CLUSTERING OF WALL GEOMETRY FROM UNSTRUCTURED POINT CLOUDS

Abstract

The automated reconstruction of Building Information Modeling (BIM) objects from point cloud data is still ongoing research. A key aspect is retrieving the proper observations for each object. After segmenting and classifying the initial point cloud, the labeled segments should be clustered according to their respective objects. However, this procedure is challenging due to noise, occlusions and the associativity between different objects. This is especially important for wall geometry as it forms the basis for further BIM reconstruction.
In this work, a method is presented to automatically group wall segments derived from point clouds according to the proper walls of a building. More specifically, a Conditional Random Field is employed that evaluates the context of each observation in order to determine which wall it belongs too. The emphasis is on the clustering of highly associative walls as this topic currently is a gap in the body of knowledge. First a set of classified planar primitives is obtained using algorithms developed in prior work. Next, both local and contextual features are extracted based on the nearest neighbors and a number of seeds that are heuristically determined. The final wall clusters are then computed by decoding the graph and thus the most likely configuration of the observations. The experiments prove that the used method is a promising framework for wall clustering from unstructured point cloud data. Compared to a conventional region growing method, the proposed method significantly reduces the rate of false positives, resulting in better wall clusters. A key advantage of the proposed method is its capability of dealing with complex wall geometry in entire buildings opposed to the presented methods in current literature.

Full text

CLUSTERING OF WALL GEOMETRY FROM UNSTRUCTURED POINT CLOUDS
M. Bassier∗
, and M. Vergauwen
Dept. of Civil Engineering, TC Construction - Geomatics
KU Leuven - Faculty of Engineering Technology
Ghent, Belgium
(maarten.bassier, maarten.vergauwen)@kuleuven.be
Commission II
KEY WORDS: Building Information Modeling, Clustering, Wall, Building, Point Clouds
ABSTRACT:
The automated reconstruction of Building Information Modeling (BIM) objects from point cloud data is still ongoing research. A
key aspect is retrieving the proper observations for each object. After segmenting and classifying the initial point cloud, the labeled
segments should be clustered according to their respective objects. However, this procedure is challenging due to noise, occlusions
and the associativity between different objects. This is especially important for wall geometry as it forms the basis for further BIM
reconstruction.
In this work, a method is presented to automatically group wall segments derived from point clouds according to the proper walls
of a building. More specifically, a Conditional Random Field is employed that evaluates the context of each observation in order to
determine which wall it belongs too. The emphasis is on the clustering of highly associative walls as this topic currently is a gap in the
body of knowledge. First a set of classified planar primitives is obtained using algorithms developed in prior work. Next, both local and
contextual features are extracted based on the nearest neighbors and a number of seeds that are heuristically determined. The final wall
clusters are then computed by decoding the graph and thus the most likely configuration of the observations. The experiments prove
that the used method is a promising framework for wall clustering from unstructured point cloud data. Compared to a conventional
region growing method, the proposed method significantly reduces the rate of false positives, resulting in better wall clusters. A key
advantage of the proposed method is its capability of dealing with complex wall geometry in entire buildings opposed to the presented
methods in current literature.
1. INTRODUCTION
As-built Building Information Modeling (BIM) models are a widely
researched topic. These models reflect the state of the building up
to as-built conditions and are used for quality control, quantity
take-offs, maintenance and project planning (Volk et al., 2014,
Patraucean et al., 2015). An as-built model is obtained by up-
dating an existing as-design model of the structure or by reverse
engineering it from measurements taken on the site. This research
focuses on the creation of a BIM without a prior model since few
buildings currently have a model. A key aspect in the reconstruc-
tion process is the association of the observations with the dif-
ferent walls in the structure. Currently, these objects are created
by manually designing them based on point cloud data acquired
from the built structure. However, this process is labor intensive
and error prone. The retrieval of the walls is especially important
since this geometry forms the basis for other objects.
Automated reconstruction approaches focus on the unsupervised
processing of point clouds. The interpretation of this data is chal-
lenging due to the number of points, noise and the complexity of
the structure (Tang et al., 2010). Also, most point clouds are ac-
quired with remote sensing techniques which are bound to Line-
of-Sight (LoS). As a result, crucial parts of the structure are oc-
cluded due to clutter or inaccessible areas. Reasoning algorithms
make assumptions about these zones which are prone to misinter-
pretation.
