Aerial laser scanning for creating digital relief models has been widely applied in Russia for over 20 years. For processing results of aerial laser scanning, it is necessary to classify cloud of laser points. Classification of cloud of laser points is performed via commercial software products (produced abroad), which frequently use refinement algorithms of “Earth” class data, which consider the relief particularities. The paper puts forward a proprietary algorithm of laser scanning data interpolation, enabling to remove redundant cloud of laser points of “Earth” class when data granularity reduces, in the first place, for flat terrain. The paper provides a detailed stepwise description of algorithm operation, and the results of constructing a digital relief model on the basis of the cloud of laser points of “Earth” class, processed via the proposed algorithm.

1. http://www.iaeme.com/IJCIET/index.asp 306 editor@iaeme.com
International Journal of Civil Engineering and Technology (IJCIET)
Volume 10, Issue 05, May 2019, pp. 306-311, Article ID: IJCIET_10_05_031
Available online at http://www.iaeme.com/ijmet/issues.asp?JType=IJCIET&VType=10&IType=5
ISSN Print: 0976-6308 and ISSN Online: 0976-6316
© IAEME Publication
PROPOSED ALGORITHM OF ELIMINATING
REDUNDANT DATA OF LASER SCANNING FOR
CREATING DIGITAL RELIEF MODELS
Kochneva O.E.
PhD, Associate Professor, Department of Geology of Oil and Gas,
Saint Petersburg Mining University
Russian Federation, 199106, Saint Petersburg, Vasilievski Ostrov, 21 line, 2
Kryltcov S.B.
Department of Computer Science and Technologies
Saint Petersburg Mining University
Russian Federation, 199106, Saint Petersburg, Vasilievski Ostrov, 21 line, 2
Feshchenko R.Y.
PhD, Associate Professor, Department of Automation of Technological Processes and
Production, Saint Petersburg Mining University
Russian Federation, 199106, Saint Petersburg, Vasilievski Ostrov, 21 line, 2
ABSTRACT
Aerial laser scanning for creating digital relief models has been widely applied in
Russia for over 20 years. For processing results of aerial laser scanning, it is
necessary to classify cloud of laser points. Classification of cloud of laser points is
performed via commercial software products (produced abroad), which frequently use
refinement algorithms of “Earth” class data, which consider the relief particularities.
The paper puts forward a proprietary algorithm of laser scanning data interpolation,
enabling to remove redundant cloud of laser points of “Earth” class when data
granularity reduces, in the first place, for flat terrain. The paper provides a detailed
stepwise description of algorithm operation, and the results of constructing a digital
relief model on the basis of the cloud of laser points of “Earth” class, processed via
the proposed algorithm.
Key words: Processing algorithm, aerial laser scanning, point cloud refinement, cloud
of laser points of ―Earth‖ class, digital relief models
Cite this Article: Kochneva O.E., Kryltcov S.B., Feshchenko R.Y., Proposed
Algorithm of Eliminating Redundant Data of Laser Scanning for Creating Digital
Relief Models, International Journal of Civil Engineering and Technology 10(5),
2019, pp. 306-311.
http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=10&IType=5

2. Kochneva O.E., Kryltcov S.B., Feshchenko R.Y.
http://www.iaeme.com/IJCIET/index.asp 307 editor@iaeme.com
1. INTRODUCTION
Currently, the aerial laser scanning technology is successfully used for creating three-
dimensional terrain models, digital topographic plans and maps.
The essence of the laser scanning method is obtaining spatially-defined terrain model,
which consists of cloud of laser points describing both the Earth surface and all the objects
located on it, in the form of XY coordinates and Z applicate of which obtained point.
Via the results of aerial laser scanning, it becomes plausible to obtain cloud of laser points
with the density required for creating digital relief models. One of the stages of aerial laser
scanning data processing is classification of cloud of laser points. The following standard
classes can be specified: earth surface, earth model points, dropped out points, short, medium-
height and high vegetation. The most important class is the class of earth points. Via ―Earth‖
class, digital relief models and digital terrain models are created.
In selecting cloud of laser points in the automatic mode, it is possible that minor cloud of
laser points will appear in the automatic mode, with these points located clearly above the
main cloud of cloud of laser points [1] or clearly below. The percentage of such points is not
high, but even one wrong point can distort the relief, and for this reason, manual check is
always performed of the classification of earth surface points via viewing profiles (cross-
sections), building horizontal relief models and height-painted relief models [2-4].
As the number earth surface points (―Earth‖ class) can be fairly large – up to one million
points per 0.5 km2
, it is necessary to execute thinning for building digital terrain models [5-8].
It should be noted that the density of cloud of laser points (of all classes) is about 10 points/
1 m2
. The density of cloud of laser points of “earth” class is 2-3 points/1 m2
. Such precision is
redundant for building topographic maps and results in decrease in productivity [6,7,9-13].
2. METHODS
2.1. Description of proposed algorithm
For thinning the data, the following criterion of redundancy of coordinates was formulated: if
it is possible for arbitrary point from the data array to find three adjacent points in different
directions, this point is considered redundant if the length of the normal drawn from the
reference point to the plane built through the three adjacent points, turns out to be lower than
the specified allowable value.
For eliminating redundant cloud of laser points according to the criterion which was put
forward, data interpolation algorithm has been elaborated, implemented in the form of
software in Python language. Hereinafter, the stepwise description of the algorithm operation
is provided.
The software is fed with a set of text data with coordinates of cloud of laser points in X Y
Z format as input data, after that, the text data are converted into numerical values, and the
coordinate array of A points is filled, every line in the coordinate array corresponds to an
individual point, and the first three columns correspond to the point coordinates in three-
dimensional space. Thus, A array is a matrix of ]3[ n dimensionality, where n is the number
of cloud of laser points in the initial data set.
Let us set the value of minimal data refinement – the maximal point deviation from the
plane built through its three adjacent to it: ΔD. The next operations are performed for each
point in A array, for this reason, for further algorithm description, let us set arbitrary point O
with coordinate (x0, y0, z0) from A array.
Data array A is copied in full, except for point O which is under scrutiny, forming B array.
Two columns are added to B data array, they contain data about l length and the rotation angle

