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This paper presents a comparative study about of 3D reconstruction based on active and passive sensors, mainly LiDAR – Terrestrial Laser Scanner (TLS) and raster images (photography), respectively. An accuracy analysis was performed in regard to the positioning of outcrop point clouds obtained by both techniques. To make the comparison feasible, datasets were composed of point clouds generated from multiple images in diff erent poses using a consumer digital camera and directly by a terrestrial laser scanner. After preprocessing stages to obtain these point clouds, both were compared using positional discrepancies and standard deviation. A preliminary analysis showed that the use of digital images for 3D reconstructions is a feasible method for digital outcrop modeling, with a low cost of data acquisition and without a signifi cant loss of accuracy compared to LiDAR.
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3-D RECONSTRUCTION OF A DIGITAL OUTCROP MODEL BASED ON
MULTIPLE VIEW IMAGES AND TERRESTRIAL LASER SCANNING
Reconstrução 3D de Modelo Digital de A oramento Baseado em Múltiplas
Imagens e Laser Scanner Terrestre
Reginaldo Macedônio da Silva1,2, Maurício Roberto Veronez1,2,
Luiz Gonzaga Júnior1,3, Francisco Manoel Wohnrath Tognoli1,2,
Marcelo Kehl de Souza1,2 & Leonardo Campos Inocencio1,2
1Universidade do Vale do Rio dos Sinos – UNISINOS
2Advanced Visualization Laboratory - VIZLab
Campus São Leopoldo: Av. Unisinos 950, Cristo Rei, São Leopoldo/RS, Brasil
{macedonios; veronez; ftognoli; lcinocencio}@unisinos.br, {lgonzagajr; marcelo.k.souza}@gmail.com
2Universidade do Vale do Rio dos Sinos – UNISINOS
Graduate Program on Geology – PPGEO
Campus São Leopoldo: Av. Unisinos 950, Cristo Rei, São Leopoldo/RS, Brasil
3Universidade do Vale do Rio dos Sinos – UNISINOS
Applied Computer Science Graduate Program – PIPCA
Campus São Leopoldo: Av. Unisinos 950, Cristo Rei, São Leopoldo/RS, Brasil
Received on March 16, 2016/ Accepted on April 14, 2016
Recebido em 16 de Março, 2016/ Aceito em 14 de Abril, 2016
ABSTRACT
This paper presents a comparative study about of 3D reconstruction based on active and passive sensors, mainly LiDAR
– Terrestrial Laser Scanner (TLS) and raster images (photography), respectively. An accuracy analysis was performed
in regard to the positioning of outcrop point clouds obtained by both techniques. To make the comparison feasible,
datasets were composed of point clouds generated from multiple images in diff erent poses using a consumer digital
camera and directly by a terrestrial laser scanner. After preprocessing stages to obtain these point clouds, both were
compared using positional discrepancies and standard deviation. A preliminary analysis showed that the use of digital
images for 3D reconstructions is a feasible method for digital outcrop modeling, with a low cost of data acquisition
and without a signifi cant loss of accuracy compared to LiDAR.
Keywords: LiDAR, 3D Reconstruction, Digital Outcrop Model, Terrestrial Laser Scanner, Digital Image.
RESUMO
Esse artigo apresenta um estudo comparativo sobre reconstrução 3D baseado em sensores ativos e passivos, principal-
mente LiDAR (Terrestrial Laser Scanner) e imagens raster, respectivamente. Uma análise de exatidão foi realizada para
o posicionamento das nuvens de pontos para ambas as técnicas. Para tornar a comparação possível, nuvens de pontos
foram geradas a partir de várias imagens tomadas de diferentes locais utilizando câmeras digitais de alta resolução. Após
o pré-processamento para obter as nuvens de pontos, estas foram comparadas com as nuvens de pontos obtidas com o
Brazilian Journal of Cartography (2016), Nº 68/6, Special Issue GEOINFO 2015: 1203-1210
Brazilian Society of Cartography, Geodesy, Photgrammetry and Remote Sense
ISSN: 1808-0936
S B C
Silva. R. M. et al.