The emphasis of this work is on the clustering of walls from large
unstructured point clouds of buildings. More specifically, we
∗Corresponding author
look to group wall observations on object level for the purpose
of BIM reconstruction. The proposed method is able to prop-
erly detect and cluster wall geometry even in highly cluttered and
noisy environments. Also, our approach deals with highly asso-
ciative wall geometry as it operates directly on the 3D point cloud
itself and is designed for multi-storey buildings.
The remainder of this work is structured as follows. The back-
ground and related work is presented in Section 2. In Section 3.
the methodology is presented. The test design and experimen-
tal results are proposed in Section 4. Finally, the conclusions are
presented in Section 6.
2. BACKGROUND & RELATED WORK
The automated procedure of creating BIM objects from point
cloud data commonly consists of the following steps (Nguyen
and Le, 2013). First, the data is preprocessed for efficiency. In 2D
methods, the point cloud is represented as a set of raster images
consisting of a slice of the data or other information (Landrieu
et al., 2017a, Anagnostopoulos et al., 2016). In 3D methods, the
point cloud is restructured as a voxel octree which allows efficient
neighborhood searches (Vo et al., 2015)(Fig. 1left). After the pre-
processing, the data is segmented. A set of primitives is detected
that replaces the point representation with the purpose of data
reduction. Typically, lines are used in 2D methods and planes or
cylinders are used in 3D methods (Vo et al., 2015, Lin et al., 2015,
Fan et al., 2017, Vosselman and Rottensteiner, 2017). Next, the
segments are classified by reasoning frameworks exploiting lo-
cal and contextual information (Fig. 1mid). Class labels such as
floors and walls are computed for each segment by using heuris-
tics or machine learning techniques (Bassier et al., 2016, Wolf
The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLII-2/W9, 2019
8th Intl. Workshop 3D-ARCH “3D Virtual Reconstruction and Visualization of Complex Architectures”, 6–8 February 2019, Bergamo, Italy
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101

Figure 1: Overview of the different steps in the data association workflow: unstructured point cloud (left), extracted classified planar
wall segments (mid) and the grouped wall observations per wall (right).
et al., 2015, Xiong et al., 2013, Nikoohemat et al., 2017). The
resulting labeled wall segments are processed by a second rea-
soning framework to merge segments belonging to the same wall
(Fig. 1right). Finally, these groups serve as input for the applica-
tion specific reconstruction algorithms.
Several researchers have proposed methods for the clustering of
wall geometry. Popular approaches include region growing, model
based methods, graphs and machine learning techniques (Nguyen
and Le, 2013). Most researchers employ a simple box definition
for the wall clustering. Moreover, the majority of methods only
considers one side of the wall which reduces the problem of wall
detection to a plane segmentation paradigm (Mura et al., 2014).
For instance, Oesau et al. (Oesau et al., 2014) assume collinearity
of the segments of a wall face. They employ a Hough transform
to extract all the points on the wall face in a 2D slice of the point
cloud. Similar results are presented by Previtali et al. (Previtali
et al., 2014), Budroni et al. (Budroni and B¨
ohm, 2010), Valero
et al. (Valero et al., 2012), Nikoohemat et al. (Nikoohemat et al.,
2017) and Adan et al. (Adan and Huber, 2011). Typically, these
methods prove successful in scenarios where wall detailing and
complex wall geometry is not an issue.
Some researchers do actually cluster both sides of a wall into a
box or rectangle. For instance, Mura et al. (Mura et al., 2014)
project their detected wall segments onto a 2D plane and cluster
them accordingly. A first directional clustering yields the main
orientation of the walls. For every orientation, a 1D mean-shift
clustering (Furukawa et al., 2009) is performed which identifies
all possible offsets of parallel wall segments of that orientation.
Finally, they compute a representative line for each wall cluster
in 2D that is then used in the reconstruction step. Ochmann et
al. (Ochmann et al., 2016) on the other hand use heuristics to
cluster parallel and coplanar wall segments. Each potential pair
of wall surface lines fulfilling certain constraints is considered as
the two opposite surfaces of a wall separating adjacent rooms.
