Decoding the Past: A Genetic Algorithm-based Method for Extracting Decorative
Patterns in Heritage Digital Twins
Siyuan Meng 1, Guangji Xu 2, Wenjin Zhang 3, Fan Xue 4*
This is the authors’ version of the paper:
Meng, S., Xu, G., Zhang, W., & Xue, F. (2024). Decoding the past: A
Genetic Algorithm-based method for extracting decorative patterns in
Heritage Digital Twins. Proceedings of the 28th International Symposium on
Advancement of Construction Management and Real Estate, 2021–2032,
Springer. doi: 10.1007/978-981-97-1949-5_141
This file is shared for personal and academic use only, under the license CC
BY-NC-ND 4.0 (Non-Commercial, No Derivatives, and with an Attributed
citation when you use). The final published version of this paper can be found
at: https://doi.org/10.1007/978-981-97-1949-5_141. Any uses other than personal
and academic purposes must obtain appropriate permissions from Springer first.

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Abstract: In the smart construction era, Heritage Digital Twin (HDT) is increasingly
created as the digital replica of physical heritage buildings and relics. Extraction of the
unique patterns and decorative elements on the HDTs is not only of academic interest
to heritage conservation but also of business interest to fashion and design, such as the
recent Hanfu fever. However, the patterns’ complex curvature surfaces and subtle
protrusions make it challenging to extract and analyze them accurately and efficiently.
This paper presents a Genetic Algorithm-based semi-automatic method for extracting
decorative pattern texture from HDTs. This method has three steps: (i) extraction of
cross-section contour as Non-uniform rational B-spline (NURBS) curves; (ii) Fitting of
arcs and curvature projection based on Genetic Algorithm (GA); and (iii) clustering and
extraction of patterns of interest. We tested the method on 3D data of a heritage building
and a heritage bronze drum preliminarily. The high accuracy of the results, i.e., 𝐹𝐹1-value
> 90% in all tasks, validated our automated extraction method for detailed patterns and
decorations. The proposed GA-based method can enrich the literature of HDT in smart
heritage and smart construction, whereas the extracted heritage’s patterns and
decorations have the potential for cultural and business applications.
Keywords: Heritage Digital Twin; Heritage decorative patterns; 3D point cloud;
Genetic Algorithm; Smart Construction.

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Siyuan Meng
Department of Real Estate and Construction, The University of Hong Kong, Hong Kong SAR, China
2 Guangji Xu
Anthropology Museum of Guangxi, Nanning, China
3 Wenjin Zhang
Guangzhou Okay Information Technology Ltd., Guangzhou, China
4* Fan Xue
Corresponding author, Department of Real Estate and Construction, The University of Hong Kong, Hong Kong
SAR, China
E-mail: xuef@hku.hk
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1 Introduction
1.1 Background

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Smart construction implies the incorporation of automation and information
technologies in the construction sector to tackle engineering challenges, such as cost,
quality, safety, and sustainability[1, 2]. Benefiting from the rapid development of
information technology, Digital Twin (DT), a network physical integration, has played
a greater role in smart construction[3] since it enables interoperability, automation, and
intelligent systems for whole-life-cycle buildings management. From the perspective
of real-time geometric information (one of the DT objectives), 3D point clouds serve
as a suitable data source because they can accurately depict the shape and texture of
detected object surfaces. With expert handling, these point clouds can be transformed
into digital documents such as Building Information Models (BIMs) and DT models[4].
The Heritage Digital Twin (HDT) is a digital representation of the intricate
knowledge structure pertaining to heritage assets[5], in which both generating a highfidelity virtual model of physical objects and efficiently processing the gathered data
and diagnosing the digital twin to facilitate decision-making are challenging[6]. One of
the objectives of HDT is to create 3D models with semantically rich coverage[7].
More specifically, in heritage conservation, the preservation of texture, material,
and decorative elements is essential for experts to evaluate the detailed status[8]. Besides,
the decorative pattern found in cultural heritage possesses significant commercial value
due to its extensive applicability in design and fashion industries, such as Hanfu. The
feature of decorative pattern texture is slightly raised at the edges of the pattern. Current
literature mainly focuses on presenting image level of texture information. For instance,
[9]
utilize a photogrammetry method to acquire masonry patterns as the texture for BIM
objects, and [10] create a detailed restoration map for HBIM through photogrammetry.
Furthermore, detail texture should not only be limited to image presentation but also
provide the appearance with further information[11], such as performance assessment,
texture detection, extraction, and classification. Hence, from the perspective of
integrating texture semantic information, there is a need to extract pattern texture
characterized by slight protrusions from point cloud data.
1.2 Texture-related extraction method