1204 Brazilian Journal of Cartography, Rio de Janeiro, Nº 68/6 p. 1203-1210, Jun/2016
Laser Scanner Terrestre por meio da análise de discrepâncias posicionais e desvio-padrão. Os resultados mostram que
a utilização de imagens digitais para reconstruções 3D é adequada para a modelagem digital de afl oramentos e tem
como vantagens a rapidez e o baixo custo de aquisição dos dados sem perda de exatidão signifi cante quando comparada
com os modelos digitais resultantes da técnica LiDAR.
Palavras chaves: Reconstrução 3D, Modelo Digital de Afl oramento, Laser Scanner Terrrestre, Imagem Digital.
1. INTRODUÇÃO
Increasing advances in new technologies
have produced a couple of unexplored new
opportunities in the field of technologies
applied to geosciences. Thus it is important
to test and evaluate the best way to use these
technologies. Currently, in geology, we have
effi cient tools to obtain three-dimensional (3D)
data that include color and intensity, allowing
accurate measurements of layers thicknesses
for inaccessible places, for example, outcrops.
Three-dimensional digital models, especially
those obtained from a terrestrial laser scanner,
and more recently from multiples digital images
have been intensively employed.
One technique that has quickly evolved
is georeferenced geological information by the
GNSS (Global Navigation Satellite System). This
system has allowed more effi cient integration,
both in accuracy and in time gain, of the diff erent
products in a single geological reference system,
ensuring greater reliability in the processes of
generation three-dimensional geological models
(PRINGLE et al., 2004; THURMOND et al.,
2005; WHITE & JONES, 2008).
The use of digital mapping technologies
has grown in the last ten years, in particular the
use of terrestrial laser scanners and topography
equipment, integrated systems with satellite
navigation and geographic information (XU
et al., 2001; ALFARHAN et al., 2008), thus
replacing numerous photographic mosaics that
are routinely used in the interpretation of large
outcrops.
Terrestrial laser scanners are able
to capture a few hundreds of millions of
georeferenced points. This device, to defi ne
the three-dimensional coordinates of points on
a surface, emits laser pulses with the aid of a
scanning mirror. When a pulse hits an object,
a portion of the energy returns back to the
equipment. The distance between the sensor and
object is measured based on the time lag between
the emission and return of the pulse. Calculation
of the coordinates of each point, obtained by
the laser scanner is possible from a point with
known coordinates in the source pulse. Thus, the
study of outcrops is stimulated by the ability to
quantify the data estimated or ignored due to the
lack of access.
The use of LiDAR technology, especially
terrestrial laser scanner, in studies of outcrops
is expanding due to the ease of acquisition of
precise, fast and automated georeferenced data.
This technology has been used for this purpose
for a decade (BELLIAN et al., 2002), but only
in recent years has the number of scientific
articles increased signifi cantly. However, the
topics of interest are quite diverse, and include:
methodological approaches (BELLIAN et al.,
2005; ABELLAN et al. 2006; ENGE et al.,
2007; BUCKLEY et al., 2008; FERRARI et
al., 2012), reservoirs (PRINGLE et al., 2004;
PHELPS & KERANS, 2007; KURTZMAN
et al., 2009; ROTEVATN et al., 2009; ENGE
& HOWELL, 2010; FABUEL-PEREZ et
al, 2009, 2010), fractured rocks (BELLIAN
et al., 2007; OLARIU et al., 2008; JONES
et al., 2009; ZAHM & HENNINGS, 2009),
erosion rates (WAWRZYNIEC et al., 2007), a
synthetic seismic model (JANSON et al., 2007),
orientation of basaltic lava fl ows (NELSON et
al., 2011) and classifi cation of spectral patterns
(INOCENCIO et al., 2014).
Photo-realistic 3D modeling is a research
topic that addresses the quick generation of three-
dimensional calibrated models using a hand-
held device (SE & JASIOBEDZKI, 2006). This
technique allows for the creation of 3D models,
both for visualization and measurements, based
on multiple images. Several studies (LEUNG,
2006; ALIAGA et al., 2006) have used this
photogrammetry technique for the reconstruction
of 3D models, and have analyzed the eff ects and
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Brazilian Journal of Cartography, Rio de Janeiro, Nº 68/6 p. 1203-1210, Jun/2016
3-D Reconstruction of a Digital Outcrop Model
methods for image-based modeling from multiple
images (SZELISKI, 2010). In geology, our goal
is that this technique will be able to applied to the
analysis of outcrops in three dimensions in the
laboratory at low cost compared with LiDAR.
