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The terrestrial laser scanner is an equipment developed for surveying applications and is also used for many other purposes due to its ability to acquire 3D data quickly. However, before intensity data can be analyzed, it must be processed in order to minimize the edge or border effect, one of the most serious problems of LIDAR's intensity data. Our research has focused on characterizing the edge effect behavior as well as to develop an algorithm to minimize edge effect distortion automatically (IRA). The IRA showed to be effective recovering 35.71% of points distorted by the edge effect, providing significant improvements and promising results for the development of applications based on TLS data intensity to many studies.
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Europe an Journal of Re mote Sensing - 2016, 49: 301-315 doi: 10.5721/EuJ RS20164917
Recei ved 14/12/2015 accep ted 18/05/2016
European Journal of Remote Sensing
An ofcial jour nal of the It alian Society of Re mote Sen sing
An intensity recovery algorithm (IRA) for minimizing
the edge effect of LIDAR data
Fabiane Bordin1,4,6*, Fabrício Galhardo Müller4, Elba Calesso Teixeira1,2, Sílvia Beatriz
Alves Rolim1, Francisco Manoel Wohnrath Tognoli3,4, Luiz Gonzaga da Silveira Júnior4,5,
Maurício Roberto Veronez3,4 and Marco Scaioni7
1Graduate Program in Remote Sensing, Federal University of Rio Grande do Sul,
Av. Bento Gonçalves, 9500, 91501-970, Porto Alegre, Brazil
2State Foundation of Environmental Protection Luiz Henrique Roessler,
Av. Borges de Medeiros, 261, 90020-021, Porto Alegre, Brazil
3Graduate Program in Geology, University of Vale do Rio dos Sinos,
Av. Unisinos, 950, 93022-000, São Leopoldo, Brazil
4Advanced Visualization Laboratory (VIZLab), University of Vale do Rio dos Sinos,
Av. Unisinos, 950, 93022-000, São Leopoldo, Brazil
5Graduate Program in Applied Computing, University of Vale do Rio dos Sinos,
Av. Unisinos, 950, 93022-000, São Leopoldo, Brazil
6itt Performance - Technological Institute of Performance and Civil Construction,
University of Vale do Rio dos Sinos, Av. Unisinos, 950, 93022-000, São Leopoldo, Brazil
7Department of Architecture, Built environment and Construction engeneering (ABC),
Politecnico di Milano, Via Ponzio, 31, 20133, Milano, Italy
*Corresponding author, e-mail address:
The terrestrial laser scanner is an equipment developed for surveying applications and is
also used for many other purposes due to its ability to acquire 3D data quickly. However,
before intensity data can be analyzed, it must be processed in order to minimize the
edge or border effect, one of the most serious problems of LIDAR’s intensity data. Our
research has focused on characterizing the edge effect behavior as well as to develop an
algorithm to minimize edge effect distortion automatically (IRA). The IRA showed to be
effective recovering 35.71% of points distorted by the edge effect, providing signicant
improvements and promising results for the development of applications based on TLS data
intensity to many studies.
Keywords: Intensity recovery algorithm, classication edge effect, LIDAR, remote
sensing, terrestrial laser scanning.
In the last decade, terrestrial laser scanning (TLS) and proling have been consolidated
to provide one of the most effective technologies for 3D geospatial data acquisition
[Vosselman and Maas, 2010; Shan and Toth, 2009]. Geometric information obtained from
Bordin e t al. Inten sity recovery a lgorithm (IR A) of LIDAR data
laser scanners is commonly used in many distinct research domains to estimate volumes,
to characterize geometric features, to measure deformations, and to detect changes like
accumulation or loss of material [Scaioni et al., 2013; Lindenbergh and Pietrzyk, 2015;
Longoni et al., 2016]. In each eld, methodological approaches have been developed to
cope with specic features and problems [Pirotti et al., 2013]. There are many studies about
methodologies based on geometric coordinates data of TLS but few studies have provided
methodological and operational approaches to use TLS intensity data [Eitel et al., 2010;
Burton et al., 2011; Inocencio et al., 2014; Pavi et al., 2015].
