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16th Computer Vision Winter Workshop
Andreas Wendel, Sabine Sternig, Martin Godec (eds.)
Mitterberg, Austria, February 2-4, 2011
Automatic Tree Detection and Diameter Estimation in Terrestrial Laser
Scanner Point Clouds
Anita Schilling, Anja Schmidt and Hans-Gerd Maas
Institute of Photogrammetry and Remote Sensing,
Dresden University of Technology, Germany
anita.schilling@tu-dresden.de
Abstract. We present a method to detect trees in 3D
point clouds of forest area acquired by a terrestrial
laser scanner. Additionally, a method to determine
the diameter at breast height of the detected trees is
shown. Our method is able to process large data sets
bigger than 20 GB in a reasonable amount of time.
Results from scans on our test site with different sea-
sonal vegetation are shown. Tree diameters can be
reliably determined from the same trees in different
scans.
1. Introduction
Terrestrial laser scanners gained widespread pop-
ularity in the last years because point cloud repre-
sentations of 3D objects can be acquired rapidly and
easily. Applications cover a wide range from docu-
mentation of cultural heritage sites or accidents to en-
vironmental change detection or industrial engineer-
ing. We are interested in the development of methods
to extract forestry related parameters from scans of
forest area. These so-called inventory parameters for
a particular forest site, e.g. tree height, diameter at
breast height, crown diameter and basis, are impor-
tant for forest monitoring and management. Usually,
a sample set of trees is measured manually by time
intensive methods to determine values for a forest. In
some cases destructive methods cannot be avoided to
obtain reliable results.
Laser scanning is especially attractive for this kind
of tasks since it allows fast capturing of scenes in a
non-destructive way. The scene analysis can then be
performed off-site and already acquired point clouds
can always be processed again if other parameters are
needed.
Our aim here is the automatic generation of a map
of the trees within the laser scanned scene. The
actual number of trees within the area is unknown.
Each tree has to be characterized by its diameter at
breast height defined at 1.3mw.r.t. the lowest tree
trunk point. Furthermore, the tree position is consid-
ered to be the center point of the circle from which
the diameter is obtained.
A lot of work has also been done on detecting and
segmenting trees in airbourne laser scans as reported
in [11]. Our focus lies on terrestrial laser scanning
within the scope of our ongoing project to recover the
3D forest structure, from which we present prelimi-
nary results. Similar work on tree detection and di-
ameter estimation was described in [1], but the stud-
ied test site was less than half the size of ours. Our
study site consists of a birch stock covering an area
(160m×80m) of about 1.3ha. The site was captured
from 12 separate scanning positions in winter and
spring 2010. The scenes show substantial seasonal
changes in vegetation. Because of the size of the test
area, our focus is on developing a robust method that
can calculate the tree diameter reliably with different
understorey vegetation present.
The paper is organized as follows: Section 2 gives
an overview of laser scanner techniques and the data
specifications. In section 3, the investigated meth-
ods are explained in detail. Following, experimental
results using scans from our test site are presented in
section 4. Finally, section 5 summarizes our findings.
2. Data Acquisition
A terrestrial laser scanner determines the distance
to an object by emitting a laser pulse and measuring
the time of flight until the reflection of an object is
observed at the device or by a phase comparison of
the reflection to the initial value. Usually, a laser in
the near-infrared is utilized. The strength of the re-
flected laser pulse affects the measurement accuracy
and is dependent on the incident angle and object ma-
terial properties.
Most scanners work in their own polar coordinate
systems with the scanning mechanism as origin. The
vertical and horizontal directions are divided by an
angular sampling interval of αrdegrees obtaining
a spherical grid around the scanner head. A laser
beam is sent through each of the spherical grid points
(θ, φ). The distance dto the first object hit by the
laser beam is measured. Thus, a particular object
can only be measured if the line of sight between
scanning mechanism and object is unobstructed. For
this reason lower trunk parts are occasionally insuf-
ficiently represented due to understorey vegetation
which is closer to the scanner than the targeted trees.
Additionally, the laser exhibits a beam divergence re-
sulting in an increasing beam diameter with distance.
