(5) 
centre of 
r andr, - 
54). The 
duct E*A 
nake the 
(6) 
(7) 
try. It is 
| by time: 
(8) 
and the 
(9) 
(10) 
(11) 
(12) 
(13) 
different 
ese pixel 
hows the 
(centre). 
lated the 
WAOSS 
led pixels 
ation of À 
ted Euler 
4 1995 
17 
angles stand for the corresponding angular velocity vector. Note that these vectors belong to in general non orthogonal 
axes. The relation is (Schulz/Ludwig, 1954): 
9 - Q, - y'sin(9) = c, - [o, * cos(o) - o, * sin(o)]tan(9) (14) 
0 - Q, * cos(q) «o, * sin(q) (15) 
y = [w, * cos(o) - o, * sin(q)] /cos(?) (16) 
The time integration of this system of non-linear coupled differential equations gives the development of the three Euler 
  
pixel traces and line positions on the projection plane 
600 i i T | i i T | T T T | 1 1 i | 1 T 1 | T T 1 
  
400 F7 
2001 
L200 
  
  
  
  
—6000 —4000 —2000 0 2000 4000 6000 
  
  
  
Fig.2 Pixel dynamic in the projection plane 
angles in time. The used procedure is presented in (Scheele, Terzibaschian, 1994). Then, we can calculate the 
development of A(t) and of the velocities in the projection plane. : : 
The deformations of the lattice and the varying mesh sizes in Figure 2 give an impression of the local velocity in the 
projection plane. This is a measure for the motion blur. An important conclusion is, that the motion blur can be 
corrected only regarding the image in the projection plane. But in addition to the collinearity equations its time 
derivation is needed. The effect of oversampling depends on the true terrain heights an can not be described using 
only the projection plane. 
The imaging process is completely described with the collinearity equations and the given velocity of each pixel 
projection onto the projection plane. 
3. DISCUSSION OF IMAGE DISTURBANCES 
The equations allow the description of different image disturbances: Under/oversampling, motion blur, image 
distortions. These disturbances change the image geometry and the image radiometry. If we ignore the stabilised 
platform, then different strategies are possible to solve the problems. They can be classified as active and passive 
methods. Active methods influence actively and on-line the imaging process. Passive methods use only the given raw 
images and additional information and can be used on-line or off-line. 
IAPRS, Vol.30, Part 5W1, ISPRS Intercommission Workshop "From Pixels to Sequences", Zurich, March 22-24 1995