The aim of this research is to recover laser intensity data distorted by the so called ‘edge
effect’ [Eitel et al., 2010], in the case data acquisition was operated using TLS. The basic
consideration is that laser intensity data can be used to obtain information regarding water
content or other characteristics of target objects, provided that the edge effect has been
totally or partially corrected. The edge effect occurs in two main cases. The rst case is
when the laser beam is divided by an object and returns as a combination of reected
signals from at least two objects. An example is the edge of a leaf plus an object behind the
leaf. The signal returning to the sensor provides information that merges data from the leaf
and data from the target behind the leaf. The second case is when part of the laser beam
collides with the target and part of radiation is lost. In other words, only a fraction of the
laser beam returns to the sensor or is too weak to trigger a signal.
Although the problem of the edge effect has been already reported in the literature, no one
provided satisfactory solutions to eliminate or minimize its consequences on laser intensity
data. As intensity data are related to physical and chemical characteristics of the target
object [Inocencio et al., 2014], the reduction of the edge effect is benecial for research that
intends to infer, correlate or interpret these data. The research described here contributes
to understand of the edge effect and to provide an algorithm that automatically mitigates
its consequences. This achievement has been made possible by the development of the
intensity recovery algorithm (IRA), which can be used in a wide number of applications
belonging to different research domains.
Terrestrial Laser Scanning
Laser light has important properties that distinguish it from ordinary light, such as coherence,
wavelength, spectral purity, directivity and divergence of the beam, modulation of power
and polarization of light. Terrestrial laser scanning (TLS), also referred to as ground-based
LIDAR (Light Detection and Ranging), is based on the emission of a narrow laser beam
toward the target object, which pulses with high repetition frequency. The scanner can
directly measures the round-trip time (ToF - Time-of-Flight) of the pulses between the
sensor and the target before calculating the position of each point. As an alternative, the
phase-shift of a modulated laser signal can be measured to derive the distance from the
sensor to the object. Figure 1 schematically illustrates data acquisition performed with a
Most TLS instruments output a data le containing coordinates of points in a 3D space (X,
Y, Z), the returned laser intensity value I, and, if available, the RGB values recorded by a
digital camera. These data result in a record of X, Y, Z, I, R, G, B per each point that is stored
as a text or binary le. The intensity data may be also used to obtain information about the
objects characteristics (classication) as a remote sensor [Burton et al., 2011]. Based on
Europe an Journal of Re mote Sensing - 2016, 49: 301-315
Colwell’s concept [1983] the intensity denition is the variation of the ux of energy per
unit by solid angle irradiated in the same direction from the point source. In other words,
intensity is the quantity of energy that passes through a unit area per second, per steradian
[Colwell, 1983].
Figure 1 - Schematic representation of geometric
coordinates (X, Y, Z) and intensity data acquisition
(I). Adapted Reshetiuk [2009].
One of the problems affecting the intensity data is the edge effect. The main cause of the
edge effect is due to the outline of the object generated when laser pulses partially collide
with the target being scanned (i.e., stop colliding with the target and start colliding with
the background). Figure 2 shows a rectangle with circular holes, where the blue area is the
internal portion of the object and the red area is the border of the object.
Figure 2 - Representation of an object with circular
holes. The red color represents the areas where the
edge effect will appear.
The edge effect will take place at the edge of the target and can be understood as the
difference between the recorded intensity and the expected intensity after colliding with
the target. This effect occurs due to the variable diameter of the laser beam, which is
proportional to the distance between the laser scanner and the target, and is referred to as
laser divergence or beam divergence [Popescu, 2011].
Bordin e t al. Inten sity recovery a lgorithm (IR A) of LIDAR data
Material and Methods
The TLS instrument adopted for this study was an ILRIS 3D Optech, whose active ranging
sensor operated based on ToF. This instrument also incorporates a digital camera that
is installed off-axis, causing parallax misalignment between point cloud data and color
information in the case of objects located at a distance closer than 35-40 m from the
Modeling the edge effect
In order to acquire intensity data including an edge effect generated under controlled
conditions, a specically designed single target, a topographic tripod, a planar white board,
and a laser scanner ILRIS 3D have been used to set up the experimental facility (Fig. 3).
The target was made of a wooden board with eight holes, whose number has been chosen
arbitrarily. To this end, a white board has been positioned behind the main target in order to
collect the laser returns after collision with both the wooden target and the white board. The
target was scanned at two distances from the instrument, i.e., 5m and 10m, respectively.
