from voxel data of the object with a computer instead of the 
data of surfaces. 
Because various interpretation in determining a surface is 
possible, many different surface construction algorithms are 
proposed, but needs to intervene with a man' hand for 
complicated shapes. So the aim of this research is to generate 
automatically a complete surface model from slice images of 
very complicated shape measured with an X-ray CT. 
So far all the restoration task is done by the manual operation at 
present. As long as we manipulate the relic fragment in virtual 
space, efficiency in this restoration task is not improved. Then, 
the automatic restoration is desired. 
The precise shape information of a cross section of each 
fragment, which cannot be acquired with the laser 
measurement, can be easily got with our method using CT. 
Therefore, we aim at the automatic restoration using the 
information. 
2. RELIC MEASUREMENT BY USING X-RAY CT 
The laser measurement can measure only the shape of the 
irradiation range, the measurement doesn’t suit to reproduce a 
cross section and the back of relics. In this research, we used X- 
ray CT to measure a complicated shape. X-ray CT is the 
measurement device that measures 3-D space by the slice 
image. Because CT measures 3-D space, we don't have to place 
fragments in a plane. A resolution of CT is not inferior 
compared with the laser measurement. 
We fill fragments into the box (15cm x 15cm x 30cm) with the 
sponge that the CT value is different from the fragment. X-ray 
CT needs 20 seconds to measure 30 cm distance. And, the time, 
which produces a slice image from the CT exclusive use data, is 
30 minutes. X-ray CT can measure the luster surface that it is 
difficult to measure by the laser measurement. However, the 
texture in the surface cannot be measured. 
3. SURFACE MODEL GENERATION BY THE RELICS 
FROM SLICE IMAGES 
The general model generation method using slice images is 
marching cube method. The method forms a triangular polygon 
based on the pattern of picture elements that are within eight 
neighborhoods of an element on the contour of an image. A 
surface model of the high quality can be generated with the 
method. There is, however, the danger that a different shape 
may be formed if several polygons are erroneously set up. If a 
shape includes intense changes between two levels of slice, 
wrong faces are patched there. As a result, the resultant shape is 
wrong because portions to be originally connected one another 
are tom to pieces. 
For modeling of increasing relics, we must avoid manual 
operation. In this chapter, we state an automatic modeling. Not 
to be influenced by the size and the complexity of the slice 
image, we do process of grid unit. By introducing an 
intermediate point, we can do process of grid unit even if the 
gap between two slice images with intense change. We show 
3.1 Pre-processing 
An X-ray CT image is processed before setting up faces. The 
image that is provided with an X-ray CT for each slice image is 
expressed with gray shaded picture elements of monochrome. 
Figure 2 is slice image taken with X-ray CT. This image 
sequence is slice images of 1-mm interval but is actually 
measured in 0.2-mm interval. Because gray shaded images 
cannot be expressed in polygons, they must be binaries. It is 
called threshold process. A threshold value is set at an intense 
place of alteration. And, we extract contours. 
Figure 2. Slice image measured with X-ray CT 
3.2 Approximation of a contour using a set of grid points 
A salient characteristic of this research is a face tension with a 
grid unit. The finer a grid unit becomes, the more precise the 
approximation is. Points that a contour and the grid cross are 
selected to approximate the contour as shown in the Figure 3. 
Figure 3. Approximation of a contour using a set of 
grid points 
Intermediate points 
A salient characteristic of this research is an intermediate point. 
An intermediate point is a point on the image obtained by 
taking difference of one slice image and another one. A detailed 
procedure is described using the Figure 4 as an example. 
AND information: An AND collection is an intersection of 
two pieces of slice image. This portion is the region which 
polygon isn't set. Using this information, wrong selection of 
points nearby is avoidable even if the gap between two slice 
images with intense changes is interpolated.