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Distinguishing obstacles from ground is an essential step for common perception tasks such as object detection-and-tracking or occupancy grid maps. Typical approaches rely on plane fitting or local geometric features, but their performance is reduced in situations with sloped terrain or sparse data. Some works address these issues using Markov Random Fields and Belief Propagation, but these rely on local geometric features uniquely. This article presents a strategy for ground segmentation in LiDAR point clouds composed by two main steps: (i) First, an initial classification is performed dividing the points in small groups and analyzing geometric features between them. (ii) Then, this initial classification is used to model the surrounding ground height as a Markov Random Field, which is solved using the Loopy Belief Propagation algorithm. Points are finally classified comparing their height with the estimated ground height map. On one hand, using an initial estimation to model the Markov Random Field provides a better description of the scene than local geometric features commonly used alone. On the other hand, using a graph-based approach with message passing achieves better results than simpler filtering or enhancement techniques, since data propagation compensates sparse distributions of LiDAR point clouds. Experiments are conducted with two different sources of information: nuScenes’s public dataset and an autonomous vehicle prototype. The estimation results are analyzed with respect to other methods, showing a good performance in a variety of situations.
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Date of publication xxxx 00, 0000, date of current version xxxx 00, 0000.
Digital Object Identifier 10.1109/ACCESS.2017.DOI
Ground Segmentation Algorithm for
Sloped Terrain and Sparse LiDAR Point
Cloud
VÍCTOR JIMÉNEZ1, JORGE GODOY1, ANTONIO ARTUÑEDO1and JORGE VILLAGRA1
1Centre for Automation and Robotics (CSIC-UPM), Ctra. Campo Real, Km 0.200, Arganda del Rey - 28500 Madrid, Spain
Corresponding author: Víctor Jiménez (e-mail: victor.jimenez@csic.es).
This work was supported in part by the Spanish Ministry of Science and Innovation with National Projects PRYSTINE and SECREDAS,
under Grant PCI2018-092928 and PCI2018-093144, respectively, in part by the Community of Madrid through SEGVAUTO 4.0-CM
Programme under Grant S2018-EMT-4362, and in part by the European Commission and Electronic Components and Systems for
European Leadership (ECSEL) Joint Undertaking through the Project PRYSTINE under Grant 783190 and the Project SECREDAS under
Grant 783119
ABSTRACT Distinguishing obstacles from ground is an essential step for common perception tasks
such as object detection-and-tracking or occupancy grid maps. Typical approaches rely on plane fitting
or local geometric features, but their performance is reduced in situations with sloped terrain or sparse data.
Some works address these issues using Markov Random Fields and Belief Propagation, but these rely on
local geometric features uniquely. This article presents a strategy for ground segmentation in LiDAR point
clouds composed by two main steps: (i) First, an initial classification is performed dividing the points in
small groups and analyzing geometric features between them. (ii) Then, this initial classification is used
to model the surrounding ground height as a Markov Random Field, which is solved using the Loopy
Belief Propagation algorithm. Points are finally classified comparing their height with the estimated ground
height map. On one hand, using an initial estimation to model the Markov Random Field provides a better
description of the scene than local geometric features commonly used alone. On the other hand, using a
graph-based approach with message passing achieves better results than simpler filtering or enhancement
techniques, since data propagation compensates sparse distributions of LiDAR point clouds. Experiments
are conducted with two different sources of information: nuScenes’s public dataset and an autonomous
vehicle prototype. The estimation results are analyzed with respect to other methods, showing a good
performance in a variety of situations.
INDEX TERMS Belief Propagation, Channel-based, Geometric features, LiDAR, Markov Random Field,
Obstacle-ground segmentation, Sloped terrain, Sparse point cloud.
I. INTRODUCTION
Autonomous driving is a challenging goal for which a re-
liable perception of the environment is essential. To that
end, many automated vehicles are equipped with laser range
scanners (LiDARs), as they provide a large amount of ac-
curate 3D measurements. However, not all the information
obtained is relevant; measurements relative to obstacles have
to be distinguished from measurements relative to ground.
This is crucial for typical perception tasks such as object
detection-and-tracking or occupancy grid map generation.
Simple height thresholding strategies have been used in
some situations. Nevertheless, flat world assumption is rarely
met, especially in driving environment where outdoor and
uncontrolled scenarios are commonly found. Indeed, slopes,
road imperfections, vegetation and the complexity related
with road users make this segmentation process much more
complex than expected.
Several approaches for ground segmentation have been
proposed in the literature. Dividing the point cloud into
small groups (e.g. channels), and analyzing local geometric
features inside them is a common strategy with proved good
results. However, locally focused analysis is prone to noise
in areas with few data. In contrast, different authors choose
to model the ground height by analyzing the point cloud
information as a whole and then perform the segmentation
task comparing the points with the obtained estimation. The
most frequent approximation is done by plane-fitting, but
this approach has a strong dependency on a flat world as-
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Víctor Jiménez Bermejo et al.: Ground Segmentation Algorithm for Sloped Terrain and Sparse LiDAR Point Cloud
sumption. Both sloped terrain and sparse data still motivate
the research on ground segmentation in point clouds. Less
commonly seen approaches rely on Markov Random Fields
(MRF) and Loopy Belief Propagation (LBP) for this task.
These methods are less reliant of the plane ground condition,
allowing local relieve changes, and have shown promising
results in situations with sparse information [1], commonly
found in LiDAR data. However, the approaches found are
not strictly focused on ground segmentation, do not address
sparse data or use simple geometric conditions to model the
initial data cost.
The main contributions of this article are:
The combination of a channel-based approach with
a multi-label MRF approach, obtaining a novel strat-
egy called Channel Based Markov Random Field (CB-
MRF).
The design of a channel-based ground segmentation
algorithm, proposing additional rules and processes de-
signed to overcome commonly found problems.
The modeling of the data cost of the MRF in base of
an initial estimation instead of local geometric features
alone.
The evaluation is carried out with real data from pub-
lic datasets and from an automated vehicle prototype
[2]. The proposed strategy is compared with similar
approaches with qualitative and quantitative results.
The remainder of this paper is organized as follows.
Section II provides an overview of related works and the
different motivations that led to the chosen strategy. Section
III presents the details of the strategy proposed, including
the algorithm for initial classification and the calculation of
the ground height map. Section IV gives some guidelines
on how to parametrizate the proposed algorithm. Section V
shows the experiments performed with two different sources
of data. Finally, Section VI summarizes the presented work
and proposes related future research areas.
II. RELATED WORK
The use of LiDAR for environment perception and situation
understanding in Autonomous Vehicles (AVs) has signifi-
cantly evolved in the last years (from [3] to [4]). Throughout
this time, both feature-based ( [5]) and grid-based ( [6])
approaches for object detection have highlighted the need to
differentiate ground impacts from object measurements. To
that end, several approaches have been proposed for ground
filtering in point clouds.