Table 1 shows the spacing between points, the number of points collected, and the time
necessary to complete data acquisition. After completion of the measurement stage, the
intensity data of the point cloud was processed using 8-bits (256 gray levels) and the edge
effect has been modeled.
Figure 3 - Experiment set up to investigate the edge effect
in a controlled environment.
Europe an Journal of Re mote Sensing - 2016, 49: 301-315
Table 1 - Properties of scans gathered in the controlled
experimental setup.
Resolution (mm) Number of points
Distance 5 m
0.5 480,244
1.0 120,150
1.5 53,550
2.0 30,082
3.0 13,500
4.0 7,605
5.0 4,860
7.0 2,522
10.0 1,224
Distance 10 m
0.6 387,138
1.0 139,944
1.6 54,912
2.0 34,986
3.0 15,572
4.0 8,772
5.0 5,658
7.0 2,940
10.0 1,449
The Intensity Recovery Algorithm (IRA)
Thanks to the experimental facility described in the previous subsection, the edge effect
could be generated in a controlled environment. The results provided enough information
in order to understand how this effect occurs and how it affects the intensity data. In order
to correct them, the Intensity Recovery Algorithm (IRA) was developed. It works in two
steps: a) segmentation and b) intensity recovery.
Initially, a clustering k-means algorithm [MacQueen, 1967] is used to split the intensity
data values into different groups. The algorithm groups those points that are distorted by
the edge effect into a specic class that can be used to recover correct intensity data. The
clustering based on k-means technique accomplishes the classication by partitioning the
data set in a k number of groups [Gan et al., 2007]. Initially k centroids were dened as 3
Bordin e t al. Inten sity recovery a lgorithm (IR A) of LIDAR data
groups based on the clustering algorithm. Each point of the cloud has an intensity value that
is associated with the recorded intensity value returning from the target. For each point, the
algorithm seeks for the nearest centroid. In this case, the nearest centroid has an intensity
value similar to the one of the group of points. Thus, each point becomes part of the group
of the nearest centroid. When all the points are grouped, the centroids will be recalculated
to verify that each point belongs to the appropriate group. The algorithm iteratively repeats
this operation more times as far as the values converge. Convergence takes place when
points stop to switch between different groups, but other criteria can also be implemented
to control iterations. For instance, the maximum number of exchanges between groups or
the maximum number of total iterations may be used to this purpose. In such a case, the
maximum number of iterations must be dened in order to limit the process, i.e., the user
enters the number of iterations and the result is dependent upon this choice.
After segmentation of the database into different groups, the recovery of intensity data can
be operated by using the following simple Equation [1] that was implemented in IRA:
where Ic is the corrected intensity value, Im is the actual laser intensity value as measured
by TLS sensor and ranging from 0 to 255 DN, and k is the estimated collision value of the
laser pulse with the target, being (k Є R ; 0 < k ≤ 1). Once k value is dened, it is possible
to restore the intensity value. Considering that Q is the set of all points in the database, P is
then dened as the set of clustered points, which belong to the edge effect group, p is a point
from set P, and q is a point from set Q. For each point p that belongs to P, an Axis-Aligned
Bounding Box (AABB) is created that is centered on p. The size of AABB is dened on
the basis of the spacing between points, performed before the scanning setup. All points q
from set Q are tested to verify whether q is inside AABB, whose size is dened through the
spacing between points generating the spacing variable. The scanning setup is necessary
in order to have a minimum number of points to calculate the collision approximation. If
a point q is inside AABB, then q is inserted in a quadtree 1 of n levels created in the same
AABB’s position and with the same AABB’s size. Figure 4 shows AABB with point p in
the center colored in blue.
Using the number of points in each quadrant of the quadtree, the number of collisions
between the laser beam footprints and the target is estimated. Each quadrant has a collision
percentage (perc) which depends upon the quadtree level n, Equation [2]:
perc n
if quadtree level n=1, then quadtree has 4 quadrants. In such a case, each quadrant
corresponds to 25% of a collision.
Europe an Journal of Re mote Sensing - 2016, 49: 301-315
Figure 4 - Example of Axis-Aligned Bounding
Box (AABB) with quadtree level 1. (a) AABB
with points inside. (b) quadtree 2D structure
centered in the same position of AABB with
AABB points included.
