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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

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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102

(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

8th Intl. Workshop 3D-ARCH “3D Virtual Reconstruction and Visualization of Complex Architectures”, 6–8 February 2019, Bergamo, Italy

This contribution has been peer-reviewed.

https://doi.org/10.5194/isprs-archives-XLII-2-W9-101-2019 | © Authors 2019. CC BY 4.0 License.

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

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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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This contribution has been peer-reviewed.

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