Towards Wiki-based Dense City Modeling - Institute for Computer ...

Towards Wiki-based Dense City Modeling
Arnold Irschara
Institute for Computer Graphics and Vision, TU Graz
irschara@icg.tugraz.at
Horst Bischof
Institute for Computer Graphics and Vision, TU Graz
bischof@icg.tugraz.at
Christopher Zach
VRVis Research Center
zach@vrvis.at
Abstract
This work reports on the advances and on the current
status of a terrestrial city modeling approach, which uses
images contributed by end-users as input. Hence, the Wiki
principle well known from textual knowledge databases is
transferred to the goal of incrementally building a virtual
representation of the occupied habitat. In order to achieve
this objective, many state-of-the-art computer vision methods
must be applied and modified according to this task. We
describe the utilized 3D vision methods and show initial results
obtained from the current image database acquired by
in-house participants.
1. Introduction
Recently, 3D vision methods demonstrate increased robustness
and result in high quality models, hence multiview
modeling appears more often in industry projects targeted
at large scale modeling of environments. In particular,
efforts like Google Earth and Virtual Earth aim on the systematic
creation of virtual models from aerial images. In
this work we focus on the uncoordinated generation of digital
copies of urban habitats from community supplied images.
Hence, more 3D vision methods will become known
in a larger audience. Panorama creation tools like Autostitch
[4] are already well-established in the public. Now,
even end-user applications for the more sensitive structure
from motion determination exist at least as technology previews.
Currently, the Photo Tourism software [19] (and the related
PhotoSynth application) is the most-well known application
for automatic structure and motion computation from
a large set of images. A collection of supplied images is
analyzed and correspondences are established, from which
a relevant subset of views and the respective 3D structure
are determined. Photo Tourism does not explicitly incorporate
calibrated cameras, but relies partially on the focal
length specification found in the image meta-data to obtain
the initial metric structure. Images with incorrect or missing
meta-data can be registered by DLT pose estimation.
In contrast to Photo Tourism we employ calibrated cameras,
thereby substantially easing the structure and motion
computation. Performing the calibration procedure proposed
in our framework can be easily done by end-users.
One additional advantage of using calibrated cameras is
the higher accuracy of the computed poses, which enables
the subsequent generation of dense geometry using multiview
stereo techniques. In the first instance, we aim on
textured dense models in quality similar to the results presented
in [1]. Apparently, these raw models need to be postprocessed
in subsequent steps to allow an efficient Internetbased
visualization.
The majority of 3D modeling approaches is intended
for a decentralized use on personal computers. Vergauwen
and Van Gool [23] present a Web-based interface to their
3D modeling engine, again working with uncalibrated cameras
[14]. Registered users can upload their images and subsequently
receive the resulting depth maps. Their proposed
system is targeted at reconstructing individual sites, but it is
not aimed on building and maintaining a global image and
3D model database.
The goal of our work is the creation of a 3D virtual model
representing an urban environment from captured digital
images. Instead of using publicly available photo collections
(as done in [19]), we rely on images submitted by
interested users, since the participants need to provide the
camera calibration data in addition. By adding more images,
the virtual representations of an urban habitat can be
incrementally maintained and refined gradually. Hence, we
apply the famous and effective Wiki principle on the objective
of creating a photorealistic 3D city model. The following
sections describe the utilized methods and the results
available so far in more detail.
1

(a)
Figure 1. 96 calibration markers arranged in a 4 by 4 layout on the
floor.
2. Camera Calibration
In order to avoid to distinguish between scenes with and
without dominant planar structures (e.g. [15]), we require
the cameras to be calibrated. Additionally, our experience
with self-calibration techniques indicates, that the accuracy
of structure and motion computation is expected to be
higher with a calibrated setup. In particular, accurate pose
is essential to obtain a faithful reconstruction using dense
depth techniques.