Plane-fitting and line-fitting has been widely tested. Au-
thors in [7], [8] use a RANSAC algorithm to fit points into a
single plane. However, ground is rarely flat, thus the assump-
tion of a single ground plane leads to false-classifications. To
overcome this issue, similar approaches divide the scene in
different sectors for which local planes or lines are estimated
(e.g. [9]–[14]). The flexibility of plane fitting is increased
with these techniques, but on the one hand, wide sectors still
struggle fitting all points inside a single local plane and, on
the other hand, small sectors may suffer from a local lack of
points. Some additional techniques can be used to improve
the inliers classification, such as the point-wise normal [15]
or the tangent to the curves produced by the sweep of the
laser beams [16].
A different strategy consists on analyzing local geometric
features from neighbouring points, such as height differ-
ences, gradients or normal vectors. The elevation maps com-
monly used in DARPA Urban Challenge [17] divide the point
cloud into cells and compute the maximum height difference
within them. If this difference exceeds a threshold value, all
points within the cell are considered as obstacles. This simple
approach is able to handle irregular terrains, but its simple
feature criteria may produce wrong classifications in cells
with few points or in cells which contain overhanging struc-
tures. [18] computes the point’s normal vector and a quality
value using the 8-neighbouring points so that the point is a
ground candidate if the obtained normal vector is similar to
the ego-vehicle’s upward edge. Afterwards, candidates are
grouped using a distance based clustering algorithm, and
large clusters are classified as ground. This method uses a
more complex feature analysis, but may suffer in scenarios
with heavy slopes or regions low density of points. [19] takes
advantage of the multi-layer LiDAR sensors common oper-
ation pattern and analyses the relationship between points
from different layers, but with the same azimuth angle (in
the vertical direction); this type of approaches are commonly
known as channel or scan-line based algorithms. Assum-
ing that these points may behave similarly unless obstacles
appear, each point inherits the classification of its previous
point. Certain geometric conditions of gradient, distance
and height trigger the change from ground to obstacle or
vice versa. This strategy adapts correctly to ground height
changes, thus is able to correctly classify scenarios with
sloppy terrain and vegetation, but ignores the relationship
between angular adjacent points and is strongly dependant
of parameters configuration. An enhanced version of this
strategy was proposed in [20], where vertical and horizontal
directions are analyzed an combined together. Nevertheless,
it is still highly dependant on geometric parameters and
does not allow the joint analysis of multiple LiDAR sensors.
Similar approaches that divide the point cloud in smaller
groups and classify points following their relationships can
be found, [21], [22].
Other authors use these local features too, but perform
additional processes in order to take into account the point’s
context information. [23] applies a channel-based algorithm
for initial classification and then improves this estimation by
taking into account the inter-relationship between channels.
Initial ground points are projected into a grid map where each
cell stores the mean height. Then, a median filter is applied
smoothing the height in the grid map and filling some of
the empty cells. Finally, points are re-classified in according
to their height over the cells’ ground height. [24] also use
the same strategy to correct the estimation achieved with
[10]. This grid-based representation and smoothing process
corrects occasional false-classifications produced during the
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Víctor Jiménez Bermejo et al.: Ground Segmentation Algorithm for Sloped Terrain and Sparse LiDAR Point Cloud
initial classification and relaxes its parameter dependency.
However, the points density highly affects this enhance-
ment step, leading to false-classifications in farther distances,
where point cloud data is sparse. Higher order inference
algorithms have been proposed in order to handle sparse
point cloud situations. [25], [26] use MRF with Belief Propa-
gation algorithms (BP) in order to classify navigable regions,
demonstrating that the data propagation can successfully han-
dle low point density areas. Inspired by them, [1] proposed
a ground segmentation method based on multi-label MRF
and LBP, where the data cost is fed by height difference
and potential occlusions. This strategy obtains a robust seg-
mentation in rough terrain and compensates the sparse point
cloud distribution. However, its outcome is dependant of
the single height condition which, as stated previously with
elevation maps, struggles with overhanging structures and
lack of points. Other representative techniques with higher
order inference algorithms can be found, for example, in [27]
which models the point cloud as a MRF, in [28], which uses
Gaussian Process regression (GP), or in [29], which uses
Conditional Random Fields (CRF) and extends the spatial
dependencies to spatio-temporal dependencies.
Approaches based on deep learning [30], [31] use Convo-
lutional Neuronal Networks (CNN) to identify obstacles in
the point cloud data. These techniques can take into account
features that can be hardly modeled by traditional methods.
Nevertheless, large amounts of data have to be used for
training and good results may be limited to scenes with
similar conditions than the training set.
Finally, it is worth considering some airborne LiDAR
based works. Despite the different field of application,
some authors have used airborne LiDAR approaches in
autonomous vehicles applications. For example [29], men-
tioned above, was inspired by [32], which proposed in turn
a new hybrid CRF model to extract Digital Terrain Model
(DTM) and [33] applied the Cloth Simulation Filter (CSF)
[34] to detect rocks on the road.
Table 1 shows a high-level summary of the different fam-
ilies of techniques with regards to some key features for
ground extraction.
Motivated by the analysis of previous methods, this article
proposes a strategy composed of two steps:
1) Initial point cloud segmentation: Inspired by [19],
[20], [23], points are clustered by azimuth angle and
analyzed in an ordered way from close to far, the
classification of each points depends on its previous
points and different geometric features. Two of these
mentioned works already introduced the necessity of a
posterior filtering step to correct noise. However, the
proposed methods are not adequate for regions with
sparse information.
2) Ground height modeling with final point cloud seg-
mentation: Following the strategy proposed by [1],
[25], [26], the surrounding ground height is estimated
using a multi-label MRF and LBP. As a result, data
is propagated along nodes to obtain a good ground
LiDARs' point cloud
Input
Obstacle-ground classi cation
Output
Ground map and nal classi cation
Grid map representation
Multi-label MRF and LBP
Height map based re-classi cation
Channel-based initial classi cation
Point cloud division into channels
Geometric features based classi cation
Noise ltering
FIGURE 1: Ground segmentation algorithm scheme.
estimation even in areas with reduced information. The
final point cloud classification is obtained with respect
to this ground height map.
III. GROUND SEGMENTATION STRATEGY
The CB-MRF method is divided in two main steps: (i) an
initial channel-based classification and (ii) the final classifi-
cation based on MRF and LBP. Fig. 1 displays a general view
of the algorithm, whose main stages are described below.
A. CHANNEL-BASED INITIAL POINT CLOUD
CLASSIFICATION
LiDAR sensors used in autonomous driving tasks usually
have multiple layers. These layers commonly share the same
horizontal Field of View (FOV), but have different pitch
angle. Laser beams from different layers can thus be directly
clustered by azimuth angle or capture time, obtaining a sorted
sequence of points, each one from each layer, with increasing
distance over the plane proportionally to the layer’s pitch an-
gle, i.e. typical concentric point rings around the ego-vehicle.
Henceforth, these clusters will be referred as channels.
Under the assumption that the ground height may not
heavily vary between subsequent layers’ scans, ground and
obstacle points are identified. Thus, points inside a channel
are analyzed in an ordered way, from the closest to the far-
thest. An additional virtual point is located under the sensor,
at the theoretical ground height and it is always classified as
ground. During the analysis, points can get three possible
labels: obstacle,ground our doubt, but, at the end, all the
points of the channel have to be classified either as obstacle
or ground.
As shown in Fig. 1, a noise filtering task is performed
previously. During this first step, points considered as outliers
or without valuable information receive an additional label
noise and are ignored during posterior steps. The process for
filtering the noise is explained in Section III-C1.