Therefore, several objects might be hit by one laser
beam resulting in multiple reflection at the scanner.
Some scanner models utilizing phase-comparison av-
erage the range values from several observed reflec-
tions ([1]), which decreases the accuracy of the scene
representation.
The point cloud acquired in polar coordinates
(θ, φ, d) is then converted to Cartesian coordinates
(x, y, z). The resulting point cloud is a sampled rep-
resentation of the object surfaces around the scan-
ner. To represent an object from all sides, several
scans have to be acquired providing full object cov-
erage. The separate scans need to be registered to
the same coordinate system using natural or artificial
markers. Although the basic principle of laser scan-
ners is straightforward and provides 3D coordinates
of the objects around the device, accuracy depends
on the characteristics of the utilized device as well
as the object properties. An in-depth description of
terrestrial laser scanning can be found in [11].
We used the terrestrial laser scanner Imager 5006i
from Zoller+Fr¨
ohlich to capture the test site. The
scanner uses a phase comparison technique which
can resolve distances up to maximal 79m([12]). Ob-
ject points which are hit further away are treated as
if they would lie within the maximum distance, i.e.
d=d−79m, resulting in ghost points. As re-
ported in [1], these points have usually a very low
reflection strength and can be removed by applying
a suitable threshold. Therefore, we set the thresh-
old value for the reflection strength to 0.005. The
reflection strength of the measurements is in the in-
terval [0 . . . 1]. Only points with a reflection strength
Session 1 Session 2
time of scan March May
binary file size 24 GB 27.6GB
total no. points 1,738,900,000 2,005,000,000
no. of points used 1,269,056,557 1,471,058,980
Table 1: Laser scanner data specifications. One
point consists of 3D coordinates and a value indicat-
ing the reflection strength of the particular measure-
ment as floats. The number of points used denotes
points with an reflection strength greater than 0.005.
greater than the threshold are used. This reduces the
point cloud sizes by about 15% to 29%. Since nat-
ural materials, e.g. bark or leaves with low incident
angle, also yield low reflection strengths, it cannot be
ruled out that a fraction of those are removed as well.
The angular resolution used was 0.0018◦result-
ing in 20,000 range measurements per 360◦. The
field of view in the vertical direction is limited to
310◦due to the scanner tripod. The test site is cap-
tured by 12 scans from fixed positions as indicated
by figure 1. The 12 separate scans for each scanning
session were co-registered by fixed spherical markers
mounted on same trees. Registration was performed
manually with the Zoller+Fr¨
ohlich scanner software.
Each separate point cloud was limited to a radius of
37maround the scanner and exported as 3D Carte-
sian coordinates. The data specifications are sum-
marized in table 1. The first session was scanned
in March 2010 when there was no foliage on the
trees and the understorey vegetation had been freshly
pruned. In May 2010, the second session was ac-
quired when the vegetation had grown significantly
and trees were covered by foliage again.
3. Methods
The generation of a Digital Terrain Model (DTM)
is necessary to determine the lowest trunk point of
each tree. The DTM represents the ground as 2D
matrix containing height values as elements. For the
DTM generation a method presented in [3] is ap-
plied. The actual detection of trees within the point
clouds is based on the assumption that the highest
density of scan points is on the tree trunks. This was
also exploited in [5], [4], [8] and [1]. A problem of
the tree detection is the possible mutual occlusion of
trees and other vegetation in the scans at different
heights. Therefore, the detection method needs to
consider several different heights. The targeted birch
Figure 1: Distribution of the 12 scanner positions
per session with radius of 37m.
trees in the area are 38min height. Smaller trees and
some coniferous trees are also present within the area
as well as shrubs of different extent. As the number
of trees within the test site is unknown, the detection
method needs to be robust enough so that no birch
trees are missed.
Following tree detection, the points contributing
to single trees are analysed separately to find points
in breast height. Based on the previously determined
DTM plane, the breast height of a particular tree is
computed. Then, points at breast height are used to fit
a circle to obtain the trunk diameter. Since a tree usu-
ally does not grow up perfectly straight, it can hardly
be completely located using one 3D point. In spite of
this, we use the center point of the fitted circle to in-
dicate the position of a tree. The tree position is used
to create an overview map of the test site. For fur-
ther processing an ample radius around the reported
position has to be considered.