To ease the calibration effort for the end-user, we employ
a procedure aiming for the accuracy of target calibration
techniques without the need for a precise calibration
pattern. The approach is based on simple printed markers
imaged in several views. Using specific markers enables to
establish robust and correct correspondences between the
views. Image-based city modeling requires generally an infinite
focus and a wide angle setup, hence the calibration
pattern needs to be sufficiently large. Thus, the marker patterns
are printed on several sheets of paper and are typically
arranged on the floor (see Figures 1(a) and (b)). These pages
can be laid out arbitrarily, hence the well-known method of
Zhang [27] is not applicable. It is not necessary to have all
markers visible in the captured images, but for good calibration
results most markers should be visible and well distributed
in the images.
The first step in the calibration procedure is the detection
of the circular markers in the images and the extraction
of the unique marker ID. The 2D feature point associated
with a marker is either the center of the extracted ellipse,
which only approximates the true marker center. Additionally,
the 2D feature position can be refined using the central
checkerboard pattern. In this case a non-linear search
for the correct center is performed by aligning a synthetic
checkerboard pattern with a suitable section of the marker
image.
Matching feature points across multiple views is trivial,
since unique and easily extractable IDs are available. Of
course, the uniqueness of extracted markers in every image
needs to be checked to avoid incorrect detections in case of
blurred or otherwise low-quality images.
Since the marker images are laid out on a planar surface,
(b)
corresponding feature points are related by a homography.
Hence, the first estimation of lens distortion parameters attempts
to minimize the reprojection error between extracted
feature points with free homography and lens distortion parameters
[13]. More formally, if x k i denotes the position of
marker k in the i-th image, the initial distortion estimation
determines
∑
arg min | ˜D(x k j , θ) − ˜D(H ij x k i , θ)| 2 , (1)
H ij,θ
i,j
where H ij denotes the image homography from view i to
j and ˜D(x, θ) is the inverse distortion function with coefficients
θ. The distortion model is
˜D(x, θ) = (x − (u 0 , v 0 ) T ) · (1 + k 1 r 2 + k 2 r 4 ), (2)
with r = ‖x − (u 0 , v 0 ) T ‖. θ is the vector (u 0 , v 0 , k 1 , k 2 )
consisting of the distortion center (u 0 , v 0 ) and the coefficients
k 1 and k 2 .
The center of radial distortion (u 0 , v 0 ) is independent
from the optical principal point, thus essentially removing
the need for decentering distortion parameters [22]. The initial
homographies are set to the gold standard results and the
distortion parameters are initialized with the image center,
and 0 for the coefficients k 1 and k 2 , respectively. The nonlinear
minimization is performed with a (sparse) Levenberg-
Marquardt method. Note, that the homographies are not
independent: a consistent set of inter-image homographies
should satisfy H ij = H lj H il for all l. This can be enforced
in our implementation by using a minimal parametrization
solely based on homographies between adjacent views,
H i,i+1 , and representing H ij = ∏ j>l≥i H l,l+1.
After determining the initial estimate for the lens distortion,
the focal length of the camera is estimated from the set
of homographies. Both [21] and [10] employ a non-linear
minimization technique for intrinsic parameters estimation
and an initial estimate is required. We utilize a much simpler
search technique to quickly determine the camera intrinsics:
At first, we assume that the principal point is close
to the image center and that the aspect ratio and skew are
one and zero, respectively. Hence, we search for a constant,
but unknown focal length f determining the calibration matrix
K. If the correct intrinsic matrix K is known, the
image-based homographies H ij can be updated to homographies
between metric image planes, ˜Hij = K −1 H ij K.
For a particular view i assumed with canonical pose, ˜Hij
can be decomposed as ˜H ij = R ij − t ij n T i /d i, where
(R ij , t ij ) depicts the relative pose and n i and d i denote
the plane normal and distance (according to the coordinate
frame of view i), respectively. Note, that each ˜H ij provides
its own estimate of n i = n i ( ˜H ij ).