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Víctor Jiménez Bermejo et al.: Ground Segmentation Algorithm for Sloped Terrain and Sparse LiDAR Point Cloud
TABLE 1: Comparison of ground extraction approaches
Plane/line fitting Local features Enhanced channel-based Higher order inference Deep learning
Performance in general scenarios ++ + ++ +++ +++
Performance in sloped terrain 0 ++ ++ +++ +++
Performance with sparse data + 0 + +++ ++
Simplicity ++ +++ ++ 0 0
Parameter independency ++ 0 + + +
Dataset independency +++ +++ +++ +++ 0
In the following, the algorithm to classify points inside a
channel and the heuristic rules applied are explained.
1) Algorithm description
Algorithm 1 shows the pseudo-code for classifying points
inside a channel. Note that prefers to a point inside the
channel Cand lto the point’s classification label. Subscripts
irefer to the current analyzed point, gto the last point
classified as ground and 0to the virtual point. As shown, each
point is classified based on its previous points:
If the previous point is ground, the algorithm seeks for
obstacle evidences (CheckObstacle). If obstacle condi-
tions are met, the point is either classified as obstacle or
doubt. Otherwise, it inherits the ground classification.
If the previous point is obstacle, the algorithm seeks
for ground evidences (CheckGround). If ground con-
ditions are met, the point is classified as ground. If not
it inherits the obstacle classification.
If the previous point is doubt, the algorithm seeks for
evidences of both, obstacle and ground (CheckB oth).
If obstacle conditions are met without doubt, the current
point and all previous doubt points are classified as
obstacle (Cor rectDoubtP oints). An analog reasoning
applies for the case that ground conditions are met. If
none of these two situations happen, the current point
inherits the doubt classification.
If the current point is considered as noise, the algorithm
ignores it.
2) Heuristic rules
As just explained, each point classification relies on its
previous points. The relationships between these points are
analyzed in order to determine whether a new classification
is assigned or the previous one is inherited. This analysis is
empirically based on different geometric conditions that can
be inferred from common point cloud distributions, the Li-
DAR functioning and the considered application. Therefore,
different heuristic rules are defined, that are described below
and showcased with representative examples in Fig. 2.
Two heuristic rules are defined to find obstacle evidences.
If anyone of them is met, the current point can be classified
as obstacle:
Maximum slope allowed: if the gradient between the
current point pi= (xi, yi, zi)and the previous one
p(i1)= (x(i1), y(i1) , z(i1))exceeds a threshold
αθ, the current point is considered to belong to an
obstacle:
Algorithm 1 Channel ground segmentation
Input: Channel’s points
Output: Obstacle-ground labels
l0Ground
for all p∈ C do
if CheckN oise(p)then
continue
end if
switch l(i1) do
case Ground
liCheckObstacle(pi, p(i1) , pg)
case Obstacle
liCheckGround(pi, p(i1) , pg)
case Doubt
liCheckBoth(pi, p(i1) , pg)
if li6=Doubt then
Cor rectDoubtP oints(li)
end if
end switch
end for
arctan ziz(i1)
p(xix(i1))2+ (yiy(i1) )2!> αθ
(1)
The use of the gradient is selected because the ground
may have small slopes. Moreover, since point cloud data
becomes sparser as distance to the sensor increases, it is
common to detect obstacles as heavy slope changes and
not as vertical structures. An example is shown in Fig. 2
a).
Abnormal distance: if the current point pi= (xi, yi, zi)
is closer to the sensor than the previous one p(i1)=
(x(i1), y(i1) , z(i1)), in terms of radial distance, the
current point is considered to belong to an obstacle:
qx2
i+y2
i<qx2
(i1) +y2
(i1) (2)
As explained before, if all laser beams hit on the ground,
points are sorted by distance, and a disturbance in this
order may mean the presence of an obstacle. An exam-
ple of this situation is shown in Fig. 2 b).
These two obstacle rules can be triggered by ground im-
perfections or small objects which do not provide valuable
obstacle information, such as bumps, grass or curbs. In
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Víctor Jiménez Bermejo et al.: Ground Segmentation Algorithm for Sloped Terrain and Sparse LiDAR Point Cloud
a)
b)
c)
d)
Virtual point
Noise
Ground - inherited
Ground - height
Obstacle - inherited
Obstacle - abnormal distance
Ground - corrected
Obstacle - corrected
Obstacle - high gradient
FIGURE 2: Illustrative examples for obstacle-ground classi-
fication.
order to avoid this false-classification, obstacles have to be
confirmed:
Relevant height difference: if the height between a ten-
tative obstacle point pi= (xi, yi, zi)and the last ground
point pg= (xg, yg, zg)exceed a certain threshold
αh, the point is considered as obstacle, otherwise it is
classified as doubt:
obstacle, zizgαh
doubt, otherwise (3)
Fig. 2 d) shows an example of a point corrected to
ground and a point validated as obstacle.
Likewise, three heuristic rules are defined to find ground
evidences. In contrast to the obstacle rules, the three of them
have to be simultaneously met in order to consider a point as
ground.
Expected distance: the current point has to be farther
than the last ground point, satisfying the second obstacle
rule.
Height reduction: the height of the current point pi=
(xi, yi, zi)has to be lower than the height of the previ-
ous point p(i1)= (x(i1), y(i1) , z(i1)):
zi< z(i1) (4)
This may mean that the obstacle is over and the beam is
hitting again on the ground.
Similar height to last ground point: the height of the
current point pi= (xi, yi, zi)has to be similar or
lower than the height of the last ground point pg=
(xg, yg, zg):
zizg< αh(5)
The last ground point is the strongest reference of the
ground available. In this case, the height relationship is
chosen instead of the gradient because long distances
may easily appear between the last obstacle point and
the new ground point, thus gradient thresholding would
allow high height differences. Fig. 2 c) shows an exam-
ple.
Finally, in order to control wrong obstacle confirmation by
long slopes or the ending of the channel, if doubt points are
not solved before a certain distance or the end of the channel,
the obstacle evidences are assumed not to be strong enough
and, therefore all doubt points are corrected to ground.
B. GROUND HEIGHT MAP ESTIMATION AND POINT
CLOUD FINAL CLASSIFICATION
The initial obstacle-ground segmentation relies on clustering
the points into small groups. This division provides different
advantages, but it also constrains the information used, ignor-
ing valuable dependencies between channels and making the
estimation susceptible to local errors.
Dependencies between adjacent channels can be easily
addressed with different methods, but obtaining a good es-
timation in areas with few point cloud data is a harder task.
To meet this objective, the elevation of the ground surround-
ing the ego-vehicle is represented as a ground height map.
This map is modeled in terms of a MRF and solved using
LBP algorithm [35]. Thereafter, every point receives a final
obstacle-ground classification by comparing its height with
an estimated ground map.
1) Grid representation
During this step, data is represented as a polar grid map. Each
cell defines a portion of the surrounding area in terms of angle
and radial distance (θ, r). The data relative to the points’
height and initial classification is gathered inside these cells.
Points classified as noise are not included.
