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SURFACE MODEL GENERATION BY THE RELICS FROM SLICE IMAGES, AND THE 
TRIAL TO THE AUTOMATIC RESTORATION 
Y. Watanabe 3 ’*, K. Tanaka 3 , N. Abe 3 , H. Taki b , Y. Kinoshita c 
a The Faculty of Computer Science and System Engineering, Kyushu Institute of Technology, 680-4, Iizuka, Fukuoka, 820-8502, 
Japan - watanabe@sein.mse.kyutech.ac.jp, (kazuaki, abe)@mse.kyutech.ac.jp 
b The Faculty of Systems Engineering, Wakayama University, 930, Sakaedani, Wakayama, 640-8510, Japan 
c Munakata Suikokai General Hospital, 341-1, Fukuma, Munakata, Fukuoka, 811-3298, Japan 
Commission VI, WG VIM 
KEY WORDS: X-ray CT, Relic, Intermediate point, Grid unit, Face tension algorithm, Normal vector, Cross section & point, 
Automatic restoration 
ABSTRACT: 
The relics that unearthed from the monument break well. The restoration work is necessary to the research, the analysis and the 
exhibition. The restoration task uses relics directly, and it takes very terrible time at the expert. Moreover, we have the possibility to 
inflict damage on the relics because we glue together and restore fragments. Therefore, we generate 3-D shape models in the 
computer and the restoration task is done. The measurement doesn't use the laser measurement that excels in getting the small shape 
of the surface, and uses the X-ray CT that measures the thickness of the fragments. We state the method that generates surface 
models automatically using the X-ray CT, and the restoration task is done in the computer. 
The restoration task in the computer never inflicts damage on the relics. However, because the restoration task is manual 
operation, the restoration time doesn't change. That we use as the restoration simulator that returns the value of the fragment is very 
inefficient. Then, the automatic restoration is desired. Because X-ray CT maintains the cross section shape information of the 
fragment that is difficult in the laser measurement, we aim at the automatic restoration using the information. We find out normal 
vectors in the cross section and show an automatic restoration result. 
1. INTRODUCTION 
A relic excavated from remains appears as a collection of 
smaller fragments. For the research of the culture or technique 
of the age when the relic was produced or the exhibition of the 
original shape, re-constructing task is necessary to have these 
fragments joined together. Such a restoration task is taken place 
using excavated fragments directly up to now. But this 
restoration task is very complicated generally, and there are 
many cases that the restoration succeeds as a result of thinking 
error. Further there is the problem that fragments can't be 
returned to the original states after the restoration because they 
are adhered together with glue. Consequently, a re-constructed 
relic will fairly receive breakdowns compared with the original 
one. Further we can't examine an individual fragment in 
excavation after the restoration task. On the other hand, the 
development of 3-D measurement technique makes it possible 
to measure correct 3-D shapes of fragments. Further, the 
development of computers makes it possible to display data of 
high capacity. So we can measure the shape of each fragment in 
excavation, and practice restoration without using genuine 
fragments because a computer successfully reproduce fragments 
using computer graphics. 
So far a laser measurement device has been principally used for 
measuring each fragment, but it is difficult to get the backside 
and thickness of a fragment although the device can get the 
close shape and color information of each face. So an X-ray CT 
is began to use for measuring the internal shape of an object by 
acquiring a slice image (profile image) as shown in the Figure 
1. Further because it has the transitivity, research on a relic or 
remains will have the broad possibility. Besides, for the 
restoration of a sophisticated model with a computer, a 
measurement with an X-ray CT is indispensable. Though a 
measurement with an X-ray CT can get a close internal shape, it 
becomes a problem that a connection between slice images 
becomes discontinuous. The image measured with the CT is 
modeled with voxels, but the data volume becomes so big that a 
strong machine power is necessary. So the surface model 
making the data volume comparatively small becomes 
necessary. 
Laser CT 
Figure 1. Difference in measurement methods 
A surface model consists of a set of surfaces or boundary 
surfaces. Any surfaces of a 3-D object completely separate the 
outside from the inside of it, and must intersect with neither it 
nor any other surfaces. Besides, it is a very complicated 
problem to decide the surface including an arbitrary 3-D object 
* Corresponding author. This is useful to know for communication with the appropriate person in cases with more than one author.