The collision percentage perc is the more important element of the algorithm, since the
calculation of collisions measured by the laser is operated at this point. The value perc is
calculated by considering a weight of 25% for each one of the four quadrants of AABB.
The algorithm identies which quadrant has the greatest number of points, and then it
records the weight using 25% for the average intensity of the points in this quadrant. This is
considered as the reference quadrant. The calculation of the weight of the other quadrants is
carried out by taking into consideration the fraction of points in each quadrant with respect
to those in the reference quadrant.
Testing IRA
The algorithm has been tested rst on a forestry target consisting of a single guava tree
(Psidium guajava). This choice has been motivated by the availability of such an appropriate
target near to the laboratory, on the tree’s medium size (dimensions spanning from 7m to
12m), and its regularly shaped leaves. No obstacles were present between the guava tree
and the ILRIS 3D standpoint, avoiding the risk of occlusions. Moreover, such conguration
has made sure that the edge effect would not result from another targets, but only due to the
guava tree. The target has been sampled from approximately 40m far away from the laser
scanner in order to avoid parallax distortion. After scanning, the points cloud le with 8-bits
radiometric resolution that contained X, Y, Z and I has been processed by IRA. The point
cloud has been initially classied into three groups (branches, leaves and points affected by
the edge effect) using the k-mean-based algorithm.
Results and discussion
Results of edge effect test
The greater the distance between the laser and the target, the larger is the diameter of the
laser footprint. Generally, the points affected by the edge effect have a lower intensity
value, as previously addressed by Kaasalainen et al. [2009, 2011], Seielstad et al. [2011]
and Bordin et al. [2013]. The distance also reduces the intensity values. The edge effect and
the distortions in the intensity data, in this case, occurred due to the divergence of the laser
Bordin e t al. Inten sity recovery a lgorithm (IR A) of LIDAR data
beam and the inuence of distance [Bordin et al., 2013], although Eitel et al. [2010] did
not identify distortions in intensity caused by distance ranging from 1.1 to 2.6 m from the
target. This occurs because the beam spreads more as the distance grows up. The longer the
distance, the longer is the distribution of the radiation over the area, or the same amount of
radiation interacts with a greater area of the target (see Fig. 5).
Figure 5 - Variation of the area (A and A’) of interaction
of radiation from the laser beam depending on the
distance (d and d’) between sensor and target.
This relationship is shown by Equation [3], where shorter distances might cause non-
signicant distortions:
where A is the area illuminated by the laser beam, d is the distance between sensor and
target, and θ is the divergence angle of the laser beam.
During this test, two types of distortions in the point cloud data caused by the edge effect
have been identied. The rst type is that the edge effect affects the data resulting in
distortions of intensity values. The second type is that the edge effect shifts points in the
space along a certain spatial direction.
The modication of laser intensity values occurs when the sensor records the return of laser
beam as a mixture of reections from the white board behind the target and from the target
itself (wooden board with holes), since the aperture of the sensor receives the radiation that
returns from two targets during the range of time. An average of both intensity values is
then recorded. In Figure 6a in green or 6b in gray scale, the points inside the circles and
in the outer portion of the wooden board show distortions in their intensity values caused
by the edge effect. Overall, the points affected by the edge effect have lower values than
others, as also reported by Eitel et al. [2010].
Europe an Journal of Re mote Sensing - 2016, 49: 301-315
Figure 6 - Edge effect generated in the initial test. (a) Figure in
grayscale (b) Figure in false color. The green points inside the
circles and around the blue rectangle represent the edge effect seen
in the 3D point cloud.
Moreover, the spatial scanning resolution also contributes to the distortion of intensity
values. Three possible situations can be observed from the experimental results. The rst
situation is shown in Figure 7a, where the edge of the rectangle is scanned, and the distance
between centers of laser footprints are larger than the beam diameter, resulting in unrecorded
data. In the second situation shown in Figure 7b, the distance between the centers of laser
footprints is smaller than the beam diameter, so the beam borders partially overlap and
result in the noise in the intensity data of the nal point cloud. In the third situation shown
in Figure 7c, the distance between centers of footprints is equal to the diameter of the laser
footprint and leads to the best case scenario, because all the area is sampled and no noise is
generated in the point cloud.