2) MRF-based Multiple Labeling description
Let G= (V, E )be an undirected graph with nodes viV
and edges (vi, vj)Ewhich describe the dependency
between adjacent nodes viand vj. A finite set of labels L
defines the possible height values that nodes can take and a
labeling function fassigns a label f(vi)Lto each node
viV. This graph is represented by the polar grid previously
introduced. Each node of the graph corresponds to a certain
cell of the grid and the dependencies between nodes are set
to the four-connected neighbouring cells: forward, backward,
clockwise and counterclockwise. Similarly, labels refer to
height intervals (h) within which the ground height may
be found.
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Víctor Jiménez Bermejo et al.: Ground Segmentation Algorithm for Sloped Terrain and Sparse LiDAR Point Cloud
The quality of a label is calculated by the energy function:
E(f) = X
viV
D(f(vi)) + X
(vi,vj)E
W(f(vi), f (vj)) (6)
where D(f(vi)), normally referred as data cost, is the cost of
assigning the label f(vi)to the node viand W(f(vi), f (vj)),
normally referred as smoothness cost, is the cost of assigning
the labels f(vi)and f(vj)to the neighboring nodes viand
vj. The details of these 2 costs are given in the following 2
subsections.
The computation of the optimal labeling that minimizes
the energy in (6) is performed using an implementation of the
LBP algorithm (c.f. [35], [36]). Briefly explained, the LBP
algorithm passes messages along nodes in the four possible
directions. Each message consists of a vector with size equal
to the number of possible labels. After a certain number of
iterations, the belief vector for each node is computed and
the label with maximum belief (minimum cost) is selected
as optimal label. Readers may refer to [1], [26] for LBP
implementations in similar applications.
Finally, all points are classified comparing their height
with the ground height estimated for their node:
li=ground, zc
izc
m< hg
obstacle, otherwise (7)
where, liand ziare the obstacle-ground label and the height
of ith-point in the cell c,zc
mis the height relative to the cell’s
optimal label and hgis the height difference parameter.
3) Data cost modeling
The data cost defines the cost for the node vito take the label
f(vi). Its value is defined depending on the points within
the cell (node). Recall that labels refer to possible ground
height values and the most probable label has the lowest
cost. Similarly to [1], three different data cost functions are
defined depending on the points distribution and their initial
classification:
Category 1 is defined for cells without points inside it.
In this situation the point cloud does not provide any
information for the current node. Thus, ground can be
found at any label, so every label is equally probable:
D(f(vi)) = 0 (8)
Category 2 is defined for cells with one or more points
inside it and at least one of them has been initially clas-
sified as ground. Under this circumstance, the ground
height is probably located at the label with the highest
number of points initially classified as ground. In case
there is a tie, the label with the lowest height is selected.
The cost of the other labels is defined with respect to
their proximity to this label. Therefore, the data cost can
be defined as a truncated linear function such as:
D(f(vi)) = min(|f(vi)g(vi)|, τ)(9)
where g(vi)is the reference label selected as the most
probable label (highest number of ground points) and τ
is a truncation value. The truncation value is a common
tool introduced to make the cost function more robust,
e.g. against high differences between adjacent nodes or
g(vi)wrongly selected due to false-classifications.
Category 3 is defined for cells with one or more points,
but none of them has been initially classified as ground.
This situation may happen for different reasons, such
as non-vertical obstacles (Fig. 2), occlusions or false-
classifications. Therefore, the ground height is probably
located at or under the point with the lowest height
inside current cell.
D(f(vi)) = min(f(vi)g(vi), τ)f(vi)> g(vi)
0f(vi)g(vi)
(10)
where g(vi)is the reference label selected as the label
with the point with the lowest height and τis the
truncation value.
4) Smoothness cost modeling
The smoothness cost defines the cost of assigning the labels
f(vi)and f(vj)to the neighboring nodes viand vj. As
already stated on Section III-A, the ground height may not
vary abruptly, i.e. labels should vary slowly too. This is an
assumption commonly made in similar problems [36] and is
typically modeled by the truncated linear function:
W(f(vi), f (vj)) = min(s|f(vi)f(vj)|, ρ)(11)
where sis a rate to weight the cost and ρis a truncation value
in order to allow discontinuities.
C. NOISE FILTERING AND IMPROVING STEPS
This section explains three refinement steps which are in-
cluded in different sections of the CB-MRF strategy to
improve the estimation obtained with real-data but are not
considered as part of the main algorithm.
1) Noise filtering
As shown in Fig. 1, the first step consist on filtering noise
points. In order to identify these points two methods are
applied:
Safe distance thresholds: Points with irregular heights -
for example more than 5 meters under the ego-vehicle’s
height, are considered as noise. Similarly, points hitting
on the ego-vehicle do not provide valuable information,
thus points within the area covered by the ego-vehicle
are also considered noise
Simple plane-fitting: During practical experimentation,
some noise points under the ground plane have been
found, being the most harmful those close to the ego-
vehicle. In order to filter these points, it is assumed
that the patch of ground over which the ego-vehicle
is located is relatively flat, thus close ground points
may approximately fit on a plane at the theoretical
ground height. Any plane fitting method can be used for
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Víctor Jiménez Bermejo et al.: Ground Segmentation Algorithm for Sloped Terrain and Sparse LiDAR Point Cloud
this purpose; for example computing the normal vector
using eigenvectors. Therefore, close noise points are
identified by:
(ncl)T
pi+dcl < hnpiPcl (12)
where Pcl is the set of points close to the ego-vehicle
and the ground theoretical height, ncand dcare the
plane coefficients and hnis a height safety threshold.
Yet, assuming that the ego vehicle is located over a flat
patch is a strong assumption, thus it is only applied if
the number of points classified as noise does not exceed
a threshold nn.
2) Additional heuristic rule
In section III-A2, two rules to identify obstacles inside a
channel were stated. However, when using certain sensor
configurations, such as the LiDAR sensor mounted on top
of the vehicle, the distance between the sensor and first
ground points (inner ring) takes values from two to five
meters approximately, see Fig. 3. This may produce false-
classifications when not sharped obstacles enter inside the
inner ring, since the gradient condition allows a height differ-
ence proportional to the distance. Using the same assumption
made in Section III-C1, the ground inside the inner ring
should not vary abruptly. This statement introduces a new
special heuristic rule by which points found inside the area
defined by the inner ring (Pr) are classified as obstacles if
they exceed a certain height threshold αr:
ziz0> αrziPr(13)
where z0is the theoretical ground height under the sensor.
3) Enhancement of vertical structures
In the last step, named as “correct classification” in Fig.
1, the initial classification is corrected with respect to the
estimated ground height map. As explained in [23], applying
a height threshold over the estimated plane as proposed in
(7) may lead to some false-classifications in the lower parts
of vertical structures. To overcome this issue [23] compares
the number of ground points and non-ground points inside
each cell, considering a vertical structure inside the cell is
assumed if the number of non-ground points is larger. This
simple approach, while useful in some situations may fail in
others, as in overhanging structures. Instead, it is proposed to
identify cells with potential vertical structures as those with at
least nvcontiguous labels with points inside them (similarly
to the concept applied on [1] to remove overhanging points).
Additionally, since the initial classification properly performs
in this task, only the label from ground to obstacle of those
points that were initially classified as obstacle is changed.
