International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B2. Istanbul 2004 
  
Figure 10. Edge e with distance d 
If the area to the left (region interior) has a high reflectance of 
100 % and the area to the right (region background) has a low 
reflectance of 0 %, then we derive for the boundary pulse power 
as function of d 
ET : | cm dx .(5) 
XO -« 
e a” dx dy — 
  
  
à E meh 
8 
N 
Pdy=— | 
o 0 
For horizontal edges the boundary pulse power is derived in the 
same way. Since we assumed a uniform reflectance property of 
the surface, the reflectance is a linear function of the distance d 
and only valid if d is inside the mesh of the boundary pixel 
area. By this observation the distance d between the estimated 
edge and the beam center is fixed, whereas the edge orientation 
remains to be found. 
To achieve this we analyze the spatial edge neighborhood. 
There we receive another estimated edge as the tangent of a 
circle. Assuming again a straight edge, four tangents on the two 
circles are found. For circles at (0/0) and (g/0) with radius dj 
and d» we see: 
xn=d, with n= (6) 
  
Due to this the constraint of the region interior or region 
background in the spatial neighborhood is used for a unique 
position and orientation of the edge. Figure 9b sketches the 
estimated edge derived from the power values of two pixels. 
The brightness of the pixels shows the power values. 
This model is now correct for essentially straight edges. 
Obviously the model is incorrect for corners, so these will have 
to be determined by extrapolating adjoining edges. 
5. CONCLUSION 
The space-time analysis of recorded laser pulses allows a sub 
pixel estimation of the edge. Only two pulse power values of 
the boundary with respect to the spatial neighborhood are 
necessary for a unique estimation of the edge position and 
orientation. For processing the intensity cube an adaptive 
threshold operation is possible and it allows exploiting different 
features without selecting a special feature in advance. The 
simulation was helpful for develop algorithms. The data 
generation and analysis we carried out are general 
investigations for a laser system which records the waveform of 
laser pulses. Future work focuses on an improved analysis of 
the received signal. 
6. ACKNOWLEDGEMENT 
The authors would like to thank Jorg Neulist for his fruitful 
discussions during the preparation of this work. 
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