For the true calibration matrix K, the extracted normals
n i ( ˜H ij ) should coincide into one common estimate of the

plane normal. Hence, a low variance of the set {n i } indicates
approximately correct calibration parameters. A slight
complication is induced by the fact, that decomposing ˜H ij
results in two possible relative poses and plane parameters
(denoted with n + i and n − i ). Let (n+ 0 , n− 0 ) be the most separated
pair of normals from all pairs (n + i ( ˜H ij ), n − i ( ˜H ij )).
We use n + 0 and n− 0 as the estimates for the mean of the set
{n i }. Now, the score for K is the minimum of
∑
min
(∠(n + i ( ˜H ij ), n + 0 ), ∠(n− i ( ˜H
)
ij ), n + 0 ) (3)
i,j
i,j
and
∑
min
(∠(n + i ( ˜H ij ), n − 0 ), ∠(n− i ( ˜H
)
ij ), n − 0 ) . (4)
This score is evaluated for potential choices of f, e.g.
f ∈ [0.3, 3] in terms of normalized pixel coordinates. The
value of f with the lowest score is used as initial estimate
for the focal length. This procedure is both simple and very
fast, and yields to sufficiently accurate focal lengths in our
experiments.
With the (approximate) knowledge of the focal length, an
initial metric reconstruction based on two appropriate views
is generated. The remaining views are added by estimating
their absolute poses. The final bundle adjustment procedure
optimizes for the parameters of the forward distortion
function, hence the inverse of the originally obtained distortion
parameters is required. Since the employed polynomial
distortion model is not closed under function inversion,
the initial forward distortion parameters are determined by
a least squares approach. A final bundle adjustment procedure
is applied to refine the camera intrinsics and distortion
parameters and to improve the only approximately planar
3D structure and the camera poses.
3. Structure and Motion Computation
3.1. Preprocessing
The first step after image uploading is resampling the
image according to the obtained lens distortion. In order to
avoid frequent recomputation or retrieval of the corresponding
lookup table, this procedure is run as a daemon process
caching several least recently used distortion lookup tables.
Afterwards, feature points and their respective descriptors
are extracted. The current implementation uses SIFT features
[9] because of its success reported in the vision community.
3.2. Image Matching
Retrieving similar images for a given one is currently a
very active research topic (e.g. [16, 12, 7, 17]. We employ
a visual vocabulary tree approach similar to [12] to retrieve
a set of potentially similar views from a large collection of
images. Thus, other image related data to limit the candidate
images for matching like GPS position is helpful, but
not strictly necessary. The vocabulary tree enables us to efficiently
match a single image against a database containing
thousands and even millions of images. Images found in
the database with a high score according to the vocabulary
tree are investigated further by a more discriminant matching
procedure. Since the score induced by the vocabulary
tree may miss relevant images, the set of candidate images
used for further matching is augmented with the neighbors
of highly ranked images with respect to the already constructed
view network.
In our system the vocabulary tree is trained in an unsupervised
manner with a subset of 2 × 10 6 SIFT feature vectors
randomly taken from 2500 street-side images. The descriptor
vectors are then hierarchically quantized into clusters
using a k-means algorithm. We set the branch factor to
10 and allow up to 7 tree levels. For each level the k-means
algorithm is initialized with different seed clusters and the
result producing the lowest Euclidean distance error is retained.
Once the vocabulary tree is trained, searching the
visual vocabulary is very efficient and new images can be
inserted on-the-fly. Based on the scoring function a ranking
of relevant database images is reported and used for postverification.
In our current setting we rely on an entropy weighted
scoring similar to the tf-idf “term frequency inverse document
frequency” as described in [18]. Let D be an image in
our database and t be the term in the vocabulary associated
to feature f of the current query image Q, then our scoring
function is,
∑
( ) N
log
(5)
n(t)
t∈Q∩D
where N is the total number of images in the collection and
n(t) is the number of images that contain term t. In order
to guarantee fairness between database images with different
number of features, the query results are normalized by
the self-scoring result. Therefore, if a database image is
used for query, a score of 1 is returned. At the same time
we get an absolute measure of image-to-image similarity,
which enables us to set a global threshold for scoring. The
k top ranked images reported by the vocabulary tree are then
taken for post-verification. Typically, we set k to 1% of the
current database size.