IV. PARAMETRIZATION GUIDELINES
This section is intended to provide a parametrization guid-
ance for potential users of the CB-MRF algorithm.
The first step, the channel-based algorithm, is based on
heuristic rules and computes an initial classification, thus
their values can be loosely defined using pragmatic knowl-
edge. It depends on two main parameters and models both
model the surface inclination and smoothness:
Gradient threshold (αθ): it models the possible surface
slope. Flat scenarios can be handled with low values, for
example 15 degrees. On the contrary, sloped scenarios
require higher values, e.g. [20] used 30 degrees for
urban scenarios and [19] used 45 degrees for mountain
roads.
Ground height threshold (αh): it models a significant
height difference with respect to the ground, i.e. the
height of the smallest relevant obstacles. In urban sce-
narios this value may be higher than curbs or bumps,
around 20 30 centimeters.
The second step, ground height map estimation, depends
on different parameters; some of them can be deterministi-
cally set, while others may be more empirical:
The grid size is defined to cover sensors FOV and the
possible ground height variation. Cell size is related to
the ground smoothness - the bigger the cell, the lower
height variation is expected. For example, for urban
scenarios, values around 20cm and 2 deg have shown
good results.
Smoothness cost rate (s) and truncation values (τ,ρ):
are related to the cost of assigning a specific label and
should be experimentally adjusted, some references can
be found in [1], [26].
For the message passing, the scheme forward - clock-
wise - backward - counterclockwise has shown the best
results. Additionally, since the data cost of the MRF is
already based on an initial classification, convergence is
fastly achieved, thus few iterations are needed, e.g. 5or
less.
Height map’s ground threshold (hg): is a common se-
curity threshold that models the possible error of the
estimated ground height map. For urban scenarios, [16]
used a height value of 20cm and [23] used a double
security threshold: 10cm for the obstacle-ground clas-
sification and 25cm for an additional curb label.
From all these parameters, the most influential ones are: hg
that is responsible for over/under-segmentation and αhthat is
the main tool for obstacle detection.
With respect to the noise filtering techniques and refine-
ments steps suggested on Section III-C, the parametrization
highly depends on the sensor’s performance and location.
Therefore, each user should evaluate its own necessities.
V. EXPERIMENTAL RESULTS
This section describes a set of experiments conducted to
validate the feasibility of the proposed strategy.
A. EXPERIMENTAL DATASETS
The work presented on this paper has been tested with
two datasets: the one obtained using an automated vehicle
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prototype (AUTOPIA) and the open-access and well-known
repository nuScenes [37].
AUTOPIA: the prototype counts with a set of different
propioceptive and exteroceptive sensors. In this work,
the two VLP16 mounted on its roof are used. These
sensors cover 360deg around the vehicle, but they are
tilted in order to capture more information in the front
and sides of the vehicle.
nuScenes: public dataset which provides exhaustive data
from typical autonomous driving scenarios. Data is col-
lected in Boston and Singapore, two cities with dense
traffic and challenging driving situations. In this work
the information of the single LiDAR of 32 layers is used.
This sensor covers 360deg and is mounted horizontally
on top of the vehicle. In addition to the LiDAR raw
data, every point has an associated semantic label, e.g.
vehicle, flat, etc. which is used as ground truth.
The validation with two different types of datasets allow
us to show the results obtained for different sensors models
and different location configurations. Moreover, AUTOPIA’s
prototype permit to demonstrate the capability of fusing two
sensors. In addition to that, the ground truth provided by
nuScenes dataset allows qualitative validation.
B. IMPLEMENTATION DETAILS
Four different segmentation approaches have been imple-
mented, tested and evaluated:
The initial classification explained in Section III-A
alone, hereunder named as channel-based algorithm.
The channel-based algorithm proposed with a median
filter as posterior filtering step to improve the estima-
tion. Initial ground points are translated into a polar grid
map as the mean height value for each cell, a median
filter is then applied over this grid and all points are
finally reclassified with respect to their height over the
obtained height grid map.
The algorithm of [1], based on height differences, using
MRF and LBP.
The full strategy proposed in this article: channel-based
algorithm with the MRF-based to improve the estima-
tion.
The parametrization of the different steps of the CB-MRF
is as follows:
Noise filtering: hn= 50cm,nn= 1%. The rectangular
path is defined slightly bigger than the inner ring: 16 ×
10 meters.
Channel-based algorithm: αθ= 20 degrees, αh=
20cm,αr= 50cm.
MRF: The grid size is defined to cover 360 deg and a
distance up to 60 meters, LiDAR sensors used in this
work barely capture significant information at farther
distances. Possible height labels have a range from 2.5
to 4.5meters. Cell size is experimentally set to 20 cm
and 2 deg.τ= 5,s= 0.5and ρ= 3.
LBP: Scheme forward - clockwise - backward - coun-
terclockwise and 5.
Final classification: hg= 10cm
The parameters for the median filter (MF) are empirically
set, obtaining good results for the same grid configuration as
the one used for the CB-MRF strategy: [20cm, 2 deg] and
hMF
g= 10 cm.
The algorithm explained in [1] is tested with the configu-
ration specified in that article.
C. QUALITATIVE RESULTS
A qualitative evaluation is performed in order to explain the
advantages and motivations of the CB-MRF algorithm. For
this task, both datasets are used, the one obtained from AU-
TOPIAs autonomous vehicle and nuScenes datasets. First,
the channel-based algorithm is individually analyzed. Then,
the full proposed strategy (CB-MRF) is analyzed and com-
pared with other similar approaches.
1) Channel-based ground segmentation
Despite its simplicity, the channel-based ground segmenta-
tion technique is able to achieve good results. Nevertheless,
there are some situations in which wrong classifications
can appear. Fig. 3 shows an example from the nuScenes
dataset, where a simple channel-based algorithm (left col-
umn) achieves a good performance overall, but it also fails
in three challenging situations: (i) high curbs; (ii) noise under
the ground plane; and (iii) a close vehicle that crosses the first
ground scan.
The left picture shows the result of applying the algorithm
presented in [19], while the right plot shows the initial classi-
fication obtained when applying the proposed channel-based
algorithm. Vehicles are represented by their ground truth
boxes in green. The estimation obtained from the point cloud
is represented in different colours: reddish points represent
obstacles, bluish points represent ground and black points
represent noise. In the left picture, it can be noticed how
the vehicles behind the ego-vehicle are perfectly segmented,
even ground points under them. On the contrary, a big ground
area on the front-right side of the ego-vehicle has been
wrongly classified as obstacle. This area corresponds to a
sidewalk with a high curb, where two layers hit, leading to
90 deg gradients estimation. Recall measuring high gradi-
ents is one of the conditions to classify points as obstacle.
Moreover, since the height of farther points within the same
channels do not decrease, all of them inherit the obstacle
label. Following the same reasoning, the noise found in front
of the ego-vehicle and under the real ground plane, produces
a wrong classification that is inherited by all posterior points.
