CITE Xue, F., Zhang, W., Xu, G., Zhou, Q., & Wu, Y. (2023). Surface or skeleton? Automatic hierarchical

clustering of 3D point clouds of bronze frog drums for heritage digital twins. ISPRS Annals of the
Photogrammetry, Remote Sensing and Spatial Information Sciences, X-M-1-2023, 293-299.
https://doi.org/10.5194/isprs-annals-X-M-1-2023-293-2023

Surface or skeleton? Automatic hierarchical clustering of 3D
point clouds of bronze frog drums for heritage digital twins
Fan Xue1*, Wenjin Zhang2, Guangji Xu3,
Qianyun Zhou1, Yijie Wu 1
* xuef@hku.hk

1 The University of Hong Kong

2 Guangzhou Okay Information Technology Ltd.
3 Anthropology Museum of Guangxi

MATERIALS
Bronze drums (Lu et al., 2020)
● Spiritual, sacrifice, and musical instruments
● Across South China and Southeast Asia since 700s BCE
● Traditional storage: buried in soil (now >2,400 conserved)
Decorative bronze frogs
● A variety (design, size, materials) evolved over time
● “bronze drums often unearthed in Guangxi by the tillers …
with a perfect circle with bent body … five sitting frogs,
each with a baby on its back.” (Zhou 1187)
● “surrounding frogs indicate [the chief’s] title; the more
frogs, the more honorable title.” (Zhu 1948)

A1
Discovery of a 2,000-yr drum in Guangxi, on 25 May 2023
(Photo src: news.cn)

B1

C1

AIM AND METHODS
Objectives
●
●

To understand the 3D details of bronze frogs using
clustering for heritage digital twin
To compare 3D surface and skeleton (abstract,
topology-aware, light-sized) as source of clustering

Methods in 4 steps
●
●
●
●

Data curation (skeletonization using CGAL)
Geometric dissimilarity matrix (Xue et al. 2020)
Unsupervised hierarchical clustering (auto threshold)
Comparison of results from the two sources

RESULTS
Dissimilarity matrices
●
●

Similar patterns
maxske/maxsur ≈ 2

Clustering (Obj. #1)
●
●
●
●

Four groups in both
Reflecting the style
In line with the
instruments and
shape groups
Outlier (damanged)
highlighted
automatically

Dissimilarities
(a) Surface; (b) skeleton

Hierarchical clustering (threshold = (min+max)/2)

RESULTS
Comparative results (Obj. #2)
●
●

●

Same for 12 out of 14 ✔
Assuming 3D surface grouping was
true, the metrics of skeleton were:
Precision = 0.850, Recall = 0.883,
F1 = 0.866
2 inconsistencies due to: limited
presentation of traditional
(inscribed ball) skeleton in CGAL
Group using shape skeleton
I
II
III IV V
Group
using
surface
point
clouds

I. Three-legged
with baby
II. Four-legged
with baby
III. Three-legged
IV. Four-legged
V. Unusual

3
2

1
3
3

1
1

CONCLUSION
Bronze frogs on drums
●
●
●
●

Widely spread in Ancient South China and Southeast Asia
Qualitatively grouped and compared (similar to building Covid virus family tree)
Both 3D surface and shape skeleton worked well
An automatic way of grouping new 3D scans (not limited to frogs) from site

Future work
● Scale-up tests
● Examining the new values of skeletons (abstraction, topology, file size)
● Revised shape skeleton definitions for heritage data (e.g., tolerance to worn corners)
● Heritage Digital Twins with unsupervised learning

REFERENCES
Lu, Q., Li, Y., Zou, G., Gong, S., 2020: Separation or integration? Further insights from a study on chemical
datasets of ancient bronze drums from South and Southeast Guangxi, China. Journal of Cultural Heritage,
44, 15-26. doi.org/10.1186/s40494-022-00808-0
Musicco, A., Galantucci, R.A., Bruno, S., Verdoscia, C., Fatiguso, F, 2021: Automatic point cloud
segmentation for the detection of alterations on historical buildings through An unsupervised and
clustering-based machine learning approach. ISPRS Annals of the Photogrammetry, Remote Sensing and
Spatial Information Sciences, V-2-2021 (CIPA 2021), 129-136. doi.org/10.5194/isprs-annals-V-2-2021-1292021
Xue, F., Lu, W., Chen, Z., Webster, C.J., 2020: From LiDAR point cloud towards digital twin city: Clustering
city objects based on Gestalt principles. ISPRS Journal of Photogrammetry and Remote Sensing, 167, 41831. doi.org/10.1016/j.isprsjprs.2020.07.020
Zhou, Q., 1178: Bronze drums (in ancient Chinese). Lingwai Daida, 7. Reprinted in 2018 by China Bookstore
Publishing, ISBN 9787514920468.
Zhu, C., 1948: Study of bronze drums. Chronicle of Binyang County. Reprinted in 1961 by Guangxi Archives.

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