The main issue is to determine the boundary of the
tree trunk in breast height. This is complicated by the
fact that in lower heights many scan points represent
other vegetation partially obstructing the trunks. In
[1], this task was performed with only few trees on
a very small test site, taking about 10hprocessing
time. We present a method to achieve reliable results
in a reasonable amount of time for a comparatively
large data set. The method is summarized in algo-
rithm 1. The position and diameter at breast height
values for the trees are eventually summarized as a
map of the trees on the test site.
1. determine DTM plane gD T M for 3D point set E
from all positions of a scan session
2. detect trees and calculate a set of tree position
estimates T(see algorithm 2)
3. for each tree position t∈T
(a) load 3D points within bounding volume
from E,
Pt={p∈E:tx−bx≤px≤tx+bx
∧ty−by≤py≤ty+by}
(b) if |Pt|is sufficient determine DTM plane
tDT M from Pt, otherwise use gDT M
(c) calculate circle estimate cin height hs(see
algorithm 3)
(d) compute lowest trunk point height k1
zby
projecting the circle center onto the DTM
plane
(e) calculate circle update c(see algorithm 3)
(f) compute new lowest trunk point height k2
z
(g) if |k1
z−k2
z|> then repeat starting at step
(c) with hs=hs+ho
(h) log resulting diameter at breast height
tdbh = 2 ·cradius and tree position
tp= (cx, cy, cz)for the tree
Algorithm 1: Scheme of subtasks for tree detection
and diameter calculation.
3.1. Digital Terrain Model generation
The method to generate the DTM that is summa-
rized here, was originally presented in [3]. The xy-
plane is partitioned into a 2D grid with cell size sc.
When projected onto this plane, several 3D points lie
in the same cell. For each single cell, the z-axis is
divided in several bins each covering a height inter-
val of sl. Points which are located within the current
cell are counted in the bins corresponding to their z
coordinate. Thus a height histogram is built for each
cell from the point numbers. The histogram bin with
the highest number is assumed to be the ground and
the bin height is assigned to the current cell.
If a tree trunk was occluded by vegetation closer
to the scanner, then there are hardly any points at
the real ground height. In this case lower histogram
bins are empty because the trunk points are only con-
tributing to higher bins of the particular cell. The
Figure 2: Arc- or circle-like shapes caused by tree
trunks in different height layers indicated by gray
value.
maximum bin is determined far to high resulting in
a false height value. Therefore, the grid cell heights
need to be filtered. If a cell height is too high in com-
parison to its neighbouring cells and a determined
threshold then the cell value is removed.
Afterwards, cells with missing height values are
interpolated using neighbouring grid cell heights.
The 2D index of each cell is converted to (x, y) coor-
dinates in the point cloud coordinate system with the
cell height as zcoordinate. Finally, an adjusted plane
is fitted to this 3D point set.
A DTM is generated for each point cloud of one
scan session separately. To obtain a general DTM
for the entire scan session, the separate DTMs are
merged. The DTMs of separate point clouds are
overlapping in several parts of the test area. In these
cases uninterpolated height values were preferred
and averaged if multiple values were available.
3.2. Tree Detection
Our tree detection method is presented in algo-
rithm 2. As already mentioned, it is based on the
assumption that in the forest area the highest density
of scan points are located at the tree trunks. To bene-
fit from the nearly full trunk coverage in the overlap-
ping parts of the point clouds, the entire scan session
needs to be processed at once. Therefore a height
slice of the scan session is considered. Points within
that slice are projected to a 2D grid that partitions the
xy-plane. For each cell, the number of points within
the cell is counted. Grid cells with a point count less
than a defined threshold minN bP oints are cleared.
If a suitable threshold is applied, the non-zero cells
are likely to correspond to positions at the tree trunks.
The trunk boundaries appear as components with an
arc- or circle-like shape as shown in figure 2, though
the cross section of a trunk is rarely a perfect circle.