The segments are then clustered by evaluating the overlap and
the orientation of the candidates. Aside from heuristics, model
based methods are also used. Recent variants of the RANSAC
algorithm (Derpanis, 2010) are extended to not just fit simplis-
tic models such as lines or planes but match entire walls. For
instance, Oesau et al. (Oesau et al., 2014) employ a two-line hy-
pothesis created by RANSAC to detect corner configurations for
their walls. Similar to the single faced clustering, the majority
does not consider the grouping of more complex wall geometry
or highly associative walls.
Connected components Currently there is few research on the
clustering of wall segments for more complex walls. However,
several methods used in similar clustering tasks are also of inter-
est. For instance, Ikehata et al. (Ikehata et al., 2015) cluster rooms
based on k-medoids and heuristic segment clustering. They re-
structure their room observations in a raster image and use se-
lective seeds to determine which room an observation belongs
too. Armeni et al. (Armeni et al., 2016) introduce the idea of
connected component graphs. They divide the initial graph into
a set of subgraphs or connected component graphs by removing
invalid edges based on some validation criterion. This lowers
the combination complexity and also avoids misclustering. Ar-
meni et al. use this method in combination with region growing
to cluster room segments. In case a connection to a neighboring
room segment contains a wall density signature, that neighbor is
not considered. Other implementations focus on the clustering of
roof objects. He. et al. (He et al., 2018) use connected component
graphs to detect all the roof observations belonging to a single
building. The concept of component graphs is a promising tech-
nique for complex wall clustering. In our implementation, we use
a similar structure so solve the wall clustering. Machine learning
or heuristic methods can be used to remove invalid edges from
the graph after which the remaining linked observations can be
clustered. For instance, Gilani et al. (Gilani et al., 2016) use con-
nected component graphs to cluster line segments of roof edges
in aerial lidar applications. Alternatively, Mura et al. (Mura et al.,
2016) propose the use of structural paths for room segment clus-
tering. They perform region growing in a adjacency matrix based
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(a) Representation of the fully connected graph based on the eu-
clidean distance between nearest neighbors.
(b) Representation of the potential edges matching one of the
three distance criteria.
(c) Representation of the remaining edges after passing the edge
validation criterium based on the intersections with the partial
room information.
(d) Representation of the remaining edges after passing the
bounding box validation criterium based on the dimensions of
the bounding box of siand sj.
(e) Representation of the connected component graphs based on
the remaining edges.
(f) Representation of the clustered wall segments passing the val-
idation test or subsequent clustering.
Figure 2: Workflow of the graph based wall segments clustering depicting the consecutive steps. The wall segments are shown in green,
floor segments in red and graph edges in bordeaux.
The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLII-2/W9, 2019
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103

on pairwise relations. Given the connectivity of the graph, they
iteratively evaluate the edges for one of kpredefined connections.
The result of their method is a set of patches enclosing the target
space. In our research, we opt for the use of machine learning
techniques in connected component graphs since the simultane-
ous evaluation of all observations is expected to yield better re-
sults than the one-sided stopping criteria of for instance region
growing.
A promising approach for simultaneous segmentation and clus-
tering which we adopt is the use of Conditional Random Fields
(CRFs) (Sutton and Mccallum, 2011). Given the graph with a set
of node and edge features, a best fit configuration can be com-
puted by decoding the network. This can be achieved by using
graph cuts (Strom et al., 2010, Turner and Zakhor, 2014, Pordel
and Hellstr¨
om, 2015), loopy belief propagation (Landrieu et al.,
2017b, Landrieu et al., 2017a, Vosselman and Rottensteiner, 2017)
or other approximation techniques. The key to this technique is
the proper seeding to determine the number of walls which can
prove difficult with wall segments. While the parameter estima-
tion of these models can be challenging, we believe it a promising
approach to cluster complex scenarios and highly associative wall
configurations with high recall and precision.
3. METHODOLOGY
In this paper, a clustering algorithm is proposed that groups the
planar wall segments into wall clusters. The procedure consists
of the following steps. First, the point cloud data is segmented
and semantically labeled using prior algorithms (Bassier et al.,
2018). Next, a initial segmentation is performed to create a set of
connected component graphs and to establish a set of seeds. In a
final stage, the observations within each component are clustered
according to the individual walls given the seed segments. The
consecutive steps are discussed in detail in the following para-
graphs.