Finally, the vehicle inside the inner ring has some points
wrongly classified as ground. This wrong classification is
consequence of the LiDAR location, as explained in Section
III-C2. In this case, the distance between the LiDAR and the
vehicle is higher than 2 meters, thus the gradient analysis
allows high height differences too. This may be a negligible
error for obstacle detection since the footprint of vehicle is
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Víctor Jiménez Bermejo et al.: Ground Segmentation Algorithm for Sloped Terrain and Sparse LiDAR Point Cloud
Obstacle - gradient condition
Obstacle - abnormal distance condition
Obstacle - inhertied
Obstacle - close height condition
Ground - inherited
Ground - height condition
Noise - safe thresholding
Ground - corrected from obstacle
LiDAR position
LiDAR channel example
Noise - plane tting
FIGURE 3: Left: Result of applying a ground segmentation algorithm based on [19]. Right: Result of applying the proposed
channel-based algorithm.
detected almost perfectly, but for the posterior ground height
estimation step, it provides a wrong reference that can harm
the result.
In order to deal with these three situations, three modifica-
tions or additional steps have been proposed for the channel-
based algorithm:
To avoid wrong classifications due to abrupt ground
changes, the height difference between consecutive
points is compared with a certain height threshold. If
it does not exceed this threshold, the point is firstly
classified as doubt and its final classification is defined
considering the following points.
In order to filter noise points close to the ego-vehicle
and under the ground plane, the ground near the ego-
vehicle is approximated as a local ground plane leading
to classify points under this local plane as noise.
To minimize the wrong classification of obstacles inside
the inner ring, the proposed version does not only anal-
yse the gradient but also constrain a maximum height
change with respect to the theoretical ground height
under the ego-vehicle.
Fig. 3 right column displays the results obtained when
applying these changes. It can be seen how the sidewalk is
now correctly classified, the wrong classification produced
by the noise under the ground has being avoided, and the
classification of the lower points of the vehicle inside the
inner ring has been improved.
2) Complete ground segmentation strategy (CB-MRF)
This section presents the results obtained with the complete
strategy. First, the improvements achieved with respect to
the channel-based algorithm alone (Section III-A) are shown.
Then, a comparison with a basic plane fitting algorithm is
performed in order to expose the ability of the CB-MRF
strategy to handle sloped terrains. Finally, two urban scenes
are use to highlight the advantages obtained with respect to
the previously mentioned similar strategies.
Fig. 4 shows the results of two scenes collected with
AUTOPIA’s automated vehicle prototype. The point cloud
is coloured based on the estimation output, being red for
obstacles and black for ground. Vehicles’ position and shape,
drawn in green, have been manually labeled. The sensors
setup of this prototype is useful to demonstrate that the
ground height map modeling is able to fuse the informa-
tion from various LiDARs, an issue that the channel-based
algorithm is unable to handle by design. The scene shown
in the first column illustrates how high grass areas cause a
complicated situation for the channel-based algorithm. Since
they are highly irregular but low dense, some grass points
are classified as obstacles and areas beneath inherit this
obstacle condition. When applying the MRF and the LBP,
the information is analyzed as a whole and the surrounding
ground height is approximately estimated, thus most of the
initially misclassified points are corrected. The second col-
umn shows a complex situation where the proposed channel-
based algorithm is able to handle the occlusion on the right
side but not on the left. Additionally, the vehicle in front of
the ego-vehicle is not detected. This misbehaviour is due to
the fact that the channel-based algorithm estimates ground
for each point cloud separately. This effect, together with
the sparse information results in a total miss-detection of
the vehicle. It can be seen that when the ground height is
modeled, the estimation highly improves. On the left side,
the vehicle is clearly distinguished from the ground and the
detection of the vehicle in front is enhanced, as more than
half of the points are correctly classified.
The proposed approach is based on the analysis of different
strategies, but especially on two algorithms specialized in
handling sloped terrains. Fig. 5 shows the result of a scene
with a high slope variation. Fig. 5b shows the result of a
simple plane fitting approach, proving that a single plane
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Víctor Jiménez Bermejo et al.: Ground Segmentation Algorithm for Sloped Terrain and Sparse LiDAR Point Cloud
(a) (b)
(c) (d)
(e) (f)
FIGURE 4: Two scenes with common issues found in
channel-based approaches. Left column: low dense vegeta-
tion, right column: occlusions. Comparison between the ini-
tial classification and the final classification. a), b) Picture of
the scene in front the ego-vehicle. c), d) Initial classification.
e), f) Final classification.
cannot properly solve these situations. On the contrary, Fig.
5c shows that the proposed approach is able to handle heavy
slopes.
The following scene, represented in Fig. 6, is especially
selected to easily display the advantages of: (i) using MRF
and LBP rather than simpler local filters which cannot prop-
agate information; and (ii) using the estimation of an initial
ground segmentation algorithm to model the data cost of the
MRF instead of just using height differences between points
of the same cell which cannot correctly model obstacles with
few points. The scene is a common urban scene, extracted
from nuScenes dataset, where the vehicle highlighted with a
blue rectangle is only detected by a single layer of the LiDAR
sensor.
The result of the four approaches is displayed in the
different pictures of the figure: a) our proposed channel-
(a) (b) (c)
FIGURE 5: High sloped terrain. Comparison between a
plane-fitting method and the CB-MRF algorithm. a) Picture
of the scene in front the ego-vehicle. b) Plane-fitting method.
c) CB-MRF algorithm.
based algorithm, b) our proposed channel-based algorithm
with median filter, c) the approach of [1], based on MRF and
LBP, and d) the complety proposed strategy, the CB-MRF
algorithm. It can be noticed how the four versions produce
a good classification in general terms, but the detection of
the highlighted vehicle varies. It is drawn in green if it is
counted as detected and in red if not. The channel-based
segmentation algorithm by itself is able to identify some of
the points hitting on the vehicle as non-ground due to the
gradient condition. From this estimation, if the median filter
is applied, the vehicle detection is lost. This happens because
the vehicle is not close enough to truly ground points, thus
the ground height of this area is estimated just considering the
false-classifications made by the initial estimation. This leads
to a worse correction, since ground is wrongly estimated at
the height of the points belonging to the vehicle. In the case of
the algorithm proposed in [1], the vehicle is neither detected.
Since only one layer hits on the vehicle the height difference
condition to detect obstacles is not triggered. Additionally,
there are no occlusions between this vehicle and the ego-
vehicle. Therefore, the cells that gather vehicle’s points are
modeled as potential ground for the data cost. From this
wrong categorization, the LBP is not able to converge over
the correct ground labels. On the contrary, when applying the
strategy proposed by this work, the data cost receives a better
description of the vehicle, some points are wrongly classified
as ground but others not. As a result, the LBP is able to better
estimate the ground height and most of the points belonging
to the vehicle are correctly classified.
Fig. 7 shows a more complex scene from the dataset of
[37]: an urban parking with several vehicles. Different obsta-
cles can be found, and among them there are vehicles with
low height and, in some cases, few points. Detected vehicles
are coloured in green, undetected in red and unperceived
by the LiDAR (too few laser hits) in grey. Again, the four
approaches are tested and, in general, the performance is
good for all of them. Obstacles are correctly segmented from
ground points, even distinguishing ground under vehicles.
