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UNIL  University of Lausanne
Faculty of Geosciences and Environment
Institute of Geomatics and Risk Analysis
Amphipôle
CH1015 Lausanne
Faculty of Geosciences and Environment
Institute of Geomatics and Risk Analysis
                                                                                                        






















Phone +41 21 692 35 32  Fax +41 21 692 35 35  Michel.Jaboyedoff@unil.ch
Reprint
Jaboyedoff M., Metzger R., Oppikofer T., Couture R.,
Derron M.H., Locat J. Turmel D. (2007): New insight
techniques to analyze rockslope relief using DEM and
3Dimaging cloud points: COLTOP3D software. In
Eberhardt, E., Stead, D and Morrison T. (Eds.): Rock
mechanics: Meeting Society’s Challenges and Demands
(Vol. 1), Taylor & Francis. pp. 6168.
This version contains colour figures that were printed in
greyscale in the conference proceedings of the 1st
CanadaUS Rock Mechanics Symposium, Vancouver,
Canada, 2731 May 2007.
New insight techniques to analyze rockslope relief using DEM and 3D
imaging cloud points: COLTOP3D software
M. Jaboyedoff, R. Metzger &T. Oppikofer
IGAR Institute of Geomatics and Risk Analysis, FGSE  University of Lausanne, Switzerland
R. Couture
Geological Survey of Canada, Ottawa, Ontario, Canada
M.H. Derron
Geological Survey of Norway, International Center for Geohazards, Trondheim, Norway
J. Locat & D. Turmel
Université Laval, Québec, Canada
ABSTRACT: COLTOP3D software performs structural analysis of a topography using a digital elevation
model (DEM). A color is defined based on slope aspect and slope angle in order to obtain a unique color code
for each spatial orientation. Thus continuous planar structures appear as a unique color. Several tools are in
cluded to create stereonet(s), to draw traces of discontinuities, or to compute automatically density stereonet.
A new version has recently been developed to represent true 3D surfaces from point clouds. Examples are
shown to demonstrate the efficiency of the method. High resolution DEMs acquired with Lidar techniques
greatly improve topographic analyses.
1 INTRODUCTION
Digital elevation models (DEMs) are used in
many hazard assessment methods, including land
slides and rock instabilities. Slope angles are used
for stability estimation, e.g. infinite slope stability
models (Dietrich et al., 2001). Kinematic tests are
used to estimate the likelihood of failure in rock
slopes, such as slide, wedge and toppling failures
(Jaboyedoff et al., 2004; Gokceoglu et al., 2000;
Günther, 2000). DEMs are also used for modeling
rockfall trajectories.
Many GIS tools permit a mathematical analysis
of topography using slope, slope aspect, second de
rivative, curvature, flow paths, etc. (Burrough and
McDonnell, 1998). But very few are dedicated to the
analysis of the relief structure. An attempt of merg
ing slope angle and slope aspect in one document
was made by Brewer and Marlow (1993) to repre
sent topography using colors dependent on both
slope angle and slope aspect, but the results were not
used for structural analysis. Using the dip and strike
direction of each cell, a DEM can be theoretically
represented with a map having a unique color for
each spatial orientation, allowing a very simple
slope analysis. This can also be applied to triangu
lated surfaces made from 3D point clouds (i.e. x, y,
z, coordinates), should define, enabling for example,
the detection of planar structures within a cliff.
The increasing availability and accuracy of high
resolution DEMs by Lidar (LIght Detection And
Ranging) technologies allow for more detailed struc
tural and morphological analyses and increase the
potential of DEM analyses. Although if the principle
of the proposed analysis is simple, the point cloud
management and surface creation is not straightfor
ward.
In this paper we describe the principle of COL
TOP 3D software, its use for DEM analysis and its
future evolution toward a true 3D analysis. This is
illustrated with some examples from rock cliffs in
Québec and in the Swiss Alps.
2 METHOD
2.1 Document types
Airborne Lidar DEMs have been available for more
than 10 years, either as point clouds or regular grids.
Up to now most of the acquisitions have been per
formed with a nearly vertical laser beam, which
means that the cliffs are only poorly defined because
of a poor point density. The new techniques linked
to groundbased Lidar permit the creation of accu
rate 3D images by merging several scans. By com
bining the two technologies it is possible to obtain a
point cloud that has no preferential density direction
(Fig. 1), which means that the topographic surfaces
have similar point densities in all spatial directions.
The groundbased Lidar data often include vege
tation, which must be removed manually. The inter
est is also to create a routine to automatically re
move the trees from scans.