In addition to, it should be able to be used to
improve and facilitate virtual interpretations
(BALTSAVIAS et al, 2001; ENGE et al, 2007).
Thus the aim of this study is to quantify,
through control points, the positional error of
outcrops mapped by an image-based modeling
technique and by LiDAR, as well as to perform
a comparison of the positional errors.
2. 3D RECONSTRUCTION MODEL
FROM MULTIPLE IMAGES
Using multiples images (photographs), we
can (re)construct three-dimensional models. This
is the reverse process of obtaining photographs
from 3D scenes. When a 3D scene is projected a
2D plane depth is lost. A 3D point corresponding
to a specifi c image point is constrained to be
in the line of sight. From a single image, it is
impossible to determine a point in the line of sight
that corresponds to the image point. However,
if two images are available, then the position of
a 3D point can be found at the intersection of
the two projection rays. This process is called
triangulation. Therefore, this process requires
the multiple pass approach that begins with
the camera calibration process to relate the
measuring range of the sensor to the real world
quantity that it measures. It is necessary to fi rst
understand the mathematical model of a camera
to calibrate it. For this purpose, we have adopted
a projective camera model (pinhole camera),
which has been widely adopted as the camera
model in computer vision, since it is simple and
accurate enough for most applications.
The pinhole camera is illustrated in Figure
1 (a), while a slightly diff erent model, in which
the image plane is in front of the center of the
projection, is expressed in Fig. 1 (b).
To understand multi-view geometry, we
must first consider the relationship between
two cameras (or sequentially moving one
camera), which is actually called epipolar
geometry. Epipolar geometry is the geometry of
intersecting planes of images. Using the common
points between the images, along with the
intersection of planes, it is possible to calculate
the 3D position of objects in the scene.
Image Plane
Camera
Real Target
Pinhol e
X = ( )X, Y , Z
CCC
Z
Y
X
y
x
u = (x, y)
Image Coordinates
Camera coordinates
f
Fig. 1 – Pinhole camera (A), Model (B).
We have shown that there is a geometric
relationship between corresponding points in
two images of the same scene. This relationship
depends only on the intrinsic parameters of the
two cameras and their relative translation and
rotation (Figure 2).
ray
w
w
w
w
epipo lar
line
camera
plane 2
camera
plane 1
optical
center 2
optical
center 1
Fig. 2 – Two cameras with epipolar constraints.
Consider a single camera viewing a
3D point w in the world passing through x1
and optical center c1. From one camera, it is
impossible to identify the point in the ray. The
projection of the ray in image plane 2 defi nes
an epipolar line. Therefore, the point in the
rst image plane (Camera 1) corresponds to
a constrained line in the second image plane
A
B
Silva. R. M. et al.
1206 Brazilian Journal of Cartography, Rio de Janeiro, Nº 68/6 p. 1203-1210, Jun/2016
(Camera 2). This relationship is called an epipolar
constraint. The constraint on corresponding
points is a function of the intrinsic and extrinsic
parameters. If intrinsic parameters are given,
then the extrinsic ones can be determined as
well as the geometric relationship between the
cameras. Another advantage is that, given the
intrinsic and extrinsic parameters of the cameras,
the corresponding point of one image can be
found easily through a 1D search along the
epipolar line in the other image.
A mathematical model can capture the
relationship between two cameras (two images)
and can provide 3D point determination. In a
general context, the mathematical constraint
between the positions of the corresponding
points x1 and x2 in two normalized cameras
can be obtained by an essential matrix (note that
either camera calibration or a diff erent matrix –
fundamental matrix is required). Details about
the essential matrix can be obtained from any
good computer vision literature (HARTTLEY
R. & ZISSERMAN, 2004). This matrix can
provide the above described parameters, mainly
the camera matrices (resectioning process) and
their parameters. Using a series of 3D-2D image
plane correspondences, it is possible to compute
the camera pose estimation, which utilizes the
camera parameters of the right camera that
minimize the residual error of the 3D-point
reprojections.
In another approach, three or more
cameras, instead of two can be considered.