Our verification procedure is based on exhaustive matching
and RANSAC for geometric consistency check. First of
all, correspondences are computed by mutual nearest neighbor
matching of the 128 dimensional SIFT feature vectors.
We adopt the idea of [2] and match features with the same
contrast only, by taking advantage of the Laplacian sign. In
addition, the epipolar geometry is verified using a RANSAC
procedure. If sufficient reliable 3D structure for the image

(a)
Figure 2. (a) Ten sample images from a collection of 105 facade images. (b) Side view of the camera poses and 9097 triangulated feature
points.
(b)
measurements is available, we use pose estimation for verification.
The calibrated settings enable us to use the Five-
Point algorithm [11] for image-to-image matches and the
Three-Point algorithm [6] for 3D to 2D correspondences
as minimal hypothesis generators. Images are accepted as
neighbors if a quality criterion is satisfied: we generate a
number of N hypothesis in prior and then check if the number
of outliers does not exceed the precomputed threshold.
Since it has often been observed (e.g. in [20]) that the
RANSAC stopping criterion is sometimes optimistic, we
use a rather conservative confidence factor p of 1−10 −4 and
require a minimal number of 20 inliers. If an image passes
the post-verification procedure, the neighbors of this image
are also matched with the query image. Note, that this strategy
is highly efficient for our purpose, since frequently the
first ranked image by the vocabulary tree is already a candidate
match satisfying the geometry constraints.
Unlike for the vocabulary tree scoring, where the whole
set of SIFT descriptors is utilized, we limit the number of
features for exhaustive matching. In general we take the
1500 best features according to their DoG magnitude response
for matching, only. Therefore, searching for correspondences
is sufficiently fast (see Section 5 for detailed
timings).
3.3. Upgrading the View Network
Each time a new image is added to the view network,
its neighbors are computed and the reconstruction process
is started. By reconstruction we mean structure and motion
computation, namely the estimation of the camera orientations
and the sparse 3D structure of the matched features.
Since images may be taken from different locations, we
do not expect to obtain a single coherent reconstruction, but
a forest of multiple reconstructions. We require that a reconstruction
consists of at least three images (view triple)
and 20 common triangulated points. In general four different
cases can occur if a new image is processed:
1. The view can be robustly registered with exactly one
already present reconstruction.
2. The image can be aligned with multiple reconstructions.
3. The current view cannot be (robustly) aligned with an
existing reconstruction, but forms a good view triple
with two other already present views.
4. The geometric relation of this image with any of the
known views cannot be established, and structure and
motion determination is postponed until a new suitable
view is inserted.
In the first case the position of the current view can be computed
immediately by robust absolute pose estimation, since
2D to 3D points correspondences are known. Thereafter,
the camera parameters are optimized by iterative refinement
and new correspondences are triangulated to 3D points.
In the second case, where the current image takes part of
two or more different reconstructions, the reconstructions
are merged. We determine robustly a 3D to 3D similarity
transform for the registration of the two corresponding 3D
points. This process is then followed by Euclidean bundle
adjustment, where the sparse geometry and the camera parameters
are optimized.
After updating the reconstructions in this first two cases,
the epipolar neighbors of the newly inserted view are traversed
and checked, whether the updated 3D structure now
allows determination of their poses.
In the third scenario the neighbors of the current image
are estimated as described previously and a new reconstruction
is initialized from a well-conditioned view triple. The
view triple should provide a good triangulation angle and at

Figure 3. Dense reconstruction from a collection of 105 facade images.
the same time have many correspondences. Therefore, in
the first step we identify the view pair which minimizes,
1
N
N∑
i
1
sin 2 (α i )
where α i is the angle between the two camera rays for the
3D point X i . Thereafter, a third view which minimizes the
value in Eq. 6 with respect to this first configuration is estimated.