Figure 7 - Different cases of resolutions of data acquired with
terrestrial laser scanner. (a) The distance between centers of laser
footprint is larger than laser beam diameter; (b) The distance
between centers of laser footprint is smaller than laser beam
diameter; (c) The distance between centers of laser footprint is equal
to laser beam diameter.
In the second type of distortion, 3D points are shifted in space, as shown in Figure 8. This
distortion occurs on the y-axis because the sensor calculates the distance of points based
on the average return time of the pulse that returns from both the target and the white
Bordin e t al. Inten sity recovery a lgorithm (IR A) of LIDAR data
Figure 8 - Edge effect generated in the initial test. The
green points in the cloud are shifted in space on the
y-axis (gure in false color).
The study of the edge effect is a very complex subject that requires a range of complementary
experiments to address the topic. Therefore, the distortion of points in the space will not be
addressed. This study is focused only on understanding and correcting distortion of laser
intensity data values.
Application of IRA to a real forestry data set
The edge effect has been investigated on the whole guava tree. The point cloud has been
initially composed of 1,082,996 3D points. After processing and classifying initial intensity
values, using a modied k-mean algorithm for three groups (branches, leaves and points
affected by edge effect) and points have been classied according to the image shown in
Figure 9a. After the rst classication stage, 151,542 points have been classied as branches
(red color, 13.99% of total points), 390,200 points as affected by the edge effect (blue
color, 36.03% of total points), and 541,254 points as leaves (green color, 49.98% of total
points). The goal of this classication stage has been to segment out all points affected by
the edge effect before processing data in order to recover lost laser intensity values. Figure
9b veries that the algorithm has satisfactorily identied the edge effect (blue color). After
classication, those points that have been characterized as belonging to the edge effect have
been processed using IRA to recover branch and leaf points.
After IRA processing, all points have been further characterized as those shown in Figure
9b, with 221,901 points classied as branches (red color, 20.49% of total points), 250,844
points classied as affected by edge effect (blue color, 23.16% of total points), and 610,251
points classied as leaves (green color, 56.35% of total points).
Data processing of the edge effect points by IRA resulted in recovering of 139,356 points
or approximately 35.71% of lost intensity values. These 139,356 points were classied
as 68,997 points for leaves and 70,359 points for branches. The results suggested that if
laser intensity values are exploited to investigate a correlated environmental variable (e.g.,
chlorophyll, carbon or water content), the application of IRA would mitigate the estimation
errors, as shown in Table 2.
Figure 9a and 9b visually show the result of minimizing the edge effect presented in Table 2.
In Figure 9a, the quantity of blue points is visibly larger than the ones shown in Figure 9b.
Table 2 summarizes the results obtained after IRA processing. Those points still affected
by the edge effect are represented in blue, while leaves are in green and branches in red
(Fig. 9b).
Europe an Journal of Re mote Sensing - 2016, 49: 301-315
Figure 9 - Point clouds of the guava tree displayed as a 3D image before (a) and
after (b) recovering lost intensity values due to the edge effect. The tree before
processing (a) shows a large number of blue edge effect points, whereas the tree
after processing (b) shows a reduced number of blue edge effect points (gure
is in false color).
Table 2 - Summary of results obtained after IRA processing of guava tree point cloud.
Point cloud
(Number of
points) - Figure
Point cloud
processed by
IRA (Number of
points) - Figure
Point cloud
processing by
Edge effect
points 390,200 36.03 250,844 23.16 139,356 35.71
Leaves 541,254 49.98 610,251 56.35 68,997 112.75
Branches 151,542 13.99 221,901 20.49 70,359 146.43
Total 1,082,996 100 1,082,996 100 - -
From the analysis of the results, branches are more affected by the edge effect than leaves
are. This is motivated because the diameter of the majority of branches is smaller than
the diameter of leaves. In other words, the smaller the target, the more the target will be
affected by the edge effect. If leaves are smaller than branch diameters, leaves would have
been more affected. The IRA has been proved to be more effective for recovering leave
points, restoring 35.71% of points distorted by the edge effect in this study.