In three views, there are six measurements,
therefore three degrees of freedom. However,
it is for lines that there is the more signifi cant
gain. In two-views, the number of measurements
equals the number of degrees of freedom of
the line in 3D-space, i.e., four. Consequently,
there is no possibility of removing the eff ects of
measurement errors. However, in three views
there are six measurements on four degrees
of freedom therefore, a scene line is over-
determined and can be estimated by a suitable
minimization over measurement errors.
For the purpose of computation, we
implemented this sequence of concepts in an
in-house computer vision library using OpenCV
(BRAHMBHATT, 2013) – for computer vision
and image processing support, Google Ceres-
Solver library1 – for modeling and solving large
complicated nonlinear least squares problems
and Eigen library2a high-level C++ library of
template headers for linear algebra, matrix and
vector operations, and numerical solvers.
3. MATERIALS AND METHODS
The following subitems describe
the materials and and methods used in the
development of this work.
3.1 Materials
The study area is an outcrop of the Rio
Bonito Formation, Lower Permian of the Paraná
Basin, called Morro Papaléo and located at
Mariana Pimentel, Rio Grande do Sul state,
southern Brazil (Figure 3), between the geodetic
coordinate, latitudes 30°18’10”S and 30°18’40”S
and between longitudes 51°38’40”W and
51°38’30”W in the datum SIRGAS2000. The
area is an abandoned quarry that was originally
exploited for kaolin. It is a three-dimensional
outcrop with a good exposure of rocks such as
fossiliferous siltstone, carbonaceous siltstone,
pebbly mudstone and sandstone.
We implemented points that server as
a support for the georeferencing of the point
clouds obtained by LiDAR and the image-based
modeling technique. The georeferenced points
were tracked with Hyper-RTK GNSS equipment
and were supported by geodetic points layered on
top of the outcrop. These georeferenced points
(P1 and P2, Table 1) were used as a support for
measuring coordinates of points on the surface
Fig. 3 - Location map of the study area.
1https://code.google.com/p/ceres-solver/
2http://eigen.tuxfamily.org
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3-D Reconstruction of a Digital Outcrop Model
outcrop, which were subsequently used to
analyze the positional error. As a result tracking
points (P1 and P2) were obtained in the system
coordinates (Figure 3, & Table 1) UTM:
Table 1: Plane coordinates in the utm projection
of the points of support for surveying via the
central meridian at 51° sirgas2000 reference
system (geocentric reference system for the
Americas).
UTM COORDENATES
POINTS E (m) N (m)
Ellipsoidal
height – h
(m)
P1 438125,808 6646812,115 136,775
P2 438135,602 6646873,338 137,468
To obtain the coordinates on the surface
of the outcrop we used a total station (Leica
Viva TS15, Fig. 4 - Tracking of points P1 and
P2 with the use of GNSS-RTK (A). The points
of the surface outcrop were measured with Total
Station (B).
Fig. 4 - Tracking of points P1 and P2 with the
use of GNSS-RTK (A). Points on the surface
outcrop measured with Total Station (B).
This was adopted as a criterion for the
selection of local points emphasizing on the
contrast of colors and other well-defined
characteristics. This facilitated the identifi cation
of the point cloud, both in a terrestrial laser
scanner and image-based modeling. With the
total station, 21 points on the surface of the
outcrop were measured, as illustrated in Figure
4B. These coordinates were used as parameters
to determine the positional quality of the outcrop
study.
For imaging the outcrop, we used a Leica
Scanner Station C10, with a resolution point
cloud ranging between 2mm and 4cm.
The point cloud was processed to eliminate
unnecessary information such as vegetation
and fallen rocks in front of the outcrop. In the
outcrop, sandstone predominates in Morro
Papaléo and these rocks are in the point cloud
shown in Figure 5.
F ig. 5 - Point cloud obtained with the terrestrial
laser scanner.
The same outcrop was photographed
with a Nikon D3000 digital camera at a
resolution of 7 Megapixels. The procedure
for the collection of photos in the eld was
adopted to maintain approximately the same
distance between the camera and outcrop
(Figure 6). Another procedure was adopted to
consider the top and bottom of the outcrop in
the same photo. The photos were taken from
diff erent positions to obtain approximately
60% overlap between the images.