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Ornamental pattern texture exhibits subtle elevations along the boundaries; thus, the
extraction of pattern texture is often modeled as discontinuous characteristics extraction
from input 3D point cloud. Such discontinuous characteristics extraction methods have
been developed for two decades, e.g., in the field of rock surface[12]. Features that are
often used for classification are angles, normal vectors, curvatures, planar parameters
(e.g., Random sample consensus, RANSAC), and density (e.g., density-based spatial
clustering of applications with noise, DBSCAN). Current rocks discontinuities analysis
contains two major groups of methods, i.e., K-means and region growing, while there
existed other algorithms as well.
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obtained the mesh vertices features from the point cloud and used K-means
to cluster gentle and discontinuous regions semi-automatically. This approach exhibits
high computational requirements, and its efficacy depends on the acquired mesh quality
(e.g., a point cloud with high morphological complexity will result in incorrect and
distorted polygonal surfaces) and easy-to- neglect small features[12]. The region
growing methods choose seed points randomly and expand the region by including
neighboring points that satisfy predetermined criteria[15]. It has significant advantages
in reducing computation time compared to the K-means method but still requires 90%
of time to calculate millions of vertices features. Besides, supervised deep learning
method such as Artificial Neural Networks (ANN) is considered in extracting rock
discontinuities[16], which is less effective for heritage due to the uniqueness of each
pattern’s features (such as color, shape complexity, and curvature) across different cases.
It should be noted that rock discontinuity identification and texture extraction are
different in at least two aspects. Firstly, the subtle features along the pattern edges can
be easily overlooked when dealing with complex global features. Secondly, in contrast
with patterns, rocks are typically characterized by planar surfaces and sharp edges,
resulting in relatively straightforward feature extraction. Whereas patterns in heritage
are sometimes attached to curved surfaces, making it difficult to extract features
accurately using methods such as RANSAC and resulting in the wrong discontinuity
analysis output. To conclude, current discontinuity extraction methods are insufficient
for achieving the semantic interpretation of the given pattern texture in heritage point
cloud data. Therefore, inspired by[17], we introduce the Genetic Algorithm (GA) to
address the above issues through global arc fitting.
1.3 Research objectives

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This paper aims to present an automated method to extract heritage texture and
decorative elements from HDTs, such as 3D high-resolution point clouds or mesh
models. Three objectives are arranged:
1. To detect cross-sectional contour nonuniform rational B-splines (NURBS)
curves;
2. To apply GA to arc-fitting of NURBS curves; and
3. To extract features using the adapted K-means clustering method and
DBSCAN method.
As a result, the input point cloud is segmented into two parts: the continuous and
smooth base regions (including planes and curved surfaces) and the raised regions that
are extracted and clustered into object instances.
The main theoretical novelty in the proposed method lies in the sectional-arc
fitting formulation. The formulation transforms the traditional discontinuous pattern
analysis into a novel optimization problem solvable by modern computational
algorithms such as GA. The method proposed in this paper enables the detailed
semantic interpretation for the semantic enrichment of HDTs. Additionally, the patterns
and decorations extracted from heritage assets through this method hold promise for
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further industrial applications in culture and business.
2 Research methods

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Figure 1 shows the three steps of the proposed method and the required parameters. The
input to this method is the original point cloud. Firstly, generate sectional contour
NURBS curves. In Step 2, transform NURBS curves into arcs through fitting. And in
Step 3, partition the unfitted regions and cluster pattern objects. Finally, the output is
clustered pattern objects at different locations.

Fig. 1. General workflow of the proposed three-step method.