Data preprocessing Prior to the clustering, the data is seg-
mented and classified. First, the unstructured point cloud is repre-
sented as a voxel octree after which planar patches are extracted
from the data as presented in our previous research (Bassier et
al., 2017). Next, the planar patches are subjected to a reason-
ing framework that computes class labels for each patch. A pre-
trained Random Forests model is used for the classification (Bassier
et al., 2018). The result is a set of labeled segments that replaces
the point cloud representation of the building.
The connected component graph is constructed as follows. First,
a densely connected graph G(N, E )is defined with a set of nodes
Nrepresenting the wall segments sand a set of edges Erepre-
senting the connections between neighboring segments (Fig. 2 a).
The adjacency matrix is constructed based on the euclidean dis-
tance between the boundaries of the segments. Each nis con-
nected to its knearest neighbors. Each edge eij is conditioned to
comply with at least one of the following criteria (Eq. 1): The ab-
solute distance between boundaries, the distance between copla-
nar segments and the distance between parallel segments given
the overlap between siand sj0with sj0the projected geometry
of sjonto sialong ~ni(Fig. 2 b).
eij ∈G:









ksi, sjk≤ td
~ni·~nj≥tθ&~ni·(~csi−~csj)≤tcopl &
ksi, sjk≤ td,copl
~ni·~nj≥tθ&ksi, sj0k≤ tpar
(1)
Figure 3: Illustration of the clustering using Conditional Ran-
dom Fields within a connected component graph: given the seeds
t1→ufrom the region growing, one of ulabels is computed for
each sgiven the factor graph with the edge and node potentials.
The three clusters are depicted in red, cyan and purple, the edges
are shown in red and the edges between clusters are shown in
yellow.
Subsequently, the valid edges are subjected to the following two
validation criteria. An edge eij may not intersect with a set of
reference surfaces. This set is composed of both wall segments
as well as basic room information. For this evaluation, the ceil-
ing geometry is extruded to the height of the underlying floors to
form enclosed spaces (Fig. 2 c). The boundaries of these volumes
along with the wall segments are tested for collisions with the
edges and intersecting edges are removed. The second criterion
is a model based evaluation that tests the potential wall thickness
(Fig. 2 d). A bounding box is constructed between every con-
nected siand sjand the thickness is tested along the normal of
the largest wall segment. If the thickness exceeds a threshold tb,
the edge is considered invalid. By removing the invalid links from
the network, a set of connected component graphs G0is created
that each contains a number of connected segments (Fig. 2 e).
Clustering In this work, the clustering paradigm is considered
a classification task that can be solved with supervised pattern
recognition techniques. More specifically, we propose the use
of Conditional Random Fields (CRF) as discussed in the related
work. A major advantage of this technique is that every seed is
evaluated simultaneously so that the clustering is not dependent
on heuristic stopping criteria as is the case with region growing
methods. This is expected to result in a more balanced clustering
where each sis assigned to the best fit cinstead of the cluster
with the largest seed. The objective is to find the most optimal
labeling of the set of nodes represented by sthat can take one of
c∈u={c1, c2, . . . , cu}states. This is performed by comput-
ing the a posteriori probability distribution of the states over the
nodes in the graph. In order to do so, the graph is restructured
as a factor graph (Fig. 3). Depending on the number of output
clusters in the component graph, a set of unary and pairwise po-
tentials is established for each node and edge. The set Eof edges
eij in the network is given non-negative weights along with a set
of feature vectors. Additionally, we replace the nodes that func-
tion as the seeds by terminal nodes similar to the graph structure
used in graph cuts. These nodes ttake one of ufixed states since
they serve as seeds. The labeling is performed by maximizing the
probability over the network. Each of the above steps, including
the seeding for the number of outputs, the edge potential initial-
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104

(a) Representation of the ground truth data with each wall in a
seperate color.
(b) Representation of the clustered wall segments using Condi-
tional Random Fields (CRF).
Figure 4: Test data set of a school facility on the Campus.
ization and the labeling are discussed in the paragraphs below.