2.2 Software principle
The first version of COLTOP3D (Jaboyedoff and
Couture, 2003) displays a square DEM grid using
the Hue Saturation Intensity (HSI) wheel. The color
displayed is linked directly to direction of the nor
mal (pole) of the DEM cells by representing the HSI
wheel, in a stereonet and showing the link between
pole orientation and colors (Fig. 2). The dip direc
tion of the surface elements are represented by the
hue (H) of the wheel from 0 to 360° and the dip of
the pole using the saturation (S). The intensity (I)
can be changed for representation purposes. The link
with RGB value is performed following the relation
ship proposed by Gonzalez et al. (2004).
Figure 1. Example of an airborne Lidar DEM on top, and the
merge of the groundbased and airborne Lidar DEM on the
bottom (DEM from Åknes project, Stranda Commune, Nor
way; after Derron et al., 2005).
2.3 The 2D representation
Basically, COLTOP3D was designed to use
square grids. Contrary to standard methods, the col
ored pixels are created by using the normal of the
plane defined by 4 neighboring grid points and by
placing the HSI value corresponding to the normal
vector orientation at the center of these points (Fig.
2). If the grid's cell size is d and the four points’ alti
tudes are z1, z2, z3 and z4, then the surface orienta
tion can be defined by two following vectors:
>
@
)(½;0; 42311 zzzzdv
& (1)
>
@
)(½;;0 43212 zzzzdv
& (2)
They correspond to the line passing through the cen
ter of the cell and linking the middle of the edges de
fined by the segment linking the 4 grid points. The
pole is given by the cross product:
21 vvp
&
&
*
u (3)
Another solution has been used to represent sur
faces created by TIN (triangulated irregular net
work) techniques by simply applying the color re
specting the above method to each triangle.
Figure 2. Illustration of the principle of the COLTOP3D color
scheme. (A) The orientation is defined by four nearest
neighbors on a square grid or by three points of each triangle
of a TIN. (B) Relationship between SchmidtLambert projec
tion and HSI wheel. (C) The HSI wheel plotted on a stereonet
that is afterward affected to the cells of A..
2.4 Other capabilities
COLTOP3D possesses several others capabili
ties besides the simple representation by means of
the HSI wheel (Fig. 3). The color scheme can be
also rotated in order to get a better visualization of
different planar features. Since the color is a direct
indicator of the orientation, one can select and click
on a colored pixel and instantaneously the dip angle
and dip direction is returned. By clicking on the im
age, the standard sign of dip is plotted on the colored
DEM and the corresponding orientation is added to
a stereonet and listed in a text window.
Figure 3. Illustration of the capabilities of COLTOP3D de
signed for a square grid DEM (The image is normally in color,
see data repository).
By selecting an area of the DEM, it is possible to
calculate the histogram of the orientations (density
stereonet), for example to obtain the mean orienta
tion of a planar surface. The DEM cells for which
the orientations corresponds to a chosen orientation
(defined by a dip angle, a dip direction and a toler
ance (cone) around this orientation) can be mapped
in a single color. By choosing up to five different
orientations, this leads to an image of the relief dis
playing only the selected orientations with user
defined colors. Results can be exported in an ASCII
grid file that can be used in any common Geo
graphic Information System (GIS) software.
Currently fault traces can be drawn in COLTOP
3D by indicating one point and the orientation of the
fault or by clicking on 3 points. Further develop
ments will implement leastsquare methods for the
determination of fault traces. The XY coordinates
of fault traces can be exported into a text file.
3 THE TRUE 3D REPRESENTATION
3.1 3D point cloud data management
Groundbased laser scanners allow for capturing
dense 3dimensional data sets (up to millions of
points) of the surface of an object, within a few min
utes. However, the posttreatment and the standard
operating use of such large data sets may impair an
indepth analysis for specific applications, such as
landslide and rockfall analysis. This is mainly due to
computer access time for the localization of data
points near a given location. To solve these prob
lems, a structure based on octrees (an index based
on spatial portioning) is used, which allows for fast
localization of points within a given region, low
consumption of RAM, and hard drive access mini
mization. First a region (root node) large enough to
enclose the entire point cloud is computed. Points
are added one by one until the root node (level 0)
contains a total number of point equals to a given
threshold. The node is then equally splitted into
eight sub regions (sub nodes) (level 1), and all
points of the root node are removed and added to
their corresponding sub nodes. This subdivision
process is repeated until the number of points in
cluded in a sub node falls beneath a given threshold.