2.1 Cross-section contour NURBS curve extraction

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The first step aims to obtain the cross-section contour curves of the input 3D data. First,
a series of reference planes are determined in the point cloud regarding the
combinations of the bounding box of the point cloud, resolution (grid size) (e.g., 1 mm),
and slicing directions (e.g., x, y, or z). The input point cloud is then separated into a
series of point cloud cross-sections according to a threshold distance value (e.g., 1 mm)
between each point and the given plane. Next, the unstructured points are sequenced
for generating NURBS curves through the sort along curve plugin in Grasshopper (ver.
1.0.0007, Rhino). The Nurbs Curve plugin then fits NURBS curves from the sequenced
point lists. The outputs of this step are cross-sectional NURBS curves.
2.2 Arc fitting using Genetic Algorithm

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The second step targets fitting arcs to the cross-sectional NURBS curves. The arc-fitting
process is divided into two steps. Firstly, split the NURBS curve into curve segments
according to the given value n, then generate arc segments based on the endpoints and
midpoints of the curve segments. Secondly, use the Galápagos plugin in Grasshopper
to complete arc-fitting optimization. The basic principle of Galápagos is GA, which is
a method that utilizes natural selection to address both constrained and unconstrained
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optimization problems[18]. The constrained optimization objective is to minimize the
sum of the mid-point distances between the arcs and the corresponding curve segments,
as shown in Eq. 1. The output of this stage is the fitted arc lists of cross-sections.
𝑛𝑛
(1)
min Σ𝑖𝑖=0
𝐷𝐷𝑖𝑖𝑘𝑘
D is the distance between i-th curve segment and i-th arc of cross-section k. After
optimization, obtained the arc lists of cross-sections.
2.3 Clustering and classification of extracted patterns

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The objective of the third step is to separate unfitted arcs and cluster unstructured points
into pattern objects. Combined with the given filter criteria (usually the mean or median
number of D), we separate the imperfect fitting regions (i.e., the slightly raised areas)
from the cross-section groups, the remaining regions are smooth planes or curved
surfaces.
For clustering pattern objects, it is insufficient to obtain only the raised regions
point clouds, as various patterns may exist in different locations within a region, and
non-pattern sharp edges may become intertwined with the pattern point clouds, leading
to mixed extraction results among different patterns and non-pattern results. Therefore,
we utilize K-means, an unsupervised machine learning method, to semi-automatically
perform secondary classification according to the specific K value = 3, with the
clustering objective as the point surrounding points count. For the 3 clusters, we further
segment the clusters based on density using DBSCAN to calculate the number of
clusters that can be formed. The least number of DBSCAN clusters represents the noise
point group, which is less dense than pattern clusters. To better partition the noise point
groups, we maintain a consistent searching radius for K-means and eps for DBSCAN.
Next, we apply a second DBSCAN clustering to the filtered point clouds, setting
the 𝑒𝑒 𝑝𝑝𝑝𝑝 as the fourth neighboring point distanced mean value plus two standard
deviations[19], and min points as 10. The final result of the third step is well-clustered
pattern objects.
2.4 Validation and evaluation
We introduced quantitative validation to evaluate the performance of the algorithm. The
validation compared the output with manually labeled ground truth at two levels, i.e.,
the point level and the object level. We adopted three evaluation metrics, precision (the
proportion of points correctly detected by the proposed method), recall (the proportion
of points identified as edges in the ground truth), and F1-value (the harmonic mean of
the precision and recall, to reflect the algorithm’s accuracy) [20], as shown in Eqs. 2, 3,
and 4.
𝑇𝑇𝑇𝑇
(2)
𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 =
(𝑇𝑇𝑇𝑇 + 𝐹𝐹𝐹𝐹)
𝑇𝑇𝑇𝑇
(3)
𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 =
(𝑇𝑇𝑇𝑇 + 𝐹𝐹𝐹𝐹)
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(4)
𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 × 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅
𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 + 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅
The value TP denotes the number of correctly detected points, while FP represents
the number of wrongly detected points. FN indicates the false rejections, i.e., points
belonging to the ground truth but not detected by the edge extraction technique.
𝐹𝐹1 = 2 ×

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3 Case study and results
3.1 Case selection