Note, that 1/sin(α i ) approximates the uncertainty
(deviation) of X i in the depth direction. In [3] the view
pair with maximal mean roundness (essentially the same as
1/N ∑ sin(α i )) is taken. Such an approach does not consider
the number of correspondences between two views.
In this work we assume, that the accuracy of further (leastsquares)
computations depending on the initial structure
scales with 1/ √ N. Consequently, Eq. 6 estimates the mean
variance of the initial structure for a given view pair. The
relative pose between the first two views is computed by
the Five-Point algorithm and the third camera is inserted by
the Three-Point algorithm with respect to the triangulated
3D points. Thereafter, bundle adjustment is used to globally
optimize the exterior camera orientations and the initial
structure. A view triple is considered as a valid reconstruction
if the sum of triangulation angles is above a threshold,
we require at least twenty 3D points with measurements in
all views and a triangulation angle greater than 2 ◦ .
Whenever a number of M (15 in our case) views is added
to a reconstruction, bundle adjustment is run by optimizing
all cameras and triangulated 3D points. Our bundle adjustment
implementation is similar to the one described in [8].
Thereafter, for each image measurement the reprojection error
is computed, 3D points with an average reprojection error
larger than 1.3 pixel and a triangulation angle less than
2 ◦ are removed. Our experiments suggest that this strategy
improves both, accuracy and robustness of the reconstruction
algorithm. A sparse reconstruction result is shown in
Figure 2.
(6)
4. Dense Reconstruction
Obtaining the initial 3D structure and motion is an essential
aspect of image-based modeling, but dense geometry
is required for a faithful virtual representation of the
captured scene. Since we face a large number of images
with potentially associated depth maps, we focus on simple
but fast dense depth estimation procedures. Additionally,
processing of multiple sensor images with respect to
a key view (in contrast to traditional two-frame stereo) is
demanded. Plane-sweep approaches to dense stereo [24, 5]
enable an efficient, GPU-accelerated procedure to create the
depth maps. In order to obtain reasonable depth values in
homogeneous regions, we employ GPU-based scanline optimization
in our framework [26]. Note, that dense geometry
generation is currently still performed in an offline fashion
for individual large and connected view networks.
In case of general view networks, a suitable selection of
sensor views used for depth estimation is necessary. We
use the following simple, but effective heuristic to select
appropriate sensor images, which is based on an estimate
for image overlap and viewing directions: for a particular
key view and a potential sensor view, we determine the correspondences
between these views and compute the convex
hull of the respective 2D measurements in the key view. The
area of this convex hull A H in relation to the total key image
area A gives an estimate of the relevant image overlap.
Note, that A does not necessarily denote the whole key image
size, since insignificant image portions like sky regions
can be excluded. Sensor view candidates with an overlap
A H /A smaller than a given threshold (typically set to 0.3)
are discarded. Image overlap is only a partial guideline for
view selection. The angle between corresponding camera
rays is another suitable criterion. Very small angles give rise
to large depth uncertainties, whereas larger angles are susceptible
to image distortion and occlusions. From a practical
point of view, triangulation angles of about α 0 = 6 ◦ are
favorable for dense stereo (meaning a distance to baseline

atio of about 10:1). Consequently, view pairs with a large
overlap and appropriate triangulation angles are preferable.
Hence, we rank the views with sufficient overlap according
to the following score:
A H
A median(ψ(α i)), (7)
where α i is the angle between corresponding rays and ψ(·)
is a unimodal weighting function with its maximum at α 0 .
We choose ψ as
ψ(α) = α 2 e −2α/α0 . (8)
The two views with highest scores are taken as sensor
views.
Dense depth estimation depends heavily on the quality
of the provided epipolar geometry. In order to reduce the
influence of inaccuracies in the estimated poses on the depth
maps, and to increase the performance, multi-view stereo
is applied on downsampled images (512 × 384 pixels for
4 : 3 format digital images). Matching cost computation
and scanline optimization for view triples (one key view and
two sensor views) take about 3s on a GeForce 7800GS.