However, depending on the approach some of the vehicles
are confused with ground reliefs. These vehicles are mainly
found in regions where point cloud data is sparse. The rea-
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Víctor Jiménez Bermejo et al.: Ground Segmentation Algorithm for Sloped Terrain and Sparse LiDAR Point Cloud
(a) (b) (c) (d)
FIGURE 6: Common autonomous driving scene. Comparison between similar approaches. a) Initial classification. b) Initial
classification and median filter. c) Algorithm in [1]. d) Proposed CB-MRF algorithm.
soning applied in the previous example applies to this case
too, as the combination of the channel-based algorithm with
the multi-label MRF performs better than the other strategies
tested.
The vehicle inside the small blue rectangle is not detected
by the initial channel-based segmentation algorithm. This is
because the distance to the previous layer hitting the ground
is long, allowing high height differences by the gradient
condition. The other three approaches, on the contrary, are
able to correctly identify this vehicle, since few points of
a second layer hit the vehicle at the bottom. These lower
points guide the height grid map estimations and, hence,
vehicle’s upper points are correctly corrected to obstacle
points. The big blue rectangle highlights an area with four
vehicles and sparse information. Most of the points hit on the
vehicles, laser beams only hit the ground before the closer
vehicle and under the farthest one (3D visualization is given
in Fig. 8). Despite most of the points hit on the vehicles,
no sharp features are captured, few sections of the vehicles
can detected as vertical structures and long distances can
be found between the vehicles and previous ground points.
Again, the CB-MRF is able to solve this situation because the
previous channel-based algorithm estimates some of these
points correctly. Conversely, the false-classifications and the
lack of dense information wrongly guides the height grid
map smoothed by the median filter. The approach of [1] also
suffers in this situation since it relies in the identification
of vertical structures inside the cells. Indeed, given a wrong
initial reference and the lack of nearby ground points, the
LBP confuses these obstacles with ground reliefs.
Fig. 8 shows the results of the proposed strategy from a 3D
perspective. Only the right-side of the ego-vehicle is shown.
The ground height grid map obtained from the MRF is also
represented. As already introduced by [23], the explicit esti-
mation of the ground surface provides valuable information
for other autonomous driving tasks, such as path planning
and control, taking into account height variations, pitch angle
estimation, etc. The same colour scheme is used for the boxes
and the point cloud. The height of the map is also coloured
from the lowest height in dark blue to the highest in bright
green. It can be seen how the estimated ground height is
consistent with the point cloud and the ground truth 3D
boxes. The worst case is found in the leftmost vehicle (the
vehicle previously highlighted alone), for which the channel-
based algorithm fails the classification of the majority of the
points. Yet, as previously explained due to some lower points,
the ground is estimated under the points of a higher layer
hitting the vehicle.
D. QUANTITATIVE EVALUATION
A quantitative evaluation is conducted with the datasets from
nuScenes. The subset mini is used since it provides four
hundred samples from ten different representative scenes. In
these samples, every point has a semantic label which is used
as ground truth, and allows the following characterisation:
True Positive (TP): Points classified as obstacle by the
applied algorithm and as non-flat by the ground truth.
False Positive (FP): Points classified as obstacle by the
applied algorithm and as flat by the ground truth.
True Negative (TN): Points classified as ground by the
applied algorithm and as flat by the ground truth.
False Negative (FN): Points classified as ground by the
applied algorithm and as non-flat by the ground truth.
As the four analyzed algorithms share some common
baselines - e.g. the use of local geometric features - the
results obtained with a different strategy is also included
in the quantitative analysis. The selected algorithm is the
CSF [34]. In this approach the point cloud is turned upside-
down and a “simulated cloth” is used to cover it, obtaining
an approximation of the ground surface. Then, points are
classified with respect to this estimation. The implementation
is taken from the library available on the MathWorks website
[38] and parametrization is done taking as reference the
works [33], [34] and adjusted with experimental tests: cloth
hardness = 3, grid size = 1m, height threshold = 0.2m,
iterations = 500, and time step = 0.65
Table 2 shows the results obtained for points in the range of
60 meters. Four classification metrics are included: Precision
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Víctor Jiménez Bermejo et al.: Ground Segmentation Algorithm for Sloped Terrain and Sparse LiDAR Point Cloud
(a) (b) (c) (d)
FIGURE 7: Complex autonomous driving scene. Comparison between similar approaches. a) Initial classification. b) Initial
classification and median filter. c) Algorithm in [1]. d) Proposed CB-MRF algorithm.
FIGURE 8: Classification and ground height grid map esti-
mated by the proposed strategy.
and Recall, in order to quantify the capability of correctly
classifying and the probability of detecting obstacle points;
F-score and Balanced Accuracy, which explain the overall
performance of the algorithm. High scores are achieved by
all the tested algorithms, proving that all of them are valid
approaches. Yet, the proposed approach achieves slightly
better scores. These results are useful to illustrate the general
performance of the algorithm. Nevertheless, most of the
points from the point cloud hit over the ground, facades or
vegetation. These points are rather easy to classify and there-
fore high scores are also easily achieved. Besides, as it has
been shown in the qualitative evaluation, vehicle detection is
a challenging task, especially when few points hit on them.
Given their reduced number of points, their influence on these
metrics is low. For this reason, a complementary evaluation
focusing on vehicles and the distance to the ego-vehicle is
performed:
(i) Score for vehicle detection: A vehicle is counted as
detectable if it has at least mlaser hits and it is within
the maximum analyzed distance. Likewise, it is counted as
detected if at least mpoints are classified as obstacles. m
is defined as 3 since it is the minimum number of points
required to compute a convex-hull. Furthermore, the footprint
indicates the size perceived of the vehicle, an important
measurement for posterior tasks such as object segmentation
or identification. For this analysis it is assumed that the best
footprint achievable detection is defined by the convex-hull
of all of its points. Knowing the points that truly belong to the
vehicle, the quality of the vehicle detection is measured as the
Intersection over Union (IoU) [39] between the convex hull
obtained from all these points and the convex hull obtained
from those points classified as obstacle. This metric is based
on an uncertainty measurement defined by [40]. Since not all
approaches detect the same vehicles, this score is computed
with the vehicles detected by all approaches. The results
of this complementary score show concordance with the
qualitative analysis presented above. The proposed approach
is able to detect more vehicles and with a better IoU than the
other methods tested.
(ii) Radial distance influence: The point cloud distribu-
tion becomes sparser as the distance to the sensor increases.
For nuScenes’ LiDAR sensor configuration a rough division
would be:
0-20 meters: data can be defined as dense. Obstacles in
this range are detected by multiple LiDAR points.
20-40 meters: data can be defined as relatively sparse.
Relevant obstacles, such as vehicles, are detected by few
points (see Fig. 6).
40 meters onwards: data can be defined as highly sparse.
Few objects are detected in general.
In order to expose this behaviour, Table 3 shows the results
obtained for different ranges of radial distance. Moreover,
in order to highlight the results obtained for relevant data,
only the points relative to vehicles and the drivable zone are
considered. For ease of reading, only the F1-score and the
vehicle detection score are given, as they are considered the
most representative scores. The obtained results demonstrate
how the obstacle-ground segmentation becomes harder as
distance increases. The effectiveness of all the tested methods
decays with the increase of sparsity. Nevertheless, the CB-
MRF algorithm is able to maintain an acceptable score,
significantly higher than the other approaches in medium-
long distances.
