| XXXIX-B3, 2012
| LiDAR point cloud.
tcomings:
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and its neighbouring
‘the points in the 3D
| question and its
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revious method, this
only when the point
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ine definition while
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ersion matrix of the
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ollows (Pauly et al.,
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entroid )
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persion matrix (Cj)
às). For planar
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es. This eigen value
'erpendicular to the
the planarity of the
> local point density
nate approach. This
Xf the approximate
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ssumes a uniform
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as the following
in question belongs
h the neighbouring
the established 3D
oplanar points are
al point density.
the established 3D
alue analysis of the
points within the
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B3, 2012
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia
established 3D neighbourhood relative to the point in question
(POI) (Figure 3).
Figure 3: Dispersion of the points within the established 3D
neighbourhood relative to the point in question
In this case, the dispersion matrix (C,) is derived as follows:
Feu a 2° 4e
C, ED ai I UE
where %=[X, Y ZT
, and hor = [x ror Yeor Zl
(3)
Based on eigen-value analysis of C,, the established 3D
neighbourhood is deemed planar if and only if the point in
question belongs to the local plane through this neighbourhood.
Once the planarity of established neighbourhood is checked, the
local point density index is estimated in the same way as the
approximate method.
Despite considering if the point question belongs to planar
neighbourhood or not, this approach is still subjected to the
inclusion of non-coplanar points within established 3D
neighbourhood for local point density estimation.
2.3 Adaptive Cylinder Method
The adaptive cylinder approach is proposed to overcome the
drawback of the previous method - inclusion of non-coplanar
points within planar neighbourhood - for local point density
estimation. In this method the planarity of the established
spherical neighbourhoods is investigated by defining a cylinder
whose axis orientation is adaptively changing to be aligned
along the normal to the plane through the majority of the points
in the defined neighbourhood (Figure 4). This axis is derived
using an iterative plane fitting procedure where the points are
assigned weights that are inversely proportional to their normal
distances from the derived plane in the previous iteration.The
cylinder diameter is equivalent to the distance between the point
in question and its n"-nearest neighbouring point within the
defined neighbourhood. The height of the defined cylinder is
determined based on the expected noise level in the point cloud.
Figure 4: Adaptive cylinder neighbourhood
In this approach, the local point density index is estimated only
when the majority of the points within the established spherical
neighbourhood, together with the point in question, are
included in the defined cylinder. The local point density index
is then computed as follows:
LPD = Eo in which k<n (4)
2
AT,
n
127
Where k is the number of the points within the defined cylinder
and r, is the distance between the point in question and its m-
nearest neighbouring point in the spherical neighbourhood. This
method estimates the local point density only by utilizing the
points inside the adaptive cylinder. This resolves the drawback
of the eigen-value analysis methods by removing the points
which do not belong to the planar neighbourhood. The only
shortcoming of this method is assuming a uniform point
distribution within the adaptive cylinder.
3. THE IMPACT OF CONSIDERING LOCAL POINT
DENSITY INDICES ON LIDAR DATA PROCESSING
As mentioned earlier, the consideration of local point density
indices will improve the LiDAR data processing results to a
great extent. In this section, some of the processing activities
which are highly affected by local point density variations are
highlighted and the impact of incorporating estimated local
density values in these activities are discussed.
3.1 Neighbourhood Definition
Neighbourhood definition is the primary step of LiDAR data
processing. This definition is a rule that determines the
neighbours of each point, and as a result has a great impact on
the reliability of different processing activities’ results.
Different neighbourhood definitions are presently being used
for LiDAR data. However, none of them consider the local
variations in the LiDAR point density. This inconsideration
leads to the exclusion of required neighbouring points and
inclusion of the points that should not be considered for the
derivation of processing parameters (e.g, segmentation
attributes). In order to define meaningful neighbourhoods for .
individual LiDAR points, while considering the characteristics
of their associated surfaces, the computed local point density
indices should be considered. In this case, when the local point
density is low, the size of the defined neighbourhood will be
increased to include the needed number of points for the
derivation of processing parameters.
3.2 Region Growing
Region growing is recognized as one of the spatial-domain
LiDAR data segmentation approaches. In this approach, the
neighbouring LiDAR points that fulfil a homogeneity criterion
(e.g., planarity or smoothness of the surface) will be segmented
in one group (Besl and Jain, 1988). The conventional criterion
for the determination of neighbouring points, in this process, is
a fixed 3D distance. However, when the local point density is
not uniform within a LiDAR dataset, considering a fixed
neighbourhood radius may result in inaccurate segmentation
results. In order to define adaptive neighbourhoods of the seed
points for region growing, the local point density index in the
seed point location should be incorporated in the definition of
the neighbourhood radius.
3.3 Derivation of Attributes for Parameter-Domain
Segmentation Approaches
The performance of the parameter-domain segmentation methods
depends on the computed attributes for individual laser points. In
most of these approaches, the segmentation attributes are derived
based on the parameters of the fitted plane through the
neighbouring points within the defined neighbourhood for each
point. The quality of plane fitting process is ensured by providing
the needed number of points for the plane definition. Therefore, the
size of established neighbourhood should be made flexible with