A more detailed analysis of the trunk points is neces-
1. at different heights hi, slices of thickness t,
project all points within onto a plane liparallel
to xy-plane
2. partition liby a 2D grid gi, count no. of points
in each grid cell
3. grid girepresented by an m×nmatrix Iiwhere
Ii(m, n) = 1gi(m, n)> minN bP oints
0otherwise
4. concatenate matrices Iiwith OR operation, thus
K(m, n) = 1Ii(m, n)=1
0otherwise
5. dilate Kwith square structure element of size
s×s
6. find and uniquely label components in Kby
connected component labelling
7. find components in Iiby connected component
analysis, join components cby component num-
ber from Kthus
M[K(cm, cn)] = M[K(cm, cn)] ∪(cm, cn)
8. for each index list in Mcalculate 2D centroid
from indices, convert to point cloud coordinate
system, resulting 2D coordinates are tree posi-
tion estimate
Algorithm 2: Detection of trees in point clouds.
sary for each tree in any case, therefore determining
approximate coordinates of the tree location is suffi-
cient for the tree detection step.
It is possible that a tree does not appear on the
2D grid of a particular height because of occlusions.
Hence, several different heights have to be analysed.
The components in each of the 2D grids are de-
tected by a connected component labelling algorithm
([9]). Because of the skewed tree growth, compo-
nents corresponding to the same tree in grids of dif-
ferent heights do not necessarily cover the same grid
cells. But components of the same tree are inevitably
close together and are joined to clusters. Seldomly,
components resulting from branches with high scan
coverage produce separate clusters, which are at the
moment treated as valid detections as well. The 2D
centroid of each cluster is computed and constitutes
the tree position.
Finally, for each estimated tree position, all points
located within a bounding volume are exported to
a separate file. The bounding volume is a box of
square base with the position estimate at its center.
The generation of these smaller point clouds for each
presumed tree is the most time intensive part using
standard hardware, because of the high number of
read and write operations. If sufficient memory, i.e.
at least 30 GB, could be provided such that all point
clouds of a scan session can be hold within memory,
the creation of temporary point clouds for the tree
position estimates would be unnecessary.
3.3. Tree Location and Diameter Determination
For tree location and diameter determination, each
point cloud section belonging to an estimated tree po-
sition is processed separately. First, a DTM is calcu-
lated for the point cloud section. If this fails because
of an insufficient number of points, an adjusted plane
is used instead that is fitted to the 3D points of the
respective section of the session DTM.
A first computation of the trunk circle center is
necessary to determine the lowest trunk point height
accurately. The largest aggregation of 3D points
within a circular slice at height hsaround the es-
timated position is assumed to be the trunk. This
subset of points can be found by taking the maxi-
mum and neighbouring bins greater than a predefined
threshold from histograms of point numbers along
the xand yaxis as indicated in figure 3. A circle is
calculated with Kasa method ([6]) using the 3D point
subset. The circle equation is rearranged to
−2cxx−2cyy+c2
x+c2
y−cr=−(x2+y2)(1)
and transformed with the given point set to matrix
representation
An×3·k3×1=ln×1(2)
with ndenoting the number of the considered points.
The solution vector k
k=−2cx−2cyc2
x+c2
y−c2
rT(3)
is obtained by least-squares minimization
k= (ATA)−1·AT·l(4)
of the algebraic distances. Following, the elements
of khave to be solved for the circle parameters.
The 2D center point (cx, cy)is projected onto the
DTM plane to calculate the trunk point height k1
z. In
(a) Plot of points on xy-plane
(b) Histogram with bin size of 0.01malong xaxis.
Figure 3: Determination of tree circle estimate using
a histogram of point amounts along the xand yaxis
with predefined threshold t.
a defined height of 1.3mw.r.t. the lowest trunk point,
a new set of points within a circular slice around
the calculated circle center is considered as summa-
rized in algorithm 3. To find a cluster of points in
the set resembling a circle the Circular Hough Trans-
form as reported in [10] is utilized. The Circular
Hough Transform is based on the fact, that the dis-
tance of every point on the perimeter of a circle cm
with known radius ris r. When a circle cpof the
same radius ris drawn around each perimeter point,
all circles cpwill necessarily meet at the center point
of circle cmas shown in figure 4.
