4 CONCLUSION 
A method for construction DEM's is presented that allows the 
combination of different types of measurements with different 
accuracies. The proposed method also provides a measure of 
accuracy for every position and allows for sequential addition 
of measured points. Foreknowledge in the form of an ex- 
isting DEM of (a part of) the examined area can easily be 
included. These properties are of specific importance in our 
approach to video image sequence analysis, wherein different 
types of measurements are obtained. The proposed method 
is based on propagation of measurements to any position and 
the combination of the thus obtained derived measurements. 
REFERENCES 
[Cochran, 1992] Cochran, S., Medioni, G. 1992. 3-D surface 
description from binocular stereo, IEEE Trans. PAMI, Vol. 
14, no. 10, pp. 981-994 
[Guillemin, 1993] Guillemin, Y., Nguyen, H.H., Cohen, P. 
1993. Automated aerial cartography from extended se- 
quences. Proceedings of the 8th Scandinavian Conference 
on Image Analysis SCIA "93, Vol.l, pp. 681-689 
[Papoulis, 1984] Papoulis, A. 1984. Probability, Random 
Variables, and Stochastic Processes. McGraw-Hill, Inc. 
Singapore, ISBN 0-07-Y66456-X 
APPENDIX 
Propagation of measurements 
Assume that for a elevation measurement at position p the 
probability distribution function is Normal (Gaussian) around 
the measured elevation zp: 
G (2p, 05) 
fa, (z(p)) — (9) 
Furthermore the orientation of the surface is distributed Nor- 
mally as: 
f^ (7) - G(0,o2) 
Then the conditional probability for the elevation at a position 
with distance A from p is given by: 
(10) 
EE) = Gz, A) 
(11) 
The unconditional probability for the elevation at this position 
can be obtained by integrating over all possible elevations at 
Zp: 
fra (z(p + AJlz(p) = 2p) = fu (3 
faa) = | Ferlzp)fralzalap)de (12) 
This integral can be solved straightforward and yields: 
fra (za) = G(zp, 02 + Aa? (13) 
822 
Z Axis 
  
  
    
   
  
      
  
o 
n J 
M N 
* (n LEA 
x o ahi NA 
a N MAU 
N PN AN 
o 
o 
o 
Oo 
os 
o 
Ax 
7 
= "000 
o 
M 
0 
mo 
u 
X 
4 
N 
  
  
Figure 4: An example of a 3d DEM estimation. From top to 
bottom: true landscape surface, estimated landscape surface 
and standard deviation of the error. The DEM was recon- 
structed using 1000 randomly chosen point feature measure- 
ments with different accuracies 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B4. Vienna 1996