 
3.3 The relative height calculation of the bottom point of the 
vertical line 
The relative height H is equal to Zs-Z , Z is the height of the 
building bottom point, Zs is the height of the camera station, so 
it is necessary to calculate Z with the monoposition theory with 
the help of the DEM, the monopositon theory is described as 
figure 1: 
In above formula, x and y are the photo coordinates of the 
fiducial marks, I and J are the corresponding scanning 
coordinates. With the four photo coordinates and the 
corresponding scanning coordinates of the fiducial marks, we 
can get the six parameters( Q 0 , a x , d 2 ? b 0 ? b\ > b 2 >) with the 
adjustment method. 
In the formulas of (2), (3), (4) the relative height H is equal to 
Zs-Z (Z is the height of the building bottom point, Zs is the 
height of the camera station). If we want to get the height H, we 
should take the space resection to get the elements of exterior 
orientation, in the formula (4), the tilt angle of photography can 
be calculated with the elements of exterior orientation, besides, 
the coordinates of the nadir point can also be calculated with the 
elements of exterior orientation. So it is necessary to take the 
space resection to get the elements of exterior orientation with a 
quantity of GCPs. 
3.2 The calculation of the nadir point coordinates 
In order to get the radicalization distance of photo nadir point, 
we should get the nadir point coordinates on the image, we can 
use the following methods: 
a x x + a 2 y - a 2 f 
c x x + c 2 y-cj 
b x x + b 2 y-b 3 f 
c x x + c 2 y-cj 
Figured The Principal of the Monoposition Theory 
X-Xs = (Z-Zs) 
Y-Ys = (Z — Zs) 
(1) When the image is horizontal or approximately 
horizontal, we can consider the photo nadir point and the 
principal point of photograph are concurrent, so the nadir point 
coordinates are (0, 0). 2 
(2) When the image tilted, there are two methods to 
calculate the nadir point coordinates: 
3.4 The building height calculation 
When the radicalization distance, projection error, relative 
flying height are all calculated, we can use the formula (2) to 
get the building height. When we use the formula (3) or (4), it is 
necessary to calculate the tilted angle of photography and 
bearing of radicalization distance of photo nadir point. 
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