In [1] the Circular Hough Transform was applied
to the non-empty cells of a 2D grid. Previously, the
point set was projected onto this grid partitioning the
xy-plane and thresholded like explained in section
3.2. Present on the 2D grid are arc- or circle-like
shapes from trunks, but also components caused by
branches. The accumulation of circles around the
component cells on the grid results in only weak sup-
port for a particular circle. Instead of the few number
of non-empty grid cells, we use each 3D point of the
considered set for the circle accumulation. We ini-
tialize an empty 2D grid partitioning the xy-plane.
The 3D points of the considered slice are projected
onto the grid and a circle of size ris drawn around
each of the points. For each cell the number of circles
passing through it are counted.
In this way many more points are voting for the
same circle center resulting in a distinct peak in the
grid. Because only an estimate crof the precise ra-
dius is known, the Circular Hough Transform is ap-
plied several times with an increasing radius r. The
maximum peak on the grid over all iterations denotes
the new circle center (cx, cy). The circle radius cris
updated with the radius rof the corresponding itera-
tion. Finally, a new set of 3D points Sis considered
containing only points at the previously determined
height hb±t
2within a radius defined by crwith an
additional offset d3. Again, the algebraic circle fit of
equation 1 to 4 is used to calculate values
c= (cxcycr)T(5)
for the circle parameters. The circle is then fitted
([7]) by a least-squares minimization as in equation 4
with
A=h−x−cx
cr−y−cy
cr−1in×3(6)
and
l=cr−q(x−cx)2+ (y−cy)2n×1
(7)
to minimized the geometric distances. The result-
ing improvements in vector kare added to the circle
parameters. The center point of the adjusted circle is
the location of the tree tc. The diameter tDBH = 2·cr
is obtained from the circle radius.
The lowest trunk point is determined again by pro-
jecting the circle center point onto the DTM. If the
resulting trunk point differs from the previously de-
fined height in comparison to a suitable threshold,
then a new iteration of the method is performed un-
less the maximum number of iterations is reached. In
this case the first circle estimate is determined anew,
starting at a height of hs=hs+ho.
4. Experiments
We applied our method to both scan sessions of
the test site. The results are summarized in table
Figure 4: Circular Hough Transform
1. create 3D point set
S=p∈Pt:hb−t
2≤pz≤hb+t
2
∧d(p, tc)< cr+d2}
2. adjust rmin , rmax, rstep according to current cir-
cle radius estimate
3. for r=rmin , r < rmax, r =r+rstep
(a) project all 3D points of Sonto a plane l
parallel to xy-plane
(b) draw a circle with radius raround each
point s∈S
(c) partition plane lby a 2D grid gwith cell
size sc, in each cell count no. of circles
passing through
4. determine radius rof iteration with maximum
cell value in grid g
5. convert grid indices to point cloud coordinates
(cx, cy)for circle cand update circle radius cr
with r
6. recreate 3D point set
S=p∈Pt:hb−t
2≤pz≤hb+t
2
∧d(p, tc)< cr+d3}
7. update circle cwith a new circle estimate using
S
8. calculate adjusted circle fit with cand S
Algorithm 3: Determination of tree points in breast
height and calculation of radius by circle fitting.
2 and processing times are reported in table 3. We
are not able to assess the results of the tree detec-
tion method regarding its completeness, because the
number of birch trees actually present on the test site
is not documented. For this reason, the number of
false negatives, i.e. trees which were not detected, is
also unknown.
We evaluated the results of the detection method
manually. 99% of all detected items in session one
and 97% in session two are actual trees present on the
test site. 91% and 92% of all detections in the respec-
tive session are the targeted birch trees, while 8% and
5% are other small or coniferous trees. 1% and re-
spectively 3% of all cases are false positives, which
means that structures have been detected which are
not trees. These detections were caused by branches
with high scan coverage. In the second session more
items were detected falsely which is probably due to
the foliage present on branches.
We do not have ground truth values for the DBHs
of the trees. The evaluation of the DBH only on basis
of the computed values is not reliable. Tree diame-
ters are quite variable, which makes the definition of
a particular interval difficult. Furthermore, a circle
fitted wrongly to a set of points belonging to a shrub
nearby the sought-after trunk can also yield a diame-
ter value, which is typical for birch trees.