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This paper employed two cases, as shown in Fig 2, to preliminarily validate the efficacy
of the method. The first case was the commemorative plaque texture of Guangtong
Association Hall, of which the input was a high-resolution 3D point cloud. The other
case was the No. 0158 bronze drum’s deformed feathered human pattern, which was a
high-resolution mesh model from the Anthropology Museum of Guangxi, Nanning,
China. These two cases are representative of their respective scales and exhibit different
pattern characteristics (i.e., one is discretely distributed and the other arranged
centripetally). Therefore, they are suitable for exploring the feasibility of the algorithm
in scenarios with different pattern distributions.
In Fig 2a, Guangtong Association Hall in Lechang, Guangdong, China consists of
various building sections, including a porch, foyer, main hall, wing rooms, corridors, a
theater building, and a courtyard. The hall’s doors, windows, beams, and pillars are
decorated with intricate and detailed patterns that hold significant symbolic meanings.
We selected the hall’s commemorative plaque as the experimental example since it
contains the title of Guangtong Association Hall. The point cloud includes 142,953
points, with bounding box size x: 3955mm, y: 202mm, z: 918mm.
Bronze drums are significant archaeological artifacts found in southern China and
Southeast Asia, with scattered discoveries from the Yangtze River of China to the
Indonesian islands[21]. The decorative elements of bronze drums reflected the
manufacturer’s purpose, era, affiliated ethnic groups, and artistic expression of the
drums[8], which are thought to be linked to the totemic worship traditions of various
ethnic groups, such as the Karen, Zhuang, Wa, and others, which developed over time.
We chose bronze drum No. 0158 for testing and performed point sampling (999,900
points, with bounding box size x: 619mm, y: 647mm, z: 25mm) of the face mesh. Fig
2b illustrates the selected example.
3.2 Experimental settings

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The proposed method was tested using an AMD Ryzen 9 5900HS computer with
Radeon Graphics 3.30 GHz and 32 GB RAM. The slicing direction of the experimental
object was determined based on its geometric shape. For instance, for the
commemorative plaque, the slicing direction and grid sizes were set as XY, XZ planes,
and 500 planes in each direction; while for the drum, they were set as XZ, YZ planes,
and 500 planes in each direction. We selected parallel lines on the corresponding section
planes as reference curves to sort the section point cloud. In addition, the generated
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cross-sectional NURBS curves were curves with sharp changes in curvature instead of
smooth curves. This was because the given surface of the point cloud produced slight
undulations on the smooth surface due to the unavoidable quality problem of the
collected data, which would not influence the texture extraction results since we
introduced the arc-fitting procedure.
Following the establishment of the objective and automatic value range for
Galápagos (0-100 curve segments number), 100 iterations were performed to obtain
the final convergent solution arc-curve lists for all cross-sections. For the drum, the
most appropriate segment number was 100, while for the commemorative plaque, it
was 98. The progress of GA effectively separated the imperfect fitting surfaces, i.e., the
slightly undulating point cloud regions. Thereafter, we filtered the noise points using
K-means and DBSCAN; the search radius was set as 90mm for the commemorative
plaque and 7mm for the drum.

Fig. 2. The original point cloud and mesh model of two test cases. (a) The commemorative plaque of
Guangtong Association Hall; (b) No. 0158 bronze drum’s deformed feathered human pattern.

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Fig. 3. The pattern extraction results of two experiment objects. (a) The commemorative plaque texture of
Guangtong Association Hall; (b) No. 0158 bronze drum’s face texture.
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3.3 Results of extracted patterns
Fig 3 shows the pattern extraction results from the two cases. The upper sub-charts
display the cross-sectional NURBS curves, with one example curve highlighted in each
sub-chart. The bottom sub-charts demonstrate the clustered pattern objects of two
example cases. One can distinguish the object-level clusters with colors in the bottom
charts from the points and curves at lower levels during the processing.
Fig 3a presents the commemorative plaque texture of Guangtong Association Hall;
the word pattern clustering was well obtained. Whereas drum circular patterns in Fig
3b were fragmented, except for the sunburst at the center. The clustering result of the
drum was slightly inferior compared to the commemorative plaque. This is related to
the production age, excavation from underground, and lack of maintenance, resulting
in excessive noise (e.g., drum face broken and rusted) and the circular and centripetal
distribution of the drum pattern.
Overall, the extraction of point-level patterns was satisfactory, and the clustering
results of object- level patterns were good in the case of discrete patterns. However,
noise and variations in pattern distribution probably impacted the accuracy of pattern
cluster results.
3.4 Evaluation using error metrics
Table 3.4. The validation results at Point-level and Object-level
Point-level accuracy