The processing of digital photos and
reconstruction of the outcrop were an image-
based modeling technique. We reconstructed
the 3D outcrop and generated a cloud of the
points and georreference following the same
procedures used in the generation of Digital
Outcrop Model (DOM) obtained with the TLS.
Silva. R. M. et al.
1208 Brazilian Journal of Cartography, Rio de Janeiro, Nº 68/6 p. 1203-1210, Jun/2016
4.RESULTS AND DISCUSSION
By comparing the results for the generation
of the DOMs based on the LiDAR technique,
and reconstruction of 3D objects from photos,
we determined that the image-based modeling
(Figure 7A) for photos allowed a visual resolution
of better quality. However, the model generated by
the terrestrial laser scanner (Figure 7B) allowed
the spacing (resolution) of the points in the point
cloud to be controlled, whereas, there is no such
control in image-based modeling from photos.
Fig. 6 – Pictures obtained with the camera (A).
Positions of the camera (B).
Fig. 7 3D Reconstruction from photos (A) and
the terrestrial laser scanner (B).
Assembling the image-based modeling
and terrestrial laser scanner point cloud, the Chi-
Square test indicated a 95% confi dence level for
georeferencing the diff erences, indicating that
there was no signifi cant diff erence between the
control data and techniques evaluated. In the
comparison of the relative error models of the
techniques used, we observed that the diff erence
became smaller than 5 cm, as shown in Table 2.
T able 2: Diff erence between linear measurements
obtained from the models generated.
Lines
Terrestrial
Laser Scanner
(meters)
Image-Based
Modeling
(meters)
Diff erence
(meters)
11.6134 1.6375 -0.0241
22.3313 2.3451 -0.0138
31.8380 1.7960 0.0420
41.7010 1.6892 0.0118
52.8580 2.8669 -0.0089
5. CONCLUSION
The digital outcrop modeling technique
can assist in outcrop interpretation, mainly for
places that are hard to reach due to the large size
and height of an outcropping, or for security
reasons. This papers results have shown that
the image-based modeling techniques can be
feasible in this application instead of LiDAR
because the average linear error is under 40 cm.
The cost of LiDAR equipment is much higher
than that of a digital camera; hence, image-based
modeling can provide good quality results at a
lower cost as well.
The relative precision measurements
performed from the point cloud obtained from
the image-based modeling had an error below
5 cm (Table 2) than that for the point cloud
obtained from a terrestrial laser scanner, which
allows the geological features to be analyzed for
data modeling.
This study argue that image-based
modeling techniques can assist in obtaining
a point cloud in places with occlusions from
shading or obstructions around the object of the
study, which is not possible to obtain using the
LiDAR technique.
The georeferencing of the point clouds
from the image-based modeling technique
allowed overlapping of the point cloud from
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Brazilian Journal of Cartography, Rio de Janeiro, Nº 68/6 p. 1203-1210, Jun/2016
3-D Reconstruction of a Digital Outcrop Model
the LiDAR technique, proving that the model
generated from photos can be associated with a
reference system. This, in turn, allows integration
of other information obtained from other data
sources.
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Advances in data capture and computer technology have made possible the collection of 3D high-resolution surface and subsurface digital geological data from outcrop analogues. This paper describes research to obtain the 3D distribution and internal sedimentary architecture of turbidite channels and associated sediments at a study site in the Peak District National Park, Derbyshire, UK. The 1D, 2D and 3D digital datasets included Total Station survey, terrestrial photogrammetry and remote sensing, sedimentary logs and a Ground Penetrating Radar (GPR) dataset. A grid of 2D GPR profiles was acquired behind a cliff outcrop; electromagnetic reflection events correlated with cliff face sedimentary horizons logged by Vertical Radar Profiling. All data were combined into a Digital Solid Model (DSM) dataset of the site within reservoir modelling software. The DSM was analysed to extract 3D architectural geometries for petroleum reservoir models. A deterministic base model was created using all information, along with a suite of heterogeneous turbidite reservoir models, using 1D, 2D or 3D information. The model suite shows significant variation from the deterministic model. Models built from 2D information underestimated connectivity and the continuity of geobodies, but overestimated channel sinuosity. Advantages of using 3D digital outcrop analogue data for 3D reservoir models are detailed.