For a better understanding of somehow IRA processes the point cloud, histograms are
presented to show the variation of the laser intensity values before and after processing
(Fig. 10). The recovered 35.71% intensity data is directly correlated to the recovery of
the radiation that has been lost; therefore, points originally classied as edge effect may
continue to belong to this group even after processing. This result explains the recovery of
the intensity data of 35.71% of total points. In fact, part of the database classied as edge
effect continues to be part of the class of edge effect points after processing.
Bordin e t al. Inten sity recovery a lgorithm (IR A) of LIDAR data
Figure 10 - Distribution of laser intensity of the guava tree point cloud before column (a)
and after column (b) segmentation and processing by IRA.
The histograms in Figure 10 show the variation of the laser intensity of the point cloud of
the entire tree in 8 bits before (Fig. 10a) and after IRA processing (Fig. 10b). The histograms
show a normal distribution with the greatest number of points having intensities between
0 DN and 100 DN before IRA processing. The average intensity was approximately 52.99
DN with a standard deviation of 22.55 DN. After processing, the normal distribution of the
histogram shows a greater range of intensities between 0 DN and 140 DN (Fig. 10b).
Processing using IRA provides some interesting information that can be seen in Figure
10. Points that have been identied as branches are also those points with higher intensity
values. For example, branches reect a larger amount of radiation for mid-infrared
wavelengths than leaves do. Thus, the average laser intensity values of leaves range from
58.68 DN to 78.34 DN after IRA processing and shows a standard deviation of 8.19 DN to
9.90 DN, respectively (Tab. 3).
Table 3 - Intensity values before and after application of IRA.
Classes Analysis Before After
Tree intensity (ND) Average 52.99 77.07
Standard derivation 22.55 29.23
Branches intensity (ND) Average 90.00 117.21
Standard deviation 16.80 18.47
Edge effect intensity (ND) Average 30.72 38.47
Standard deviation 11.67 15.12
Leaves intensity (ND) Average 58.68 78.34
Standard deviation 8.19 9.90
Final remarks
The results presented in this study demonstrate that laser intensity of points gathered using
terrestrial laser scanning (TLS) sensors can be used to classify different components of
trees, such as branches and canopy. On the other hand, a signicant number of points may
be affected by the so called edge effect. This is because laser footprints may cover areas
Europe an Journal of Re mote Sensing - 2016, 49: 301-315
at different distances from the sensor, resulting in averaging of laser intensity returns. In
applications to estimate and/or quantify carbon and biomass composition, the edge effect
should be compensated for to avoid bias in the outcomes. In this paper, an algorithm to
accomplish this task has been presented and tested. The Intensity Recovery Algorithm (IRA)
works on laser intensity data that are classied based on k-means partitioning. Experiments
carried out in a controlled environment are fundamental to understand how the edge effect
in the point cloud occurs. Two types of distortions may occur in point cloud laser data. The
rst type affects data by causing distortions in intensity values. The second type creates an
edge effect that shifts the points in space along a certain direction. By processing a real data
set of a tree with IRA, 35.71% of the total laser intensity values that were affected by the
edge effect have been recovered. This result shows that the use of the IRA on intensity data
values is effective to decrease distortions caused by the edge effect. This algorithm will aid
in the development of methodologies to study the correlation between TLS intensity and
physical and chemical characteristics in forestry and other domain applications. The ability
to identify a correlation between TLS intensity and properties such as water, carbon and
sulfur content in trees could lead to the creation of more efcient and cheaper methodologies
to quantify physical and chemical characteristics, using remote and non-destructive data
collect on techniques.
The algorithm developed for minimizing the edge effect is a rst attempt to cope effectively
with the problem regarding the edge effect on TLS data. Therefore, more researches must
be conducted to test and improve this methodology. The usage of a structure composed
of an octree rather than a quadtree might be an alternative method to improve the results
[Samet, 2006]. In terms of clustering, algorithms based on other classication methods
should also be tested and compared. Although the algorithm has been used in a case study
where three classes sufced, this does not limit its application to those cases where a larger
number of classes may be necessary.
This project has been nancially supported by the projects Modelagem Digital de
Aoramentos utilizando GPU (MCT/FINEP - Pré-Sal Cooperativos ICT - Empresas
03/2010 - Contract 01.23.4567.89) and FINEP-PROINFRA (Contract: 01.13.0302.00).
MRV thanks the Brazilian Council for Scientic and Technological Development (CNPq)
for the research grant (Process 309399/2014-9).
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