Object-level accuracy

Precision

Recall

F1

Precision

Recall

F1

Guangtong

93.05%

97.91%

95.42%

91.70%

98.90%

95.16%

0158 Drum

83.00%

99.79%

90.62%

82.26%

100.00%

90.27%

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Table 3.4 lists the evaluation results of two cases in Fig 3. The mean precision at the
point level for the experimental participants was 87.88%, while the recall was 98.85%,
and F1 was 92.99%. The instance level precision was 86.85%, with a recall = 99.45%,
F1 = 92.68%. According to the values of unbiased metric F1, the proposed GA-based
method was highly effective. In addition, the method was shown feasible and stable in
extracting taller objects like words as well as insignificant patterns on the drum. Yet,
the precision values of extracting insignificant patterns were considerably lower (for
about 10%), according to Table 3.4.
4 Discussion and Conclusion

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Heritage Digital Twins (HDT) as a method of documenting and preserving heritage
under new technological developments, complements the digital information of smart
construction. The detection of decorative patterns is a necessary complement to HDT,
as these patterns serve as a link to confirm the conservation status of heritage objects
and possess significant academic, artistic, and commercial value. Pattern texture
extraction from point clouds can be regarded as discontinuity detection of point clouds.
However, current point cloud discontinuity methods tend to ignore small undulating
edges when encountering complex point cloud shapes and have difficulty extracting
textures on curved building shapes. Therefore, the proposed method in this paper aims
to extract cross-sectional contour lines of the point cloud at the given directions, uses
GA to fit the NURBS curve into arcs, separates imperfectly fitted regions, and
reclassifies them to find slightly undulating pattern edges in the point cloud. Two
examples are given in this paper to quantitatively evaluate the feasibility of our method
for finding pattern texture edges in point clouds based on accuracy and recall. Our
contributions can be summarized in three aspects: (1) the proposed Genetic Algorithmbased contour edge extraction; (2) edge extraction applicable to small edges and corners,
and (3) avoiding geometric feature calculation for point clouds. The results can provide
object-level patterns semantic interpretation for fields such as HDT, BIM, HBIM,
heritage protection, and Scan-to-BIM.
There are limitations in the method presented in this paper. First, the current
method can only be applied to the raised patterns on a single plane. The reference curve
obtained from the bounding box of the point cloud cannot be utilized for determining
the point order of cross-sections in cases of complex geometric shapes (i.e., exhibit
varied orientations and edges), resulting in confusing NURBS curves and inaccurate
fitting results. A possible solution is using the Alpha shape, often used to generalize
bounding polygons containing sets of points according to a given alpha value. Thus, it
can adjust the point order of complex geometric point cloud cross-sections. Besides,
the current method mainly considers the geometric features of the point cloud; for point
clouds with color (R, G, and B) attributes, the color difference can also be exploited to
improve the accuracy of pattern extraction. Finally, the computational tests exhibited a
slow computational performance due to the single-threaded computing and inefficient
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data structure in Grasshopper (Galápagos) for handling 3D point cloud data. The GA
itself consumes an ignorable portion of the computer resources. Therefore, Grasshopper
is unsuitable for processing large-scale points, though it is sufficient for proof-ofconcept of extracting patterns within a given local range in this paper.
For future research directions, we suggest improving the extraction method of the
contour curve first. It is also interesting to incorporate other features, such as colors and
normals, into GA’s multiple objectives to formulate a multi-objective optimization,
which might improve the performance of the algorithm. To enhance the computational
efficiency of the proposed method, a program incorporating advanced point clouds data
structures (e.g., k-d tree, voxel, and supervoxel), along with CPU concurrency and GPU
computation, will be implemented in Python and C++ to replace the existing
Grasshopper-based program.

Acknowledgement

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The work presented in this paper was supported by Hong Kong Research Grants
Council (No. 27200520) and Hong Kong Innovation and Technology Commission (No.
ITP/004/23LP).

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