2. RELATED WORK 
A common and well-known task is the estimation of forest 
carbon stocks. Good et al. (2001) present a compilation for 
estimating the biomass of individual trees, including double 
regression, ratio sampling, Randomized Branch Sampling 
(RBS) and Importance Sampling (IS). The most common 
method is the application of allometric functions (e.g. Zianis, 
Mencuccini, 2004). Due to the potential of terrestrial laser 
scanners to rapidly and accurately acquire suitable data for 
estimation of tree volume (Lefsky, McHale, 2008), several 
research groups are currently adapting and enhancing this 
approach. Based on techniques of Computer Graphics and 
Remote Sensing (an overview is given in Bucksch et al. (2010)) 
the aims of this research are volume determination (e.g. Lefsky, 
McHale, 2008; Raumonen et al., 2011; Dassot et al., 2010), 
structural and radiative consistency (Cóté et al, 2009), 
estimation of branch parameters, including length, radii or 
straightness of stem and branch (Bucksch, Lindenbergh, 2008; 
Bucksch et al, 2010; Gorte, Pfeifer, 2004a,b; Pfeifer, 
Winterhalder, 2004; Pfeifer et al, 2004), branch size 
distribution (Raumonen et al, 2011), dimensionality of tree 
stems (Gatziolis et al., 2010), angles between branches, and the 
reconstruction of the outer hull (Pfeifer et al., 2004). In addition 
to measurements of diameters, three basic approaches can be 
found: (i) extraction of a skeleton of a tree (Bucksch, 
Lindenbergh, 2008; Bucksch et al, 2010; Gorte, Pfeifer, 
2004a,b; Coté et al., 2009; Xu et al., 2007), (ii) fitting pre- 
defined primitives, e.g. cylinders (Pfeifer et al., 2004; Lefsky, 
McHale, 2008; Raumonen et al., 2011), free-form curves (B- 
Splines) (Pfeifer, Winterhalder, 2004; Yan et al., 2009) or mesh 
in general sense (Xu et al., 2007), (iii) structuring the point 
clouds in a voxel domain (Gorte, Pfeifer, 2004a,b; Gatziolis et 
al., 2010). The main challenges in this field of research are the 
large data requirements (varying from several thousand to 
commonly 2 million points), noise (rarely treated, e.g. Gorte, 
Pfeifer, 2004a,b, but discussed as error source, e.g. Bucksch et 
al, 2010), varying point densities (may lead to over- or 
underestimation of tree volume, e.g. Leksky, McHale, 2008), 
gaps or holes, the vast variety of branch diameters and lengths 
with a tree and a reliable estimation of complete stem and 
crown volumes — rarely presented in these approaches. 
3. DATA ACQUISITION AND PRE-PROCESSING 
The test site was located at the urban area of Karlsruhe city in 
the Upper Rhine Valley, Germany. From about 560 trees 
scheduled to be cut and weighed by the Gardening Department 
of Karlsruhe (GBA) during winter period 2009/2010, nine 
deciduous trees were chosen as suitable control data for these 
investigations. Additional aspects were a low level of 
interpenetration of the crown with adjacent trees, the absence of 
leafs, fruits, ivy or mistletoe and a variety of different tree 
species (Acer spp. (denoted by A1, A2, A3), Tilia Spp. (T1, T2), 
Robinia spp. (R1, R2), Betula spp. (B1) and Carpinus betulus 
(C1); c£. Table 1). Before felling, each tree was scanned from 
three to five positions with a Leica HDS 6000 using the finest 
scan incrementation of approx. 2mm at an average distance of 
10m and a point accuracy of about +3mm. To obtain a highly 
accurate registration of these individual point clouds (using 
Cyclone 5.8%), five sphere targets had been positioned around 
each tree. The standard deviation ranges from 41mm to +2mm 
for all investigated trees. To convert green weight at felling time 
  
   
  
  
    
  
     
   
   
   
  
    
    
   
   
    
       
    
   
   
   
   
    
    
    
   
   
   
    
   
    
     
    
    
  
     
     
   
   
    
   
  
   
   
   
   
to dry volume and carbon content several wood samples at 
different heights were collected and analysed after felling. 
A point cloud reduction using an average point spacing of 2mm 
was also carried out (Cyclone “unify” procedure) as well as a 
manual elimination of disturbing objects like traffic Signs, 
parked cars or branches of neighbouring trees. 
4. DATA ANALYSIS 
Data analysis starts with the generation of the voxel structure 
and the assignment of the laser points to this voxel domain. 
Voxels without points are not considered in the subsequent 
analysis. The necessary definition of a suitable voxel size 
depends on the applied scan resolution of the terrestrial laser 
scanner and the dimension of the finest branches to be 
measured. A certain number of points per voxel should be 
achieved, e.g. with a voxel edge length of lcm like in this 
application and diameters of finest branches of 3-4mm about 20 
points per voxel will be obtained, which can be subsequently 
distinguished from voxels containing noise or so-called 
"phantom" points, well-known in the domain of terrestrial laser 
scanning. Based on this voxel structure a specific approach was 
developed which analyses the data in horizontal layers of one 
voxel thickness. 
4.1 Noise Reduction 
Two different kinds of noise reduction are carried out: (1) 
elimination of isolated voxels and (ii) elimination of voxels with 
a small number of laser points. In the first case those voxels 
should be excluded which are not connected to the free, i.e. 
which are isolated (cf. Gorte, Pfeifer, 2004a). Based on a N26- 
neighbourhood (comparable to a N8-neighbourhood in 2D) or a 
N124-neighbourhood, the central voxel is eliminated if all 
adjacent voxels are empty, because it implies that there is a gap 
between the surface of the tree and the particular points. 
A second method of noise reduction was applied to eliminate 
voxels which are sparsely filled by laser points, ie. voxels 
containing fewer points than a pre-defined threshold. For rough 
volume estimations a threshold may be defined by experience, 
but our investigations have shown that this threshold varies 
dependent on the tree type and therefore must be determined by 
a specific method explained in section 4.4. 
4.2 Filling of Hollow Surfaces (Interior Voxel) 
One challenge of voxel-based approaches for determination of 
tree volumes is the determination of hollow surfaces, i.e. voxels 
lying inside the stem and branches which contain no laser 
points but have to be taken into account for volume 
calculations. Mathematical morphology (dilation, closing) may 
be a possible method (e.g. Gorte, Pfeifer, 2004a), but the 
problem in this application is that the dimension of the hollow 
surface exceeds the space between narrow branches leading to 
erroneously filled areas which cannot be reversed (e.g. by 
erosion). Therefore, another procedure was chosen based on the 
intersection of the four areas of obstructed vision from four 
orthogonal directions. It is robust, fast, does not need prior 
information, and fits to all forms of branches and stems. 
Additionally, repeated iterations (cf. mathematical morphology) 
are not required. 
  
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