Within one horizontal voxel layer, the algorithm searches the 
main four planimetric directions (coordinate directions) for 
surface voxels. If such voxels are detected all subsequent voxels 
in this row or column are set to value v=1, except the original 
surface voxels (Figure 1b). After executing this procedure for 
all four directions (Figure 1b-e) and intersecting the areas of 
obstructed vision (v-1), i.e. adding up the voxel values, all 
interior voxels contain the value v=4 (Figure 1f) and can be 
marked as "filled" voxels whereas all voxel values below 4 are 
set back to v=0. Therefore, it can be distinguished between 
original surface voxels, artificially “filled” voxels (v=4) and 
background voxels (v=0). Erroneously filled voxels are most 
likely to occur in tree crowns with narrow branches and twigs 
(Figure 2a). To solve these problems an extended approach was 
created (based on a region growing algorithm) for segmentation 
of regions of filled voxels. Starting at a filled voxel the N4 
neighbourhood (due to the four viewing directions) is analysed. 
If a neighbouring voxel is also a filled voxel it is accepted and 
the growing process is continued until the border of a filled 
region is reached. Then the border voxels are checked if at least 
one unfilled neighbouring voxel (background voxel) can be 
found, i.e. not exclusively filled or surface voxels. In this case 
the whole filled region is eliminated, i.e. its values are set to 
v=0 (Figure 2b). Small gaps often remain at the acquired 
surfaces of stem or thicker branches caused by occlusion effects 
of surrounding branches (even if scanning from four or five 
different directions) leading to the erroneous omission of real 
tree volume. Therefore, this rigorous algorithm could be 
modified by accepting a filled region, even if not all but most 
border voxels have an adjacent surface voxel (e.g. 95% or 
90%). 
4.3 Layer-wise Volume Estimation 
The estimation of the layer-wise tree volume is based on the 
segments generated in the previous filling process described 
above. Assuming that the diameter of a branch does not change 
significantly in a horizontal layer of one voxel thickness, the 
volume can be approximated by an oblique cylinder (Figure 3), 
i.e. by the cross-sectional area A; (=segment area) of a branch 
multiplied by height 4; (=layer thickness). Due to the fact that 
surface voxels are normally not completely filled by laser 
points, the total area A; of a cross-section, i.e. the sum of the 
area of surface voxels plus filled voxels, overestimate the real 
volume. On the other hand regarding only the filled (interior) 
voxels the real volume will be underestimated. Therefore, both 
areas are averaged for the volume estimation. The final tree 
volume results from the sum of each branch volume of all 
layers. The diameter at breast height, DBH, is derived from 
averaging the cross-sectional areas, 4,, of the stem between a 
height of l.1m and 1.5m. Tree height is determined as the 
difference between the lowest and the uppermost voxel layer of 
the point cloud. 
4.4 Determination of Threshold for Noise Reduction 
A detailed inspection of histograms of voxel point densities 
show that a high number of voxels contain only a few points. 
Due to the scan resolution and the mean scanning distance of 
about 10m even small twigs are acquired by approximately 10- 
15 points per voxel (edge length 1cm). Taking occlusion effects 
into account this number may be reduced to 8-12 points per 
voxel. It can therefore be assumed that voxels containing fewer 
points can be stated as noise. To define a suitable threshold the 
function "change in filled voxels” (Figure 4) can be analysed. 
   
  
  
b) 
Figure 2. a) Correctly filled interior voxels and erroneously 
filled voxels between branches, b) Result after elimination of 
erroneously filled voxels / voxel segments by a region growing 
approach analysing the borders of these segments 
horizontal 
   
   
  
voxel layer 
branch 
Figure 3. Layer-wise volume estimation by determination of the 
cross-section area 4; of branches multiplied by height A 
(=thickness of voxel layer) 
  
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