The value of the threshold must be large enough,
typically in the order of few hundreds of thousand,
for fast disk access, as all the points contained in a
sub node are automatically loaded into RAM and
unloaded from it as a whole. Figure 4 (top) shows an
example of a first order octree (only nonempty
nodes are shown) This first octree allow not only for
minimizing disk access, but also for minimizing
RAM consumption.
For solving hardware problems related to 3D point
topology, a second octree is built as described
above, but with a much smaller threshold: typically
it is in the order of a few hundreds to one thousand.
This leads to an octree with much more branches
(Fig. 4b).
The retrieval of neighborhood points of a given co
ordinate (x,y,z) is then straightforward. First, the
node of the first octree holding (x,y,z) is retrieved,
and, if needed, the data points are loaded into RAM.
Secondly, the procedure is repeated for the second
octree. The few hundreds of points stored in this
node are inspected to obtain the nearest neighbors of
(x,y,z).
This structure is similar to the ones proposed by
Dey and al. (2001) and Schaffer and Garland (2005).
3.2 Normal estimation
Extensive work has pinpointed that eigenvalue
analysis of the covariance matrix of a local
neighborhood can be used to determine local surface
properties, and hence its normal vector (Pauly et al.,
2002). The covariance matrix C is defined over a lo
cal neighborhood surrounding a point of interest as:
»
»
»
¼
º
«
«
«
¬
ª
zzyzxz
yzyyxy
xyxyxx
XCOVC
VVV
VVV
VVV
)( (4)
where the entries for a neighborhood containing k
points are defined as:
2
1
222 )(
1
)()()var( ¦
k
i
ix xx
k
xExEx
V
(5)
¦
k
j
iixy yyxx
k
yExExyEyx
1
))((
1
)()()(),cov(
V
(6)
with E(value) being the excepted value or the mean value
(E(x)=x), and var(x) and cov(x,y) denoting the variance of x
and the covariance between x and y respectively (Belton and
Lichti, 2002).
Since C is a symmetric and positive semi
definite, its associated eigenvalues
O
i are greater
than or equal to zero. The local normal vector is
given by the associated eigenvector ei with the
smallest eigenvalue. The direction of the normal
vector is the same as the one found by least squares
plane fitting, since the two methods are equivalent
(Shakarji, 1998).
3.3 Removing of nonsurface features
One of the main advantage of computing eigen
values for normal estimation instead of leastsquares
plane fitting, is that the eigenvectors correspond to
the principal components (directions and orienta
tions) of the neighborhood and the eigenvalues will
represent the variance in each direction (Belton and
Lichti, 2002). Thus, it is possible to estimate the
change of geometric curvature, Mcurv, in the
neighbourhood of a single point, pi, with simple cal
culation such as (Bae and Lichti, 2004):
321
1
)(
OOO
O
icurv pM with 321
0
O
O
O
ddd (7)
Points lying on the surface will have a change of
curvature value close to zero. Belton and Lichti
(2002) use the values given by eq. 7 to classify the
points as surface (plane), edges or corners (their
field of application being terrestrial laser scans of
buildings). From a slope instability or rockfall haz
ard analysis point of view, these features do not
have a particular meaning, but the change of curva
ture can be used to automatically remove vegetation
from the data set, as it is excepted that such features
have a highly variable curvature. Depending on the
scanned area, it takes up to one day to manually re
move trees from a single scan. Vegetation and foli
age are automatically detected by specifying a
threshold for the values given by eq. 7. Points with
higher curvature than the threshold can be removed
from the dataset (Fig. 5). However, the procedure is
not as straightforward, as it can be seen from Figure
5. Some surfaces or ground points located on a frac
ture or fault may also be deleted by blindly applying
the filter.
Figure 4: First order octree (A), second order oc
tree (B) and original data set of the Randa rockfall
(C).
A
B
C
3.4 Surface reconstruction
Surface reconstruction is a topic of great interest
in the computer graphics field and there are numer
ous works regarding surface reconstruction. Amenta
and Bern (1998) give a short review of the most
popular algorithms.
The surface reconstruction is very important for
landslide or rock instability studies, since it allows
firstly for the automatic delineation of faults, and
secondly for visibility culling purposes, as points in
the background may make the interpretation diffi
cult.
Figure 5. Original point cloud (A), vegetation points high
lighted in red (B) and picture of the scanned area (C) (Boule
vard Champlain, Quebec City, Canada).