Seeding It is stated that while the clustering of region growing
itself is likely to be erroneous, at least a part of each wall is rep-
resented in a region. Therefore, we use the largest segment slin
each region as the seeds for the graph. The region growing algo-
rithm operates as follows. Iteratively, the neighbors siof slare
evaluated. Starting from the largest neighbor, a bounding box cri-
terion similar to the initial graph definition is evaluated. However,
instead of computing the bounding box of only sland si, all the
sin the current care evaluated along the average ~ncweighted by
the percentual surface areas of s∈cu. Given this bounding box,
siis merged with the cluster if the total bounding box thickness
does not exceed tb. This hard constraint allows for flexible grow-
ing but restricts the cluster from becoming too large. If no more
members can be added to the cluster, the largest unclustered seg-
ment is selected as new seed and the process is repeated for the
remaining surfaces. Additionally, the clusters are conditioned to
have more than one surface or that the surface area is sufficiently
large. This avoids singular surfaces that do not fit well with other
segments to result in erroneous walls. The result is a set of clus-
ters c∈C, with each crepresenting the available observations of
a single wall. The nodes corresponding to the seeding segments
are given a fixed state and will serve as the basis for the feature
extraction in the CRF.
Potentials The potentials are initialized for each edge eij and
node sin the graph. We define both pairwise and unary poten-
tials to determine which cluster a node belongs to. The pairwise
potentials are computed given a set of edge features fe(si, sj)
and corresponding weights ωe. Associative values are computed
for the euclidean distance between the boundaries of siand sj
and the potential bounding box thickness according to the largest
segment of the two neighbors. We use exponential functions to
model the information to ensure non negative associative fea-
tures.
The unary potentials are initialized based on the affinity of a node
to a certain cluster curepresented by each of the seed nodes tu.
A set of features ft(1→u)(si, tu)and corresponding weights ωt
are defined. In this work, two feature are defined for each seed.
The features include the thickness of the bounding box of siand
tuand the absolute distance between the boundaries of si.
Probability Estimation The a posteriori probability distribu-
tion of the Conditional Random Field is found by factorizing the
graph. We define the conditional probability of the states in the
network as follows (Eq. 2).
P(c|ft, fe,ω) = 1
Z(ft, fe)exp( X
s∈S,t1→u
ωtψt(ftu, ci)
+X
i,j∈E
ωeψe(fei,j , ci, cj)) (2)
where Z(ft, fe)is the normalizing partitioning function, ψt(ftu, ci)
describes the unary potentials of the nodes with relation to the
seed nodes and ψe(fei,j , ci, cj)describes the pairwise potentials
between neighboring nodes. The graph is decoded by maximiz-
ing the conditional probability. However, exact decoding is un-
feasible in a densely connected CRF. Therefore, we approximate
the decoding using a generalized iterated conditional mode algo-
rithm as implemented by Schmidt (Schmidt, 2010). After com-
puting the most likely configuration of the graph, the segments
are clustered according to the labels. The result is a set of clus-
tered wall segments.
4. EXPERIMENTS
The algorithm is tested on a school facility on the technology
campus in Ghent, Belgium. It is a four-storey structure with a
variety of rooms including a laboratory, two classrooms, a stair-
case and a maintenance room (Fig. 4). A large amount of clutter
is present in the environment. Nearly 7000 surfaces were de-
tected, 258 of which represent wall observations. A total of 14
multi-storey walls were defined for the testing (Fig. 4). k= 20
The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLII-2/W9, 2019
8th Intl. Workshop 3D-ARCH “3D Virtual Reconstruction and Visualization of Complex Architectures”, 6–8 February 2019, Bergamo, Italy
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105

(a) Ground truth of two highly associative walls c1(red cluster) and c2(blue cluster).
(b) Region Growing clustering. (c) Conditional Random Fields clustering.
Figure 5: Comparison between the results of the proposed CRF clustering algorithm and a conventional region growing algorithm. The
seed nodes are represented in yellow and the walls are colored according to their respective clusters.
