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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B2. Istanbul 2004 
  
in the form of regions. Separating the pulse properties range and 
power in regions is fundamental to handling the ambiguity of 
multiple reflections at the same spatial position. Boundary 
pixels are labeled as shared pixels belonging to background and 
foreground. Figure 6 illustrates the region definition. 
The computed region N consisting of range values is described 
by the range image Ay. Then the pulse power values of the 
same pulses are used to generate the power image /y. In this 
manner we receive a corresponding representation of all 
determined regions (N = 1, 2, 3, ...). 
The region boundary mainly contains pixels derived from 
multiple reflections. The region interior is characterized by 
single reflections and fills up the region to the boundary. The 
region background is labeled with zero pixel values. Generally 
it can be said that nonzero pixels belong to the region and zero 
pixels constitute the background. 
Region background: 
  
Region boundary : 
Figure 6. Region components definition 
An iterative region growing algorithm considers the range 
properties of all pulses in the spatial neighborhood: if the range 
difference of a pulse and the proofing pulse is below a given 
threshold, then the pulse is connected and grouped as a new 
element to this region. Samples of range and power images as 
segmentation results are depicted in Figure 7. 
   
e f g h 
Figure 7. Segmentation results (grid mesh width g-275cm, 
Gaussian distribution of the beam at the grid line 
+26): a)-d) range image Ry=1 Ry=r, Ry=3, Ra, 
e)-h) power image /v=1 /v=, Ines, Ines 
4.4 Region edges 
For physical edge description a data driven region boundary 
(edges) approach similar to the algorithm of Besl (1988) is 
used. This approach generates a parametric function 
representation of the region boundary for higher level 
processing. To refine the region boundary the estimation of 
edge position and edge orientation from received pulse power 
and analysis of the spatial neighborhood is proposed. 
First each power image /y is processed with a 4-neighboring 
edge following algorithm to determine a parametric function 
representation of the region boundary. The algorithm traces the 
exterior boundary of the region N in the power image /y(x.)). 
As output for each trace, we construct two boundary 
parameterization functions xy(s) and ya(s) containing the row 
and column coordinates of the connected boundary pixels. 
Additionally the boundary range function zy(s) can be found 
using the range image. 
Figure 8 shows an example of an exterior edge description with 
the three parameter boundary functions xy=2(5), Vw=2(5). En=a(5) 
of the region N=2 and corresponding power image /v with 
overlaid boundary. 
  
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b) vw-2(5), €) Zw-2(s), d) power image /y-» with 
overlaid outer boundary function 
boundary labeled Æ, the region interior / and the region 
background B. By assuming a straight edge from the upper left 
pixel to the center pixel the line is undetermined without further 
information. A sample of possible edges ë, & and & is 
depicted. 
Figure 9a shows a 3-by-3 pixel neighborhood including a region 
       
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Figure 9. Edge estimation a) sample of edges e;; &; and e;, 
b) estimated edge e; 
To estimate the edge position and edge orientation the received 
pulse power is analyzed for the geometrical shape of the 
illuminated surface. With the assumption of a uniform 
reflectance property of the surface the target reflectance 
depends only on the geometrical shape. Therefore we assume 
uniform reflectance and straight object edges. The laser beam 
with its radial symmetric Gaussian distribution illuminates an 
edge. For integrating along the coordinate we assume the edge 
is vertical. Furthermore the beam center distance to the edge e 
is given by d (Figure 10). 
111