Most, if not all, of the surface reconstruction al
gorithms imply that the surface to reconstruct is
smoothed and that the sampling density is fine
enough to capture all its features. However, this as
sumption can often not be met on the scanned rock
surfaces, due to the intrinsic roughness of the study
site and/or the distance from the groundbased Lidar
device to the target (up to 1,000 m), which may lead
to an undersampling and the missing of small scale
features. Moreover, the collected data points may
easily reach values on the order of millions, impair
ing most of the standard algorithms (Shaffer and
Garland, 2005). To overcome these problems, a lo
cal reconstruction algorithm similar to the one pro
posed by Linsen and Prautzsch (2001) is used. For
each point p, all the points within a userdefined, 3D
radius are retrieved (p1,…,pk). The k points are then
projected on the plane defined by p and its normal.
A local coordinate system transformation allows for
2D Delaunay triangulation (Delaunay, 1934). The n
triangles, which hold point p as a vertex, are inserted
in the global triangle surface list, the others being
dismissed. Our experience shows that n should be in
the range of 5 to 7, which is consistent with well dis
tributed points. As stated by Linsen and Prautzsch
(2001), local reconstruction does not ensure the
topological correctness of the surface, but a post fil
tering process can easily overcome this problem.
Starting from using the above triangulation method,
the surface can be represented with COLTOP3D
color scheme (Fig. 6).
A
B
C
Figure 6. Surface reconstruction of a scattered points cloud of
the Randa rockfall. The colors correspond to the dip angle and
dip direction of the surfaces.
4 EXAMPLE
To illustrate an application of COLTOP3D, we
present the analysis of a mountain peak in the Swiss
Alps, Grand Muveran summit (3051 m a.s.l.). This
peak is transected by long faults that are very diffi
cult to measure directly on the field, because they
affect the relief at a small scale. Furthermore, such
summits are not easy to survey without perilous
climbing efforts (Figure 7A). As shown on Figure 8,
these large faults generate rock instabilities within
the cliffs.
The analysis performed with COLTOP3D indi
cates that the fault slopes have a mean dip direction
of 205° and a mean dip angle of 45°. The DEM
cells, whose orientation are within a tolerance of
±20° around this mean direction can be exported
into a GIS file. The results (Figure 9) show that the
west facing slope is clearly shaped by these discon
tinuities (Figures 7 and 9).
Figure 7. View of the west face of the Grand Muveran summit
displaying sets of faults on picture (A) and on the 1 m resolu
tion airborne laserDEM represented by a 3D shaded relief in
(B) (Source: MNTMO/MNS, (c) 2007 SIT).
This shows that it is very easy to obtain structural
data using aerial Lidar DEM. This example also
shows the need to acquire data with ground based
Lidar in order to study the instabilities within the
cliffs. For example, the instability shown in Figure 8
needs to be analyzed in detail by terrestrial Lidar
and the new COLTOP3D version.
• In the basement rock of the Swiss Alps, the
fracturing is well enough developed to shape up
to 50% of the slope orientations, or even more at
outcrop scale. Often the entire slope is controlled
by two or three main discontinuity sets
(Jaboyedoff et al., 2004).
• Structural analysis of the scar of Frank Slide
(Canada) permitted to refine previous interpreta
tions (Jaboyedoff et al., in press).
• Recent works on the Eiger collapse in Switzer
land clearly show the control of structures, and
that 3D point clouds are needed to understand the
mechanism of rock instabilities (Oppikofer et al.,
in prep.).
Figure 8. Example of rock slope instability scar (in yellow
beige) controlled by the faulting system shown in Figure 7.
The efficiency of of the COLTOP color representa
tion of the relief has also been illustrated by the fol
lowing examples:
Figure 9. Application of COLTOP3D to the Grand Muveran
summit. The faults shown in Figure 7 (mean dip direction and
dip angle is 205°/45°) are identified in grey.
5 DISCUSSIONS AND CONCLUSION
3D point clouds from airborne or groundbased Li
dar recordings permit a rapid structural analysis.
This is useful since joints and instabilities are often
in inaccessible zones.
The colors obtained from grid DEMs using the
Hue Saturation Index in COLTOP3D permit an
easy detection of the main features of a relief, such
as the main joint sets shaping rock faces. The col
ored surfaces and their interactivity, allow for a de
tailed structural analysis.
Unstructured clouds of 3D data points can serve
as a basis for surface reconstruction by triangulation.
Th
M analysis tools will
gre
point clouds open
a lot of new perspectives in relief interpretation as
sug
he management of huge
da
AKNOWLEDGMENTS
oject (Stranda Commune,
Norway) and its leader Dr. L. Blikra for providing
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