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Víctor Jiménez Bermejo et al.: Ground Segmentation Algorithm for Sloped Terrain and Sparse LiDAR Point Cloud
TABLE 2: Quantitative results from nuScenes dataset.
Approach Precision Recall F-score Balanced accuracy Detected vehicles % IoU
Channel-based 98.47 91.45 94.77 95.14 79.57 87.00
Channel-based with median filter 98.37 91.48 94.74 95.17 82.59 89.71
MRF-LBP based method in [1] 99.11 76.61 86.28 88.05 70.01 78.01
CSF [34] 94.59 91.90 92.98 93.67 86.72 90.03
CB-MRF 98.36 92.98 95.54 95.89 88.86 91.28
TABLE 3: Quantitative results from nuScenes dataset divided by radial distance only taking into account points relative to
vehicles and drivable zone.
Approach 0-10m 10-20m 20-30m 30-40m 40-50m 50-60m
F-scoreD.V
. % F-scoreD.V
. % F-scoreD.V
. % F-scoreD.V
. % F-scoreD.V
. % F-scoreD.V
. %
Channel-based 97.80 100 93.53 98.56 84.03 83.13 68.58 46.89 60.06 37.54 47.75 29.39
Channel-based with median filter 97.10 100 93.86 99.02 86.26 86.21 73.62 53.64 67.14 46.37 61.16 43.86
MRF-LBP based method in [1] 90.66 100 87.26 97.64 76.22 75.36 61.33 42.52 53.16 37.86 43.01 25.88
CSF [34] 92.67 100 87.79 99.08 81.60 88.61 78.81 66.89 74.99 61.20 73.23 54.83
CB-MRF 97.77 100 94.87 99.15 89.73 91.26 83.39 69.01 78.69 65.30 77.63 69.30
VI. CONCLUSIONS
This work presents the CB-MRF algorithm, a strategy for
obstacle-ground classification in 3D LiDAR data specially
focused on sloped terrain and sparse data. As main advan-
tage, the proposed strategy combines the benefits of using
channel-based algorithms, such as the analysis of different
geometric features and the classification inheritance along
points of the same the channel, with the ability of MRF-LBP
based algorithms to model spatial dependencies and share
information between nodes. In contrast to similar approaches
that also perform a secondary step to improve the estimation,
this work uses a higher order inference algorithm to correct
the estimation, obtaining better results, particularly, in areas
with low points density. With respect to similar approaches
based on multi-label MRF and BP, this strategy uses an initial
classification to model the data cost instead of geometric
features inside the cells uniquely. This provides a more re-
liable description of the scene, reducing ambiguities between
obstacles and ground.
Future research activities will be conducted on two dif-
ferent fronts: (i) real-time implementation, which is already
in development with promising results using parallel pro-
gramming with GPUs; and (ii) the exploration of temporal
dependencies, which may lead to a more comprehensive
description of the environment and thus a better estimation.
Works such as [29] will be used as baseline.
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VÍCTOR JIMÉNEZ was born in Madrid, Spain,
in 1993. He received the degree in industrial
electronics and automation engineering from the
Universidad Carlos III de Madrid in 2017, and
the master degree in automation and robotics from
the Universidad Politécnica de Madrid in 2019.
During 2018 and 2019 he obtained a research grant
focused on mobile robots and fuzzy logic and
competed in the SEAT Autonomous Driving Chal-
lenge 2018 as a member of AUTOPIA Program’s
team. In 2020 he joined this program as a Pre-Doctoral researcher for the
Centre for Automation and Robotics (CSIC-UPM). His research interests
include autonomous driving, perception of the environment, localization and
information integrity.
JORGE GODOY was born in Maracay,
Venezuela, in 1986. He received the degree in
electronics engineering from Universidad Simón
Bolívar in 2008, and the M.E. and Ph.D. degrees
in automation and robotics from the Universidad
Politécnica de Madrid in 2011 and 2013, respec-
tively. From 2013 to 2017, he was the Technical
Coordinator of the AUTOPIA Program funded by
research contracts from National and European
research projects. His research interests include
intelligent transportation systems, autonomous driving, path planning, and
embedded AI-based control for autonomous vehicles. In 2009, he was
granted with a Pre-Doctoral JAE Fellowship from CSIC for researching
on autonomous vehicles at the Centre of Automation and Robotics (UPM-
CSIC). In November 2017, he was granted with a Juan de la Cierva
Fellowship for Post-Doctoral Research at the Universidad Politécnica de
Madrid.
ANTONIO ARTUÑEDO received the B.Sc. de-
gree in electrical engineering from the Universi-
dad de Castilla–La Mancha, Spain, in 2011, the
M.Sc. degree in industrial engineering from the
Universidad Carlos III de Madrid in 2014, and
the Ph.D. degree in automation and robotics from
the Technical University of Madrid (UPM), Spain,
in 2019, with the AUTOPIA Program. During his
Pre-Doctoral period, he made a research stay at
the Integrated Vehicle Safety Group at TNO, The
Netherlands, in 2017. He is currently a Post-Doctoral Researcher with
the Centre for Automation and Robotics (CSIC-UPM), AUTOPIA Group,
Madrid, Spain. He has been working on both national and European research
projects in the scope of autonomous vehicles. He has published and peer-
reviewed multiple journals and conference papers focused in this field.
His research interests include system modeling and simulation, intelligent
control, motion planning, and decision-making systems. His thesis won the
prize to the best PhD on Intelligent Transportation Systems 2020 by the
Spanish Chapter of the IEEE-ITS Society.
14 VOLUME 4, 2016
This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI
10.1109/ACCESS.2021.3115664, IEEE Access
Víctor Jiménez Bermejo et al.: Ground Segmentation Algorithm for Sloped Terrain and Sparse LiDAR Point Cloud
JORGE VILLAGRA graduated in industrial en-
gineering from the Universidad Politécnica of
Madrid in 2002. He received the Ph.D. degree
in real-time computer science, robotics and auto-
matic control from the École des Mines de Paris,
France, in 2006. From 2007 to 2009, he was a
Visiting Professor with the University Carlos III
of Madrid, Spain. From August 2013 to August
2016, he led the Department of ADAS and Highly
Automated Driving Systems at Ixion Industry and
Aerospace SL, where he also coordinated all the activities in the EU
Research and Development funding programmes. He has been leading
AUTOPIA Program at CSIC, since October 2016. He has developed his
research activity in six different entities with a very intense activity in project
setup and management, through over 40 international and national R&D
projects, where he is or has been IP of 17 of these projects. He has published
over 100 articles in international journals and in international conferences on
autonomous driving, intelligent transportation systems, model-free control,
and probabilistic approaches for embedded components in autonomous
vehicles.
VOLUME 4, 2016 15
... Narksri et al. [17] proposed a RANSAC-based ground segmentation with multiple regions and addressed the problem posed by sloped terrain. Jiménez et al. [18] addressed the issue of local geometric variation of the ground by adopting the channel-based Markov random field. ...
... As mentioned in Section I, various object clustering methods [18]- [21] include ground segmentation as a prior step for object recognition. Because ground points are not the region of interest in object clustering methods, the elimination of ground points enhances both computational efficiency and accuracy. ...
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Conference Paper
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