For this reason, it was verified visually whether
the points used for the calculation of the DBH are ac-
tually located at the respective tree trunk. For 95% of
all detected birch trees in the first and 92% in the sec-
ond session sufficient correctly located points were
selected and therefore an accurate DBH value could
be calculated. The averaged standard deviation of
the point sets to the fitted circles is 7mm and 8mm.
For 5% and respectively 8% of the birch trees the
trunk was not sufficiently covered by scan points or
the points used for DBH calculation were not local-
ized on the trunk yielding an invalid DBH value.
We are interested in the seasonal change of the
vegetation. Before a comparison of the tree appear-
ance in both sessions is possible, the scan sessions
have to be registered to each other. The scan ses-
sions exhibit a rotation to each other, but the corre-
spondences and coordinates of the sphere targets are
known. The sphere targets were previously used to
register separate point clouds of one session to each
other. We applied the Iterative Closest Point algo-
rithm ([2]) to obtain a transformation matrix Mus-
ing sphere target correspondences. With Mthe tree
positions of the second scan session could be trans-
formed to the coordinate system of the first session.
Then we established correspondences between tree
Figure 5: Histogram of DBH differences between
the corresponding birch trees.
session 1 session 2
total detections 363 368
detected birch trees 331 325
false detections 3 11
other detected trees 29 32
valid point set for DBH 316 299
correspondences 323
Table 2: Results of first and second scan session.
All detections were manually checked. The number
of false detections is caused by branches which were
interpreted as separate vegetation structures.
total processing times session 1 session 2
DTM generation 9min 9min 28s
tree detection 4min 57s5min 46s
tree separation 147min 157min
DBH calculation 20min 17min
Table 3: Processing times for the first and second
scan session.
positions from both sessions manually.
A total of 323 distinct birch tree correspondences
were found. For this set the DBH values were com-
pared. The absolute differences of the DBH values of
each pair =
t1
DBH −t2
DBH
were calculated and
are shown in figure 5 as histogram. 90% of the cor-
respondences exhibit a DBH deviation of less than
2cm and even 63% of less than 5mm. Regarding a
maximum DBH difference of 1cm, the DBH value
could reliably determined in both scan sessions for
an amount of 268 birch trees present on the test site.
5. Conclusion
We have shown that the generation of a map of
trees on a comparably large test site is feasible in a
reasonable amount of computation time. Although
we cannot entirely evaluate the detections on the test
site concerning their completeness, the results look
promising. The greatest amount of detections are
the targeted birch trees and their diameters at breast
height could be determined precisely from the avail-
able terrestrial laser scanner point clouds.
There are still a lot of possibilities for improve-
ments. The tree detection method needs to be evalu-
ated whether actually all trees are detected. Further
processing would profit from a more detailed anal-
ysis by which kind of vegetation structure the de-
tection was caused. False detections from branches
or smaller, unwanted trees on the test site could be
avoided. Additionally, it is necessary to improve
on the diameter calculation. The diameter at breast
height has not been accurately calculated for all birch
trees though the scan coverage was sufficient.
The DTM generation from scans with dense un-
derstorey vegetation is more error-prone, because the
actual ground is not sampled enough. We will try to
use the DTM from winter scans as basis for all ses-
sions to obtain more reliable height values. The mu-
tual registration of the scan sessions will be neces-
sary for that. The calculation of an appropriate trans-
formation matrix might be improved by utilizing the
established tree position correspondences as well.
We have two more scan sessions captured in July
and October 2010 exhibiting considerably more sea-
sonal change in comparison to the first session.
Therefore, the changing of parameter values is prob-
ably not appropriate and a way to adaptively adjust
parameter values of the processing step would be
beneficial. Furthermore, the representation of the
tree location as a single 3D point is in fact not suf-
ficient. Instead, we will aim to capture the topology
of a tree directly.
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//www.zf-laser.com/BROSCHUERE%20Z+
FIMAGER_5006I_E_01.07.09.kompr.pdf,
July 2009. 2