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106

connections were evaluated for each s. The following parame-
ters were used for the region growing. The bounding box thick-
ness tbwas set to 0.8m, the absolute distance between bound-
aries td≤0.5m, the coplanar distance tcopl ≤1m, the coplanar
boundary distance td−copl ≤2mand the distance tpar between
overlapping parallel sis equal to tb. In total, 7 connected com-
ponents were detected in 6.7sof which 6 components consisted
of a single surface. In the validation step, 6 of the 7 components
complied with the thickness criterion tband thus were isolated.
The 216 segments within the remaining connected component
graph were processed by the proposed Conditional Random Fields
method. For the state estimation, the seeds are used that were ex-
tracted from the region growing. 7 valid seeds were detected.
As unary potentials, the bounding box thickness and edge length
were computed between the observations and each seed segment.
The pairwise potentials are initialized based on the same features
but between neighboring segments. The weights of the features
was set equally over all states as there shouldn’t be bias over
which cluster an observation belongs to. The decoding was per-
formed using a generalized iterated conditional mode algorithm
as implemented by Schmidt (Schmidt, 2010). 74.5% of the seg-
ments were properly clustered in less than 1s. Together with
the initial valid connected components, 78% of the wall geom-
etry was assigned to the proper cluster. This is promising given
the complexity of the structure and the variety of the geometry.
However, some errors still remain. Especially smaller segments
are error prone due to their high associativity with multiple seeds.
5. COMPARISON
For the validation, the results of the CRF method are compared to
the results of a conventional region growing algorithm that was
used to establish the seeds. Both methods operate with the same
parameters and features. As discussed above, the main differ-
ence between these methods is the simultaneous assignment of
the segments with the CRF in contrast to the one-sided stopping
criteria of the region growing. As an example, the results of two
highly associative walls are discussed (Fig. 5). These walls are
near coplanar with several segments of c1surrounding c2, have
different thicknesses at different heights and have protrusions,
niches and recesses. This is considered a worst case scenario
where even experienced modelers would struggle to assign the
segments to the proper clusters.
As discussed above, the region growing method prioritizes seg-
ments with a large surface area. Therefore, the algorithm iterates
through the segments and evaluates the observations with respect
to t2. As expected, the majority of the segments comply with the
validation criteria based on c2. The remainder of the segments is
assigned to c1leading to a severely unbalanced clustering. In the
CRF method, the features between neighbors and with respect to
t1and t2are evaluated simultaneously leading to a more proper
clustering. It is observed that while the results of the CRF are
far from perfect, it provides a significantly better clustering than
the conventional region growing. It is argued that with the im-
plementation of additional features, this clustering can be further
enhanced to provide a proper clustering of at least the significant
portion of each wall.
6. CONCLUSION
This paper presents an unsupervised method to cluster wall ge-
ometry from unstructured point clouds of buildings. A 3D ap-
proach is proposed that deals with complex multi-storey data sets.
First, the data is preprocessed by a segmentation and classifi-
cation framework to drastically reduce the data and to increase
the level of information. The resulting labeled segments are pro-
cessed by the clustering algorithm to group the wall observations
per wall object. First, an initial segmentation is performed to cre-
ate a set of connected component graphs and to establish a set
of seeds. In a second stage, the observations within each com-
ponent are clustered according to the individual walls given the
seed segments. A method based on Conditional Random Fields
is proposed to perform the clustering. Both unary and pairwise
features are considered encoding the associativity between neigh-
boring segments and a set of seed nodes that are extracted from
region growing. Once the state of each observation is determined,
the segments are assigned to their respective clusters. The result
is a set of clustered segments that correspond to the wall objects
in a building.
The experiments indicates that the used method is a promising
clustering framework for unstructured point cloud data. Over
78% recall is reported for the clustering of the wall segments.
When comparing the proposed method to a conventional region
growing method, it is revealed that the proposed method leads
to a more appropriate grouping of the segments. However, some
errors are still present in complex scenarios where there is con-
fusion about which cluster a segment belongs too. Especially
in highly associative scenes such as with near coplanar walls, the
clustering underperforms. In future work, additional features will
be implemented to enhance the clustering of these scenes.
7. ACKNOWLEDGEMENTS
This project has received funding from the European Research
Council (ERC) under the European Union’s Horizon 2020 re-
search and innovation programme (grant agreement 779962) and
the Geomatics research group of the Department of Civil Engi-
neering, TC Construction at the KU Leuven in Belgium.
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