uméer 
ves and 
d. Mech. 
Lattices. 
Three Dimentional Display of Aerial Photographs’ 
DAN Hanbin®, WU Lun®, CHENG Jicheng® 
PURPOSE: 
This paper presents a fast and efficient method for perspective transformation. A technique that uses photographs and DEM for 
a three-dimensional representation of the scene is discussed. This technique needn't to match the image and DEM together. The re- 
p g g 
sulted/scene is rather valid. 
KEY WORDS; DEM, Visibility, Aerophoto 3-D Display 
1. Outline 
The basic idea to form the landscape map by using computer 
is to use computer to emulate the image-producing process of an 
ideal camera. That is to rebuild the three-dimensional aimed re- 
gion with a computer to emulate a focus-changeable ideal camera 
which has been placed at some location in the space after the 
landform surface has been defined by a digital altitude network 
which is stored by grid form. The basic process is: A. to change 
the aimed region and project it into a visual system; B. To emu- 
late or match the corresponding landscape; C. The discernment 
to surface visibility. 
Because the whole process is digital and completed by com- 
puter, it is very easy to adjust the focus point and focal distance 
after the visual point has been changed, and it is able to form a 
landscape at any angle and in any size. 
2. Projection Transformation 
As shown in Fig. 1, it is supposed that the sptial coordinate 
system of material object is 0, — X, Y,Z,, the coordinate system 
of visual system is 0, — X. Y.Z. and the spherical coordinates of the 
ideal camera in 0, — X, Y ,Z, are (0,9,dd). So their correspond- 
ing spatial three dimensional coordinates are (a, b, c) and the 
focus of the camera is located at point (a', b', c') 
  
  
a 
uA 
0, 
Fig.1 The relationship between the spatial coordinate system of 
material object and the coordinate system of visual system 
  
* Sponsored by Notional Natural Sciences Foundation of China 
@ Dept. of Geography, Peking Univ. 
Q) Dept. of Mathematics, Peking Univ. 
© Institute of Remote Sensing Application, Peking Univ. 
25 
It is supposed that the coordinates of a point wherever in the 
aimed region in the spatial coordinate system of material object 
are CX,. Yws Zw) 
The corresponding homogeneous coordinates are [X,, Y,, 
7.514: 
The coordinates of this point in the coordinate system of the 
visual system are (X., Y., Z.) and the corresponding homoge- 
neous coordinates are [X., Y., Z., 1]. 
After a series of translation, rotation and transformation, 
their relationship is 
[X Y. 2. 13— [X Y. 2. 1]- V 
In the above equation, V is a 4X4 matrix, 
qu Tz T T, 
I Tu In TL 
Ta Is TS T. 
Ta lu. due Ta 
T,=k; (as b» C, a', bls c',), 5 j—1,2,3. D 
Supposing the plane coordinates in the visual system are 
V= 
(Xs, Xs), then; 
Xe Ye 
Xs—i75-, Ys-tz 
The projection transformation is carried out according to the 
; (f is the focus of the camera) 
above formulas. 
3. Emulating and Matching the Corresponding Images 
The images in the landscape map can be gained by drawing 
from matching the image data base. 
3. 1 Image Emulation 
It is supposed that digitized landform surface is in grid 
form. 
Zoo is the point which needs to be emulated, the other 
points are eight points in the neighboring area of Zoo. (As 
shown in Fig. 2) 
Zo+ Z++ 
2— 
Zoo 
DI: 
Zo— Z+— 
+ 
e ——— 
sa een = 80/0 
y 
Fig.2 The Map of Relationship among DEM Nodes