3. Proposed Algorithm of Eliminating Redundant Data of Laser Scanning for Creating Digital Relief
Models
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of vector built from each point from B array to O point in XY system of coordinates,
without consideration of Z applicate. For each point N of B array, which has coordinates
nnn zyx ,, , l distance to O point is executed as follows:
2
0
2
0 )()( yyxxl nn 
Rotation angle  of ON vector in relation to O is calculated as follows:









0
0
atan2
xx
yy
n
n .
atan2 is the function of arctangent, returning the vector rotation angle with consideration
of quadrant, versus regular arctangent.
After obtaining l and  values for each point in B array, we will sort it in ascending order
of l value, thus, the closest points to O coordinates, will be at the beginning. An example of
obtained data structure is given in Table 1.
Let us set three directions, in which, search of the closest points will take place, we will
conditionally name them North-East, where  3/2;0  ; West, where
   3/2;;3/2  ; South-East, where  0;3/2 .
Table 1 Structure of sorted data array B
X, m Y, m Z, m d, m 
7946748,690 8431755,570 195,910 0,0020 73,0
7946748,450 8431751,710 195,770 0,0022 05,0
7946748,420 8431752,010 195,740 0,0026 11,0
… … … … …
The algorithm successively passes through the lines of B array, finding one closest point
(min l) in each direction. Let us name these three points as A, B, C. In case if at least one of
the three points closest to N cannot be found, O point remains in initial data array A, and the
next point for consideration is selected from the array. Such a situation is typical when O
point is located on the boundary of the considered spot of cloud of laser points, and the closest
point to it in one of directions, is located in another data array of cloud of laser points, or
information about this point does not exist at all.
With successful finding of points A, B, C, ABC plane is built through them, the plane
equation in three-dimensional space is as follows:
dczbyax 
a, b, c coefficients are the coordinates of the vector of normal N to ABC plane, and they
are calculated via vector multiplication of two arbitrary vectors belonging to ABC plane, for
example, ACABcbaN ),,( . d coefficient can be calculated via scalar product of vector of
normal N and coordinates of point B or C: BNd  .
Then, the absolute distance in three-dimensional space between O point and ABC plane is
calculated by the following formula:
222
000
cba
dczbyax
Lxyz


 .

4. Kochneva O.E., Kryltcov S.B., Feshchenko R.Y.
http://www.iaeme.com/IJCIET/index.asp 309 editor@iaeme.com
If LLxyz  , we assume that О point is negligible for relief estimation, and we eliminate
it from initial array A and move on to considering the next point from this array. At this stage,
the dimensionality of array A reduces to ]31[ n , through which, data thinning is achieved.
After considering all the points of A array, the thinned data are recorded in a new file for
further work in specialized software.
For visual demonstration of the algorithm operation, a small sport of mountain relief was
selected, which includes 200 cloud of laser points. After data processing via the proposed
algorithm with setting maximal deviation Δ m, 73 cloud of laser points (36.5 %) were
eliminated.
3. RESULTS AND DISCUSSION
Visualization of surfaces before and after processing with the algorithm, which had been
elaborated, was performed in MATLAB environment based on Delaunay triangulation via
consecutive execution of the following commands:
 [Xm,Ym] = meshgrid(X,Y) – creating the surface connecting the points located on X and Y
coordinates.
 tri = delaunay(Xm,Ym) – creating Delaunay triangulation network.
 trimesh(tri, Xm, Ym, Z) – visualization of the formed surface with overlay of triangulation
dependencies between apexes.
Visualization of the surface performed in MATLAB environment, using the data under
consideration, is demonstrated in figure 2. Surface visualization after data processing is
demonstrated in figure 3 [9].
Figure 1- Original map of heights, 200 points Figure 2 - Obtained map of heights, 127 points
For visual demonstration of the algorithm operation, a mountain relief area including 200
cloud of laser points, was chosen. The surface visualization performed in MATLAB
environment, using the data under consideration, is demonstrated in fig. 1. After data
processing via the proposed algorithm with setting maximal deviation 5.0D m, 73 cloud of
laser points (36.5 %) were eliminated. Surface visualization after data processing is shown in
fig. 2. The figure indicates that the eliminated points are located as close as possible to the
plane formed by adjacent points, which confirms the effectiveness of the elaborated algorithm
[9,11].
4. CONCLUSIONS
The paper presented the interpolation algorithm of the data obtained via relief laser scanning,
which enables to effectively execute thinning of cloud of data points, which are minor in

5. Proposed Algorithm of Eliminating Redundant Data of Laser Scanning for Creating Digital Relief
Models
http://www.iaeme.com/IJCIET/index.asp 310 editor@iaeme.com
describing the relief. Data redundancy is identified via calculating the distance from the point
to the plane, which includes three points adjacent to it in different directions. It should be
noted that this algorithm is universal, it fits for various fields, including for creating digital
models of pits, mine and pit workings, which will enable to increase the accuracy of source
data for numerical modeling of various mining processes [14-21]. The way of identifying
redundancy, which was put forward, is implemented via simple mathematical operations,
through this, lower computational complexity of algorithm is achieved compared to
proprietary counterparts, which enables to increase the productivity of thinning large arrays of
cloud of laser points.
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