A Probabilistic Representation of LiDAR Range Data for Efficient 3D Object
Theodore C. Yapo1∗, Charles V. Stewart2, and Richard J. Radke1
1Department of Electrical, Computer, and Systems Engineering
2Department of Computer Science
Rensselaer Polytechnic Institute, Troy, New York 12180
email@example.com, firstname.lastname@example.org, email@example.com
We present a novel approach to 3D object detection in
scenes scanned by LiDAR sensors, based on a probabilistic
representation of free, occupied, and hidden space that ex-
tends the concept of occupancy grids from robot mapping
algorithms. This scene representation naturally handles Li-
DAR sampling issues, can be used to fuse multiple LiDAR
data sets, and captures the inherent uncertainty of the data
due to occlusions and clutter. Using this model, we for-
mulate a hypothesis testing methodology to determine the
probability that given 3D objects are present in the scene.
By propagating uncertainty in the original sample points,
we are able to measure confidence in the detection results
in a principled way. We demonstrate the approach in ex-
amples of detecting objects that are partially occluded by
scene clutter such as camouflage netting.
Light Detection and Ranging (LiDAR) scanners use
time-of-flight measurements of narrow beams of laser light
The resolution of commercially available LiDAR scanners
can be very good, achieving an accuracy of a few mm at
100m range . However, unlike digital image sensors
that use an optical low-pass filter to prevent the aliasing of
high spatial frequencies in the scene, LiDAR sensors are
very susceptible to sampling artifacts, as illustrated in Fig-
ure 1. For example, if the samples are too far apart, a Li-
DAR scan of a picket fence might be interpreted as a solid
wall. Conversely, if a solid wall is sampled at a shallow
grazing angle by nearly parallel LiDAR rays, it can be dif-
ficult to connect the distant sample points into a single sur-
∗This work was supported in part by the US Army Intelligence and Se-
curity Command under the award W9124Q-04-F-2159, and by the DARPA
Computer Science Study Group under the award HR0011-07-1-0016.
face. Hence, even though each range point is measured with
high accuracy, there can still be quite a bit of uncertainty
about the scene in each LiDAR scan.
Occlusions in the scene introduce a second source of un-
certainty into LiDAR range data. Objects may be wholly
or partially hidden from the point of view of the scanner,
resulting in uncertainty about their presence or position in
the scene. To deal with this issue effectively, a 3D object
detection algorithm must allow fusion of data taken from
different viewpoints, and model occlusion explicitly, noting
what parts of the scene are visible from each viewpoint.
Much previous research on analyzing LiDAR data is
based on generating a 3D model of the scene, either reduc-
ing the data to a polygonal model, or in some cases, pro-
ducing an implicit function representation of the scene sur-
faces. Instead of irrevocably collapsing information about
the scene into a likely “crisp” estimate, we propose to pre-
serve the inherent uncertainty of the original data when
testing hypotheses against the scene using a probabilistic
We propose a discrete scene data structure to maintain a
probabilistic model of the 3D scene, and provide a natural
and tractable means to update this model that properly han-
dles LiDAR sampling issues. The scene data structure is
fundamentally a site occupancy probability model, extend-
ing the concept of occupancy grids from robotics . We
approximate the scene by a set of random fields that de-
scribe the probabilities that any single site (3D voxel) is in
oneof threestates: freespace, occupied, orhidden. This ap-
proach provides a sound basis for fusing data from disparate
sensors that observe the scene from different viewpoints.
While we believe that the precision of available LiDAR
sensors far surpasses that required for reliable object detec-
tion (since most objects of interest in outdoor scenes are
very large relative to the uncertainty of a single LiDAR re-
turn), we cannot scan the scene with fewer LiDAR points
without exacerbating the undersampling and aliasing prob-
978-1-4244-2340-8/08/$25.00 ©2008 IEEE
Although using a logarithmic representation avoids nu-
merical issues involving the small magnitudes of the detec-
tion probabilities, these magnitudes currently depend on the
cardinality of the points in the object model. Hence, while
we can straightforwardly interpret the detection results for
a single object, comparing results derived from object mod-
els of widely different sizes is problematic. We are investi-
gating the normalization of the results relative to the object
model size so that different detection maps can be directly
Finally, we note that if multiple objects are to be tested
against a single scene, the linearity of the cross correlation
operations can be exploited to improve efficiency. If the
collection of object models can be decomposed into a com-
mon set of primitive objects, these primitives can be tested
against the scene, and the detection results combined in the
logarithmic representation of (11) to produce detection re-
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