The set of depth maps provides 2.5D geometry for each
view. These depth maps are subsequently fused into a common
3D model using a robust depth image integration approach
[25]. This method results in globally optimal 3D
models according to the employed energy functional, but it
operates in batch mode. The incorporation of this step is
the major reason for dense geometry generation to be an offline
process. The result obtained by depth map fusion for
the dataset depicted in Figure 2 (augmented with per-vertex
coloring) is shown in Figure 3.
5. Results
We tested our system on different image collections,
varying from a few hundred to thousands of pictures. All
images are calibrated with the method described in Section
2. The calibration precision (i.e. the final mean reprojection
error) ranges from 1/20 to 1/7 pixel. Our largest
test set is a database containing about 7000 street-side images
taken with four compact digital cameras from different
manufacturers. The images are captured at different days
under varying illumination conditions. Furthermore, the
images are only partially ordered. The size of the source
images varies from two to seven Megapixel. In order to remove
compression artefacts, the supplied images are resampled
to the half resolution for further processing. Adding
an image to the view network takes approximately half a
minute, most of the time is spend on exhaustive matching
and bundle adjustment. Average run-times required for each
step are listed in Table 1.
In all our tests we use a pre-trained generic vocabulary
tree of about 7 × 10 5 leaf nodes for searching the image
Operation
time [s]
Undistortion (2272 × 1704 pixel) 1.0
Feature extraction (2272 × 1704 pixel) 1.6
Vocabulary scoring 0.2
Brute force NN-matching (1500 × 1500) k × 0.35
RANSAC (3000 samples Five-Point) k × 0.4
Structure and Motion 0.50
Bundle adjustment (100 views) 60
Dense stereo 3.0
Table 1. Typical average timings of our system on an AMD
Athlon(tm) 64 X2 Dual Core Processor 4400+. The parameter
k specifies the number of images taken for post-verification. Typically,
we set k to 1% of the current database size.
Figure 4. Vocabulary tree performance for image retrieval depending
on the database size. The y-axis shows the probability to find
an epipolar neighbor in the first k-ranked images reported by the
vocabulary tree scoring.
database. Our experiments suggest that the vocabulary tree
approach for image retrieval is very efficient for large scale
structure and motion computation. In Figure 4 the change
of retrieval performance depending on the database size is
shown. On average an image has an overlap with about
eight other images in the database. However, there are
also images with no geometric relation to existing database
entries. The detailed distribution of epipolar neighbors is
shown in Figure 5. The retrieval performance is measured
by the rank of the first image that passes the geometric verification
procedure. Note, even for a relative large database
of about 7000 images, the first ranked image reported by
the vocabulary tree is a valid epipolar neighbor of the query
image with a probability of more than 90%. What we can
observe also is that the scoring saturates rapidly, therefore
employing the 1% from the vocabulary tree ranking is a
good choice between speed and retrieval quality. Finally,
two captured sites and the resulting sparse and dense models
are shown in Figure 6 and Figure 7. The final reprojec-

(a)
Figure 5. Probability density function of the number of verified
epipolar neighbors for a query image in a database of 7181 streetside
images. On average a query images has an overlap with about
eight images in the database.
tion errors of the 3D structure and camera poses for these
datasets after bundle adjustment are about 1/3 pixel.
6. Future Work
Currently, images are contributed by persons associated
with this project and with basic knowledge in 3D computer
vision. Future work needs to increase the robustness of the
structure from motion methods to allow the public to participate
in the creation of the visual database. In particular, it
needs to be assured that low-quality or defective images do
not degrade the 3D models in the generated database.
Another future option is to allow uncalibrated images to
be added for the purpose of image localization and geometric
alignment. Such images will generally not result in an
update of the 3D structure.
Dense geometry generation is currently not integrated
into the online processing workflow. Depth estimation can
be easily adapted to the online setting, but the employed
range image fusion method is entirely an offline procedure.
A novel approach for robust and efficient depth image fusion
working incrementally is a present research topic.
Acknowledgements
This work is partly funded by the Vienna Science and
Technology Fund (WWTF) and by the Kplus VRVis research
center.
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